The post How to Calculate Hysteresis for Your Uncertainty Budget appeared first on isobudgets.

]]>Hysteresis is a source of uncertainty that affects many types of measurement equipment and their associated measurement results. With a quick search on the internet, you will find a lot studies dedicated to hysteresis. If you take a look at manufacturer manuals and datasheets, you may find specifications related to hysteresis. However, you won’t see hysteresis commonly included in laboratory’s uncertainty budgets.

When I read many of the studies available, most of them were related to electrical hysteresis and magnetism. It wasn’t until searched for **mechanical or elastic hysteresis** that I begin to find the information beneficial to most calibration and testing laboratories.

However, you will not find many papers specifically studying the effects on measurement devices.

Therefore, I decided to create a guide on hysteresis for calibration and testing labs, so you could consider it in your uncertainty budgets (if it is applicable).

In this guide, you will learn the following information about hysteresis:

- What is hysteresis
- Why is hysteresis important
- When should you include hysteresis
- How to reduce hysteresis
- Formulas to calculate hysteresis
- How to perform a hysteresis test
- How to calculate hysteresis

According to the Oxford English Dictionary, hysteresis is the phenomenon where the value of a physical property lags behind changes in the effect causing it.

According to NASA, hysteresis is the response of a structure to loading and unloading that is commonly associated with energy loss under load cycling and hence damping with the structure.

This is the definition that I like the most.

For you, it means that your measurement result when increasing load, force, pressure, etc is not the same as your result when decreasing load, force, pressure, etc. If you are not taken this into consideration when performing tests or calibrations, then you will add additional uncertainty to your results.

If this is occurring with your test and measurement equipment and affecting your measurement results, you may want to consider hysteresis in your uncertainty budgets.

Hysteresis is important because it contributes to uncertainty in measurement results.

If you are not aware of the effects of hysteresis and how to reduce them, you could obtain erroneous results when performing measurements. Worse yet, you could be passing this error on to your customer’s measurement results without either one of you knowing about it.

In some cases, it may not be a big deal for you. However, when you incorporate risk and cost into the evaluation, your thoughts may change.

Try assigning a cost to your errors. If your measurement errors resulted in a monetary loss (associated with failures, repairs, downtime, or nonconforming work), would you think differently about hysteresis?

Would your perspective change if your measurement errors affected human health or life?

While this is not typically the case, you should be aware of the risks and consequences of measurement errors and the negative impacts they can cause. This is why hysteresis is important.

In case you are curious, just do a Google search on hysteresis. You will be amazed by how many studies have been published on the topic.

Consider hysteresis in your uncertainty analysis when it is commonly known to affect your type of measurement system or have an impact on your measurement results.

Hysteresis can occur in various types of measurement equipment and systems, including:

- Electrical measurement equipment,
- Mechanical measurement equipment, and
- Thermodynamic measurement equipment.

Review your equipment’s manufacturer manuals and specifications to find out whether or not hysteresis is thought to have an effect on your measurement results. If it is not specified by the manufacturer, you may find more information by reading your test methods or calibration procedures.

If hysteresis is mentioned (and given its own specification), it is most likely significant and should be included in your uncertainty analysis. If not, you may be able to omit it from your uncertainty budget.

Just make sure that you do some research before deciding whether or not to include it in your uncertainty analysis.

Hysteresis is unavoidable, but **it’s effects can be minimized**.

To reduce the effects of hysteresis, it is common practice to exercise your equipment before use or calibration. This means that you should load and unload your equipment several times before you use it.

Most manufacture manuals, calibration procedures, and test methods recommend this practice in an effort to reduce the effects of hysteresis.

Take a look at the excerpts below. I have compiled statements from several manuals, methods, and procedures that recommend exercising equipment prior to use.

If you are using equipment that may be affected by hysteresis, you can minimize the effect by exercising the equipment before use or calibration. Following the statements above, it appears that it is best practice to exercise equipment for a minimum of 3 cycles (loading and unloading) before it is used.

When you need calculate hysteresis for your uncertainty budgets, there are two methods that you can use.

This method is the most common. You will find it published in many documents, including:

- NCSLI RP-12: Determining and Reporting Measurement Uncertainties
- NIST SEMATECH Engineering Statistics Handbook

This equation takes into account the differences between loading and unloading across the entire measurement range. The benefit to this method is that you will find the maximum hysteresis error no matter where it occurs in the range.

However, the problem with this method is you may confound bias and linearity which will cause you to overstate your estimated uncertainty.

This method is less common than the first method. I found it in the MSL Technical Guide 25: Calibrating Balances several years ago and decided to give it a try.

Today, MSL has replaced this formula in their Technical Guide 25, but I still prefer to use it sometimes. I like the method because it takes changes at zero into account.

However, it only evaluates hysteresis at midscale. This can be a problem since the maximum difference does not always occur at midscale. Make sure that you take that into account when using this equation.

Performing a hysteresis test is not very difficult as long as you have the equipment. Just follow the instructions below.

Otherwise, you may already have the data in one of your calibration reports. If so, there is no need to perform this test. You can proceed to analyzing data.

1. Select an item for hysteresis testing (e.g. scale, pressure gauge, etc.)

2. Select equipment for making comparisons.

3. Exercise equipment as necessary before testing.

4. With no load applied, zero the unit under test and record the result.

5. Incrementally increase the load (e.g. 10% increments) on the unit under test and record the result after each step.

6. Incrementally decrease the load (e.g. 10% increments) on the unit under test in the reverse order and record the result after each step.

7. Analyze the results.

1. Select an item for hysteresis testing (e.g. scale, pressure gauge, etc.)

2. Select equipment for making comparisons.

3. Exercise equipment as necessary before testing.

4. With no load applied, zero the unit under test and record the result (y_{Z1}).

5. Load the unit under test to 50% of full-scale and record the result (y_{H1}).

6. Load the unit under test to 100% of full-scale.

7. Reduce the load on the unit under test to 50% of full-scale and record the result (y_{H2}).

8. Reduce the load to zero and record the result (y_{Z2}).

9. Analyze the results.

If you have measurement results from in-house testing or a calibration report, you are ready to calculate hysteresis. Just select the method that you would like to use for analysis and follow the instructions below.

Create a table in Microsoft Excel similar to the one in the image below.

Enter the results of your upscale test in the upscale column.

Enter the results of your downscale test in the downscale column.

Hysteresis is a source of uncertainty that is considered to be important by many but not included in most uncertainty budgets. Many methods and procedures give instructions to help reduce hysteresis, but you most likely will not be able to eliminate it. Therefore, you should give it consideration in your uncertainty analysis and include it in your uncertainty budget if it is applicable.

This guide has given you a lot of information about hysteresis; what is it, why is it important, and when to include it in your uncertainty budget. Additionally, you should have learned how to perform a hysteresis test and how to analyze the results for uncertainty analysis.

With this information, you should be able to easily calculate hysteresis and add it in your uncertainty budgets.

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Linearity uncertainty (a.k.a. linearity error or non-linearity) is a source of uncertainty that should be included in most uncertainty budgets. It is a common characteristic published in the manufacturer’s specifications for various types of measurement equipment. However, I do not see it included in uncertainty budgets as often as it should be.

If you have a test or measurement function that spans across a range of values, then you may need to include linearity in your uncertainty analysis. Therefore, I thought that it would be a great idea to develop a guide to show you how to estimate linearity uncertainty step by step using Microsoft Excel.

In this guide, you are going to learn everything that you need to know about linearity uncertainty, including;

- What is Linearity Uncertainty
- Why is Linearity Uncertainty Important
- When Should You Include Linearity Uncertainty
- Linearity Uncertainty Methods
- Which Uncertainty Method You Should use
- How to Calculate Linearity Uncertainty (Step By Step)

Linearity is the property of a mathematical relationship or function that can be graphically represented as a straight line.

Non-linearity is the deviation from a straight line over a desired range.

Therefore, linearity uncertainty would the uncertainty associated with non-linear behavior observed across the range of an assumed linear function.

When you think about how measurement equipment functions, you probably assume that its measurement performance is linear across the measurement range.

However, this is not typically the case.

The measurement functions of most devices are not actually linear. Instead, they are approximately linear. So, we try to correct them with coefficients and linear or polynomial equations to make their performance more predictable.

Still, prediction equations and coefficients do fully correct for their non-linear behavior. Therefore, we must take linearity uncertainty into consideration.

Non-linear behavior is most commonly observed for many mechanical devices and physical materials. For example, here is a list of devices that are commonly evaluated for linearity;

- Pressure Gauges (with bourdon tubes)
- Pressure Transducers (with strain gauges)
- Load cells,
- Force gauges,
- Scales and analytical balances,
- Torque transducers,
- Resistance Thermometers (e.g. PRT, RTD, thermistors, etc.),
- Liquid in glass thermometers (e.g. mercury, spirit-filled, etc.),
- Hygrometers,
- Dial indicators,
- and much more.

Additionally, many electrical devices can exhibit non-linear behavior too.

- Digital Multimeters,
- Multifunction Calibrators,
- Oscilloscopes,
- LCR Meters,
- Phase Meters,
- Thermocouple Simulators,
- Power Sensors,
- Signal Generators,
- and much more.

No matter what type of equipment you are using, do not forget to consider linearity in your uncertainty analysis unless it is negligible or inappropriate to do so.

Linearity uncertainty is important because it allows you to consider the effects of non-linear behavior in a measurement function. If you use an equation to estimate uncertainty across a measurement range, then you may need to consider evaluating linearity uncertainty.

I often hear people say that linearity is not important or doesn’t need to be included in an uncertainty budget. I say, test it and let the results speak for themselves.

If the result is small or negligible, great! Now, you have objective evidence to support your opinion. However, I would still include it your uncertainty budget to prove you considered it.

If the result is significant, then include the results in your uncertainty budget.

If you are unable to calculate linearity, try reading the manufacturer’s manuals and datasheets to see if they list it in the specifications.

Nonetheless, linearity uncertainty is important. At least consider whether or not it affects your measurement uncertainty.

You should include linearity in your uncertainty analysis anytime you are estimating uncertainty for a continuous measurement range.

If you plan to use a linear equation to predict the measurement uncertainty of a given measurement range, then you should include linearity into your uncertainty analysis.

When estimating measurement uncertainty across a measurement range, you will typically estimate uncertainty at test-points close to the minimum and maximum of the measurement range. Since your uncertainty analysis doesn’t estimate uncertainty at the points in between the minimum and maximum values, you need to take non-linearity of the function into consideration.

Additionally, many measurement instruments exhibit non-linear behavior below 10% of the measurement range. When you estimate uncertainty for values below 10% of the measurement range, you are more likely to see non-linear behavior the closer you get to zero.

So, be sure to take that into consideration when selecting test-points for your uncertainty analysis.

There are two common methods that you can use when estimating linearity uncertainty. They are;

- Maximum Deviation from Linearity
- Typical Deviation from Linearity

Maximum error provides the maximum deviation from the linear behavior of a fitted line prediction equation (e.g. regression, interpolation, B.F.S.L.).

Standard error provides the typical deviation from the linear behavior of a fitted line prediction equation (e.g. regression, interpolation, B.F.S.L.).

Both methods evaluate the deviation from linearity. The difference between the two methods is one method evaluates the worst case scenario and the other evaluates the most likely or most probable scenario.

The maximum deviation method is the most commonly used method for evaluating linearity uncertainty. Additionally, it is the most recommended method. If you decide to do some research, you are more likely to find information on the maximum deviation method.

NIST recommends the maximum deviation method in their NIST/SEMATECH Engineering Statistics Handbook. See the excerpt provided below.

When evaluating linearity uncertainty, **I prefer to use the standard error method**. I believe that it is more applicable to an uncertainty analysis and the development of a CMC Uncertainty predication equation, especially if I have already considered bias or error in my uncertainty analysis.

If you choose to use the maximum deviation for linearity, you need to be careful not to confound your results and overstate your estimated measurement uncertainty.

When you include bias or error in your uncertainty analysis, you are more likely to overstate your uncertainty using the maximum deviation method. Especially, since the maximum deviation and bias could end up being the same result!

If you choose to use the standard error method, you are more likely to understate your measurement uncertainty if you do not include bias in your uncertainty budget.

When you include bias in your uncertainty analysis, using the standard error for linearity uncertainty is more likely to give you a better estimate of uncertainty in measurement.

So, use the method you like best. At least you should know what options you have available and why you selected to use the method you have chosen if anyone ever asks you a question.

To calculate linearity uncertainty, I am going to show you how to perform regression analysis in Microsoft Excel and find the maximum deviation and standard error.

In Microsoft Excel, there are two processes that you can use to easily use to get results;

- Data Analysis ToolPak, and
- LINEST and INTERCEPT functions.

In this section, you will learn how to use Data Analysis ToolPak to find your linearity uncertainty following the four steps below;

- Install Data Analysis ToolPak,
- Enter Your Standard and UUT Data,
- Perform Regression Analysis, and
- Find your Linearity Uncertainty

To calculate linearity uncertainty, you will need to perform regression analysis. To do this in Microsoft Excel, you will need to install Data Analysis Tool Pack.

Since this add-in comes built into Microsoft Excel, all you need to do is activate it. To activate Data Analysis Tool Pack, follow the steps below:

**a. Click the File tab**

**b. Click Options (on the left side panel)**

**c. A new window will open. Click Add-ins.**

**d. At the bottom of the screen, use the drop-down menu to select Excel Add-ins, then click the Go button.**

**e. Check the box next to Analysis ToolPak, then click the Ok button.**

Data Analysis ToolPak will be added to Microsoft Excel. You can add under the Data tab.

**a. Enter your Nominal Values into column X**

Now that Data Analysis ToolPak is added to Microsoft Excel, pick a column and enter your nominal or standard values. You want to use all of test-points calibrated for the measurement range you are evaluating linearity uncertainty.

**b. Enter Your Actual Values into column Y**

Next, select another column and enter the calibration results for the unit under test (UUT).

**a. Open Data Analysis ToolPak**

Now, we are going to put Data Analysis ToolPak to work. Click on the Data tab. Look at the right-side of the toolbar and click on the Data Analysis button.

**b. Select Regression Analysis**

A new window will open with a list of analyses. Scroll down and select Regression Analysis. Then, click the Ok button.

**c. Select Column Y**

A new window will open that requires you to enter information needed to perform regression analysis. In the Input section, find the Input Y Range cell and click the button to the right of the cell.

Select all of the cells that contain the UUT calibration results.

**d. Select Column X**

Find the Input X Range cell and click the button to the right of the cell.

Select all of the cells that contain the Nominal or Standard values.

**e. Select a Location For the Results**

In the Output Options section, select the Output Range and click the button to the right of the input cell.

Select a cell where you would like the results reported. I recommend choosing a section to the right or below your data table. The results of regression will fill in a lot of cells, so make sure not to overwrite any of your data.

**f. Click to Show Residuals**

In the Residuals section, check the box to show Residuals.

**g. Click Ok to Perform The Analysis**

Finally, click the Ok button to perform a regression analysis. After you click the button, Microsoft Excel will perform regression analysis and show you the results.

**a. Find the Standard Error or the Max Residual**

For linearity uncertainty, you will want to look at the Standard Error or the Maximum Residual. The method that you prefer to use to evaluate linearity will determine which data you will enter into your uncertainty budget.

In this section, you will learn how to use the **LINEST** and **INTERCEPT** functions to calculate your linearity uncertainty following the four steps below;

- Enter Your Standard and UUT Data,
- Calculate the Gain Coefficient,
- Calculate the Offset Coefficient,
- Calculate your Fitted Prediction Line,
- Calculate the Residuals, and
- Find your Linearity Uncertainty

First, create a table and enter your standard or nominal values in column X. Then, enter your results in column Y.

Calculate the Gain Coefficient (i.e. slope) using the **LINEST** function in Microsoft Excel.

- Type “=LINEST(“
- Select all the cells in the Y column,
- Select all the cells in the X Column,
- Type “True” because the offset coefficient will be calculated normally,
- Type “True” for additional regression statistics,
- Type “)” and hit the Enter key.

Calculate the Offset Coefficient (i.e. y-intercept) using the **INTERCEPT** function in Microsoft Excel.

- Type “=INTERCEPT(“
- Select all the cells in the Y column,
- Select all the cells in the X Column,
- Type “)” and hit the Enter key.

Calculate the fitted straight line using the gain and offset coefficients.

- Type “=”
- Select the first value in the X column,
- Multiply it by the Gain Coefficient,
- Add the Offset Coefficient,
- Hit the Enter key
- Copy and paste for the remaining values in the X column.

**Hint:** Hit the F4 key when you select the coefficient cells to lock the cells when you copy and paste equations.

Calculate the residuals by calculating the difference between the observed Y result and the fitted Y result.

- Type “=ABS(“
- Subtract the first cell in the Y column by the first cell in the Y-fitted column,
- Type “)” and hit the Enter key.
- Copy and paste for the remaining values in the Y column

Calculate the standard error and the maximum deviation to find the linearity uncertainty.

**a. Standard Error**

**b. Maximum Deviation**

Linearity uncertainty is an important source of uncertainty that you may want to include in your uncertainty analyses. If you are using prediction equations for your CMC Uncertainty and your measurement function spans across a range of values, you might want to add linearity to your uncertainty budgets to account for the non-linearity in your measurement function.

In this guide, you should have learned;

- What is linearity uncertainty,
- Two methods for calculating linearity uncertainty,
- How to calculate it, and
- When to include it in your uncertainty budgets.

Give these methods a try and let me know which method you prefer to use. Plus, let me know what additional examples you would like me to add to the guide.

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]]>The post Proficiency Testing and Interlaboratory Comparisons: The Ultimate Guide to ISO/IEC 17025 appeared first on isobudgets.

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Proficiency testing is an important element of ISO/IEC 17025 accreditation. So important, that it has its own ISO standard (i.e. ISO/IEC 17043).

In addition to the international standard, proficiency testing has plenty of endorsement via ILAC and accreditation body policies. There is a ton of information on proficiency testing available to laboratories seeking accreditation.

So, why do so many laboratories struggle with proficiency testing?

Most of the labs that I have spoken with either have a hard time finding a proficiency testing provider or have a unique test or calibration where proficiency testing is not available.

To get accredited, you need to know;

• all of the requirements that you need to meet beyond the ISO/IEC 17025,

• how to find a proficiency testing provider,

• how to understand your proficiency testing results,

• how to submit your results to your accreditation body, and

• what to do if you fail a proficiency test.

In this guide, I am going to cover everything that you need to know about proficiency testing for ISO/IEC 17025 accreditation including the answers to your problems listed above.

So, grab something to drink and take a seat, I am about to give you a lot of information.

**Click here to download the proficiency testing cheat sheet for free!**

Personally, I have never had much of a problem meeting proficiency testing requirements.

Even with a 30+ page scope of accreditation, most of the measurement functions were able to be covered using a single proficiency testing provider.

The only measurement function that I had a hard time finding a PT provider was for chemical gas concentration.

Otherwise, I have only had to organize two interlaboratory comparisons in my career.

Looking at my experience, it seems that proficiency testing is a pretty easy requirement to meet. However, many labs seem to have a hard time.

So, what is the deal?

Is it a lack of knowledge, training, available information, or time? Whatever the reason, it appears that Proficiency Testing is a problem for many accredited labs.

On average, I probably encounter 3 clients a month who need help with proficiency testing and 20 or more subscribers who have questions.

Therefore, I decided to create a Proficiency Testing Guide to help you and others who struggle to meet ISO/IEC 17025 requirements.

In this guide, you will learn;

- What is Proficiency Testing
- Why is Proficiency Testing Important
- Proficiency Testing vs Inter-laboratory Comparisons
- Proficiency Testing Schemes
- How to Evaluate Proficiency Testing Results
- Proficiency Testing Standards
- ISO/IEC 17025 Requirements For Proficiency Testing
- ILAC Requirements For Proficiency Testing
- Proficiency Testing Requirements By Accreditation Body
- How To Find Proficiency Testing Service Providers
- How To Create A Proficiency Testing Program

If you would like to jump ahead to a particular section, just use the links provided above. Otherwise, take a seat. We have a lot of information to cover.

According to ISO/IEC 17043:2010, proficiency testing (PT) is the evaluation of participant performance against pre-established criteria by means of interlaboratory comparisons.

In other words, a proficiency test is a method used to demonstrate competency and validate a laboratory’s measurement process by comparing your results to the results of a reference laboratory and other participant laboratories.

To get a better idea of what a proficiency test is, look at the image below.

A coordinating body sends a test item or artifact to a reference laboratory for testing. Then, the coordinating body sends the item to each participating laboratory for subsequent testing.

Each participant laboratory will independently test the item, submit their results to the coordinating body, and forward the item to the next participating laboratory.

After each participating laboratory has completed testing, the artifact is returned to the coordinating body.

The coordinating body will evaluate the all the test results and issue a performance report to each participating laboratory.

This is typically referred to as Round Robin Testing, and is one of the most common proficiency testing schemes used by PT providers.

Proficiency Testing is important for several reasons. Primarily, it enables your laboratory to demonstrate competency for a particular measurement discipline which can be used to validate;

• A measurement method;

• Technical training of personnel;

• Traceability of standards, and

• Estimates of measurement uncertainty.

Imagine that your laboratory is adding a new measurement or testing capability to your scope of accreditation. You have purchased equipment, had it calibrated, written methods, trained personnel, estimated uncertainty, and performed numerous internal verification studies.

Even with all of that hard work, time, and money invested into your new process, are you confident that your results are adequate and comparable to other laboratories?

By participating in proficiency testing, your laboratory can externally validate your new measurement or testing process.

Hence, the reason your accreditation body requires you to successfully complete a proficiency test before they will add it to your scope of accreditation.

We will cover more about that later in this guide.

Proficiency testing and inter-laboratory comparisons are terms used synonymously in the Test and Measurement industry. However, they are not exactly the same.

They are similar, but slightly different.

According to ISO/IEC 17043:2010, inter-laboratory comparison (ILC) is the organization, performance, and evaluation of measurements or tests on the same or similar items by two or more laboratories or inspection bodies in accordance with predetermined conditions.

According to ISO Guide 43, Proficiency Testing is a formal exercise managed by a coordinating body which includes a standard or reference laboratory. The results are issued in a formal report that clearly provides the En and Z score.

Furthermore, ISO Guide 43 describes an inter-laboratory comparison as an exercise that is performed by agreement between two or more participating laboratories where the results are issued in a formal report.

So, **the difference is a proficiency test is an inter-laboratory comparison that is organized and managed by an independent third party**. Additionally, a proficiency test includes the participation of a reference laboratory and uses their results to determine participant performance.

An inter-laboratory comparison does not require the use of a reference laboratory or a coordinating body. Therefore, participant laboratories are only comparing performance amongst the group of participating members.

As you can see, they are similar, but different.

When it comes to proficiency testing, there are a few different schemes used to conduct interlaboratory comparisons.

Each scheme is unique to **maintain homogeneity and stability of the artifact throughout the testing process**. Otherwise, the test results could contain errors and become invalid for use.

In this section, I will show you the two most common proficiency testing schemes recommended by the ISO/IEC 17043:2010;

• Sequential Participation Schemes

• Simultaneous Participation Schemes

If you conduct interlaboratory comparisons without the use of a proficiency testing provider, these test schemes may be of value to you.

In a sequential participation scheme, artifacts are successively circulated from one participant to the next, or occasionally returned to the proficiency testing provider or reference laboratory for retesting.

Sequential participation schemes are very common in proficiency testing. Two of the most common sequential designs are;

• Ring Test

• Petal Test

The ring test (i.e. round-robin test) is a proficiency testing scheme where a reference laboratory initially measures an artifact (to establish a reference) and then successively submits the artifact to each participant laboratory.

This ring test is typically used for artifacts known to have better long term stability.

The petal test is a proficiency testing scheme where a pivot laboratory is used to measure an artifact more than once during testing. In some cases, artifacts are returned to the pivot laboratory before and after each shipment to a participant laboratory.

The petal test is typically used for artifacts with short-term stability or when the participants are national metrology institutes (NMI’s).

In a simultaneous participation scheme, sub-samples are randomly selected from a material source and simultaneously distributed to participant laboratories for concurrent testing.

Simultaneous participation schemes are very common in proficiency testing and typically used for reference materials or single use samples that are destroyed or discarded after testing.

Three of the most common simultaneous testing designs are;

• Split-Level Test,

• Split-Sample Test, and

• Partial-Process Test.

In a split-level proficiency testing scheme, similar (but not identical) levels of a measurand are incorporated into two separate proficiency test items.

In a split-sample testing scheme, material or product samples are split into two or more parts, where each participant only test one part of the sample.

In a partial-process scheme, participants only perform specific parts of the overall testing or measurement process.

If you are going to participate in proficiency testing or inter-laboratory comparisons, it is beneficial for you to know how to evaluate your testing results.

This is especially true if you need to perform an interlaboratory comparison without the aid of a proficiency testing provider.

Furthermore, it is always a good idea to **double-check your PT results even if you are using a proficiency testing provider**.

I have found mistakes in proficiency testing reports before.

One time, a provider issued a report to my accreditation body indicating that I had an unsatisfactory result. However, when I double-checked the calculation of En, I discovered that I was well within.

So, I contacted the PT provider and notified them of my findings. When they double-checked the calculations, they discovered that there was a mistake. As a result, the proficiency testing report was updated and A2LA retracted their discrepancy letter.

Every once in a while it is nice to get a lucky break. However, you will never know if you do not verify your proficiency testing results. Therefore, let’s check out some of the methods used by proficiency testing providers.

Proficiency testing results are commonly evaluated using two methods described in ISO/IEC 17043;

- Normalized Error, and
- Z-Score.

Normalized error is a statistical evaluation used to compare proficiency testing results between the participant and the reference laboratory where the uncertainty in the measurement result is included.

Typically, it is the first evaluation used to determine conformance or nonconformance (i.e. Satisfactory/Unsatisfactory) in proficiency testing.

When determining whether a participant’s results are satisfactory or unsatisfactory, the following rules are used;

• When the value of |En| ≤ 1 (i.e. between -1 and +1), the results are considered satisfactory.

• When the value of |En| > 1 (i.e. greater than +1 or less than -1), the results are considered unsatisfactory.

To calculate normalized error, use the equation provided below;

If you are having a hard time understanding the equation above, use the step-by-step instructions below to calculate normalized error (i.e. En);

- Subtract the result from the participating laboratory by the result of the reference laboratory (i.e. laboratory bias).
- Calculate the root sum of squares for both laboratories’ reported estimates of measurement uncertainty.
- Divide the value calculated in step 1 and by the value calculated in step 2.

Z-score is a statistical measurement of a score’s relationship (i.e. how many **standard deviations** above or below the population mean) to the mean in a set of scores.

It is a statistical evaluation used to review the results of all participants and identify outliers and exclude their data from proficiency testing results.

When determining whether a participant’s results are satisfactory, unsatisfactory, or questionable, the following rules are used;

• When the value of Z <=2, the results are considered satisfactory.

• When the value of Z >=3, the results are considered unsatisfactory.

• When the value of Z >=2 and Z <=3, the results are considered questionable.

To calculate z-score, use the equation provided below;

If you are having a hard time understanding the equation above, use the step-by-step instructions below to calculate z-score;

- Subtract the participant laboratory’s result by the population mean (i.e. average).
- Calculate the standard deviation of all participant results.
- Divide the result of step 1 by the result of step 2.

The International Organization for Standardization (ISO) has a standard for just about everything, including proficiency testing.

If you are interested in becoming an accredited proficiency testing provider or want to learn more about proficiency testing standards, check out the list of active and obsolete ISO standards provided below.

• ISO/IEC 17043:2010 – Conformity Assessment – General Requirements for Proficiency Testing

• ISO 13528:2015 – Statistical Methods For Use In Proficiency Testing By Interlaboratory Comparisons.

• ISO 13528:2005 – Statistical Methods For Use In Proficiency Testing By Interlaboratory Comparisons.

The new ISO/IEC 17025:2017 standard requires laboratories to participate in proficiency testing. In the 2005 standard, proficiency testing was recommended in section 5.9.1b, but not required.

Now, it is required (where available and appropriate). Therefore, I recommend that you develop and implement a proficiency testing program if you do not have one in place.

To familiarize yourself with the ISO/IEC 17025:2017 standard, let’s take a look at all of the sections that mention proficiency testing so you can be better prepared for accreditation.

In section 3.5, the ISO/IEC 17025 standard defines the term “proficiency testing.” According to the standard, proficiency testing is the evaluation of participant performance against pre-established criteria by means of interlaboratory comparison.

The definition comes from the proficiency testing standard, ISO/IEC 17043:2010.

See the excerpt below:

*“ 3 Terms and definitions
3.5 proficiency testing
evaluation of participant performance against pre-established criteria by means of interlaboratory comparisons (3.3)*

*[SOURCE: ISO/IEC 17043:2010, 3.7, modified — Notes to entry have been deleted.]”*

In section 7.7.2, the ISO/IEC 17025 standard states that laboratories shall monitor their performance by comparing their results with other laboratories.

The two methods that are recommended are:

a. Proficiency Testing or

b. Interlaboratory Comparisons

See the excerpt below:

*“ 7.7 Ensuring the validity of results
7.7.2 The laboratory shall monitor its performance by comparison with results of other laboratories, where available and appropriate. This monitoring shall be planned and reviewed and shall include, but not be limited to, either or both of the following:*

**a)** participation in proficiency testing;

NOTE – ISO/IEC 17043 contains additional information on proficiency tests and proficiency testing providers. Proficiency testing providers that meet the requirements of ISO/IEC 17043 are considered to be competent.

**b)** participation in interlaboratory comparisons other than proficiency testing.”

In section 6.6.1, the ISO/IEC 17025 standard states that laboratories must use only suitable externally provided services when it affect laboratory activities. If you read the note below the section, you will see that proficiency testing services should be included in externally provided services.

If you maintain an Approved Supplier List (like many other labs), then you may want to add your proficiency testing providers to it.

See the excerpt below:

*“ 6.6 Externally provided products and services
6.6.1 The laboratory shall ensure that only suitable externally provided products and services that affect laboratory activities are used, when such products and services:*

**a)** are intended for incorporation into the laboratory’s own activities;

**b)** are provided, in part or in full, directly to the customer by the laboratory, as received from the external provider;

**c)** are used to support the operation of the laboratory.

*NOTE Products can include, for example, measurement standards and equipment, auxiliary equipment, consumable materials and reference materials. Services can include, for example, calibration services, sampling services, testing services, facility and equipment maintenance services, proficiency testing services and assessment and auditing services.”*

In section 8.6.1, the ISO/IEC 17025 standard states that laboratories must identify and select opportunities for improvement and implement any necessary actions. If you read the note just below the section, you will see that the standard recommends using proficiency testing results to find opportunities for improvement.

See the excerpt below:

*“ 8.6 Improvement (Option A)
8.6.1 The laboratory shall identify and select opportunities for improvement and implement any necessary actions.*

*NOTE Opportunities for improvement can be identified through the review of the operational procedures, the use of the policies, overall objectives, audit results, corrective actions, management review, suggestions from personnel, risk assessment, analysis of data, and proficiency testing results.”*

As you can see, the ISO/IEC 17025:2017 standard requires you to participate in a proficiency testing or interlaboratory comparison program (where available and appropriate).

Additionally, the standard recommends that you;

• consider proficiency testing providers as service providers and

• use proficiency testing results to find opportunities for improvement.

Keep reading to find out what are ILAC and your accreditation body’s proficiency testing requirements for ISO/IEC 17025 accreditation.

In addition to the ISO/IEC 17025 standard, the International Laboratory Accreditation Cooperation (ILAC) has a policy on proficiency testing. It is known as the;

ILAC P9:06/2014 – The ILAC Policy for Participating in Proficiency Testing Activities

It is a policy for accreditation bodies that sets requirements and gives guidance on the use of proficiency testing in the accreditation process for laboratories (i.e. ISO/IEC 17025:2005) and inspection bodies (ISO/IEC 17020:2012).

To fully understand the requirements of ILAC P9 policy, I recommend that you read the policy.

However, I have summarized the core concepts of the policy for you below.

In section 4.1, the policy requires accreditation bodies to demonstrate the technical competency of their calibration and testing laboratories (i.e. your laboratory).

One of the recommended ways that your laboratory can demonstrate competency is by participating in proficiency testing activities and yielding satisfactory results.

Section 4.2 requires accreditation bodies to establish the minimum proficiency activity required for accreditation, including;

• satisfactorily completing a proficiency test before granting accreditation.

• establishing an ongoing proficiency testing plan to cover your entire scope of accreditation.

Section 4.3 requires accreditation bodies to have a policy on how proficiency testing will be used in assessments and the accreditation process which must include;

• a reference to the importance of proficiency testing,

• requirements for the minimum level and frequency of participation,

• instructions on how proficiency testing participation and performance will be used during the assessment and accreditation process.

• actions laboratories must take in response to poor performance

• how you will notify your accreditation body

• any other proficiency testing requirements set by regulators, industry, or other parties.

Section 4.4 requires accreditation bodies to fully document their proficiency testing polices and procedures. Furthermore, it requires accreditation bodies to review your proficiency testing plan for suitability in relation to your scope of accreditation.

Section 4.5 recommends that accreditation bodies provide information to help laboratories find proficiency testing providers and develop proficiency testing plans, including;

• listings of proficiency testing providers and considerations for selecting programs, and

• guidance for analyzing and formulating proficiency testing needs.

Section 4.6 requires accreditation bodies to negotiate alternative methods, with testing and calibration laboratories, to assess performance where proficiency testing does not exist or is not practical.

The **ILAC P9** policy lists a set of requirements that accreditation bodies must meet in order to maintain their status as a signatory to the **ILAC MRA**.

The way each accreditation body meets these requirements is slightly different. So, it is best for you to review your accreditation body’s policies and requirements.

Below is a list of links for you to quickly access your accreditation body’s policy.

• A2LA R103 – General Requirements: Proficiency Testing For ISO/IEC 17025 Laboratories

• ANAB GD 2001: Guidance On Proficiency Testing/Inter-Laboratory Comparisons

• NVLAP Handbooks and Lab Bulletins

• PJLA- Perry Johnson Laboratory Accreditation, Inc PL-1: Proficiency Testing Requirements

• IAS/TL/031 IAS Policy On Proficiency Testing For Laboratories

• L-A-B Policy 002 – Assuring Quality and Proficiency Testing

One of the most common problems that I encounter when working with laboratories is the ability to find a suitable proficiency testing provider to cover their scope of accreditation.

For whatever reason, many laboratories struggle to find a suitable proficiency testing provider and develop a proficiency testing plan.

To help you out, I have compiled a list of 2 methods you can use to find a proficiency testing provider; and, what to do if there isn’t any suitable options available.

Many people do not know this, but your accreditation body has documents and resources that will help you find a proficiency testing provider.

Below is a list of helpful links for each accreditation body in North America.

• A2LA: Accredited Proficiency Testing Providers

• NVLAP: Requirements Documents

• ANAB: Proficiency Testing Provider Resources

• IAS: Information on Proficiency Testing Providers for IAS Clients

• LAB: Proficiency Testing Providers

If the resources provided above are not useful, I recommend that you visit your accreditation body’s website and search their database for ISO/IEC 17043:2010 accredited providers.

For example, let’s search the A2LA database.

1. Visit the A2LA website;

2. Click on “Search Accredited Organizations;”

3. Click on the “Accreditation Field” dropdown menu;

4. Select “Proficiency Testing Provider;”

5. Search for a Proficiency Testing Provider from the results.

In this example, the search returned 34 proficiency testing providers.

Now, you can search the providers scope of accreditation and website to see if their services can help your laboratory. If not, try searching another accreditation body’s website database.

For example, let’s try the ANAB search database.

1. Visit the ANAB website;

2. Hover your mouse over “Accredited Organizations,” and click “Labs/Inspection/Forensics/PT/RMP,”

3. Click on the “Standard” drop down menu and select “ISO/IEC 17043,”

4. Now, click on the “Search Now” button at the bottom of the screen,

5. Search for a Proficiency Testing Provider from the results.

After searching each of the accreditation body databases, I was only able to find proficiency testing providers in the A2LA and ANAB databases. However, there may be more PT providers available from the other accreditation bodies. So, make sure that you search their directories.

To help you find a proficiency testing provider faster, I have provided links below to each accreditation body’s database.

• A2LA Directory of Accredited Organizations

• ANAB Directory of Accredited Organizations

• PJLA Listing of Accredited Labs

• L-A-B Directory of Accredited Organizations

• IAS Search for Accreditations

Now, some of you may be thinking, “What if there isn’t a Proficiency Testing Provider?”

First of all, don’t panic!

If you have endlessly searched for a suitable proficiency testing provider only to find one does not currently exist, it’s okay. It happens more often than you think, and the solution is rather simple.

Just follow this three-step process;

- Pick up the phone,
- Call your accreditation body, and
- Negotiate an alternative solution for your laboratory.

If you are too busy to make a telephone call, don’t like talking to people on the phone, or too scared to call your accreditation officer, then try this alternate two-step process;

- Compose an email to your accreditation body,
- Click send.

Shortly after, your accreditation body will reply to your email and help you negotiate an alternative method to proficiency testing.

Now I know that this may seem rather simple, but all you need to do is contact your accreditation body. They are obligated to help you find an alternative solution.

According to section 4.6 of the **ILAC P9**, accreditation bodies and the laboratory **shall discuss and agree on suitable alternative means** by which performance can be assessed and monitored.

If you are similar to the majority of ISO/IEC 17025 accredited laboratories, you will participate in proficiency testing. Therefore, you will need to establish a proficiency testing program.

To setup a program, you primarily need to do five things;

- Find a Proficiency Testing Provider,
- Create a Proficiency Testing Plan,
- Participate in Proficiency Testing Schemes,
- Review and Evaluate Your Results, and
- Submit Your Results to Your Accreditation Body.

Once you have decided to participate in proficiency testing, you need to find one of more proficiency testing providers to cover your scope of accreditation.

Using your scope of accreditation, identify the measurement disciplines, functions, or tests listed in your scope of accreditation.

Next, use the resources that I provided to you earlier in this guide to help you **find proficiency testing providers**. When you have found a proficiency testing provider, contact them to get test availability and pricing.

Additionally, it is a good idea to keep a record of their scope of accreditation and add them to your Approved Supplier’s List.

If you are participating in proficiency testing, you must create a plan. Most accreditation bodies require you to maintain a proficiency testing plan for a specified numbers of years.

In some cases, your proficiency testing provider will create a plan for you. If they offer to create your plan, let them. It will save you time and the hassle of doing it yourself.

However, if your provider does create a plan for your laboratory, make sure to review it and verify that the plan will cover your entire scope of accreditation. If you wish to change your plan or schedule, for whatever reason, contact your proficiency testing provider and ask them to revise your plan.

In the rare case that you wish to manage your own plan, I recommend that you create an excel spreadsheet that lists your proficiency testing activities for the next four years.

As an example, it could look like the image provided below;

Now that you have found a proficiency testing provider and created a plan, it’s time to participate in a proficiency testing scheme.

When it is your turn to participate, your proficiency testing provider will typically notify you a few weeks in advance so you can prepare to receive the artifact.

**The key to performing proficiency tests is to essentially follow the instructions** and perform the test similar to the tests or calibrations you are currently performing in your laboratory.

So, receive the artifact and run it through your normal test or calibration process similar to the work you perform for your customers.

When you have completed the test, contact your proficiency testing provider. They will tell you where to ship the artifact.

Finally, submit your results to the proficiency testing provider. Within a few weeks, you should receive your results.

After each participate has completed the proficiency test, your provider will issue a finalized report to you. This report will showcase your performance and how you compared to other laboratories.

Furthermore, it will notify you whether your performance was satisfactory or unsatisfactory.

If your performance was satisfactory, great! You successfully completed a proficiency test. Now, evaluate your results, maintain your proficiency testing report for your records, and submit copies to your accreditation body.

On the other hand, if your performance was unsatisfactory, you have some work to do. You will need to follow your accreditation body’s requirements, but you will mostly likely need to document the nonconformance, conduct a root-cause investigation, and formulate corrective actions.

Afterward, you will need to implement the corrective action and provide your accreditation body with objective evidence that the corrective actions were effective. This is typically accomplished by repeating the proficiency test and showcasing that your results were satisfactory.

Again, refer to your accreditation body’s requirements and you will be okay.

Finally, submit your proficiency testing results to your accreditation body. If your proficiency testing provider offers to submit your results to your accreditation body, I recommend that you let them.

Otherwise you will have to do it.

Now, some consultants and assessors recommend that you submit the results yourself. However, I prefer to let the proficiency testing provider do it. In my opinion, it will save you time by delegating the task to your proficiency testing provider so you can focus on completing other tasks.

Where possible, I prefer to automate or delegate tasks so I can spend more time focusing on other things.

So, determine how you want to submit your results to your accreditation body and make sure to refer to their policies and requirements.

Proficiency testing is an important aspect of ISO/IEC 17025 accreditation. Even if it is not strictly required by the international standard, proficiency testing is required and highly recommended by international committees and accreditation bodies.

If there is a proficiency testing scheme available to support your scope of accreditation, you will most likely be ~~encouraged~~ required to participate.

In this guide, I have given you 90% of everything you need to know about proficiency testing. With this information, you should be able to;

• develop a proficiency testing program,

• find a PT provider,

• find your accreditation bodies requirements,

• create a proficiency testing plan, and

• evaluate your results

Now, all you have to do is put in the work and make it happen. So, if you have been struggling with proficiency testing, use this guide to help you overcome your challenges and take action.

Develop a program, find a PT provider, and participate in your first proficiency test.

If you have any success stories, failures, challenges, or any additional helpful information, be sure to leave a comment below for others.

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Each time that you begin an uncertainty analysis, you need to create an outline before you start to estimate uncertainty.

I call this process specifying your measurement function. It is the first step in my 7 Steps to Estimating Measurement Uncertainty Guide. However, it is simply creating an outline for your uncertainty analysis.

The goal of this process is to help you focus on estimating uncertainty for one measurement function and one measurement range at a time. Ultimately, it will help you save time and avoid mistakes.

When you know where to focus your attention, it is easier to start estimating uncertainty and finish the process.

Similar to other laboratory activities, you need a procedure to complete a test or calibration. However, you need to know which procedure to use. If you outline what you are testing or calibrating, the process becomes much easier.

Each time you perform an uncertainty analysis you should create an outline by performing the following steps;

- Select the measurement function,
- Select the measurement range,
- Select the test points,
- Select the method,
- Select the equipment, and
- Find the mathematical equation or formula.

In the sections below, you will learn how to perform each of these steps in more detail.

The first thing that you want to do when starting to estimate uncertainty is to identify what you are doing.

Therefore, you need to specify your measurement function.

Just ask yourself, “What am I doing?”

Think about the process that you are performing and the results that you will record. How would you describe them?

For example, maybe you are;

- Measuring DC voltage with a digital multimeter,
- Generating DC voltage with a multifunction calibrator,
- Measuring temperature with a thermometer,
- Measuring frequency with a counter,
- Calibrating pipettes with a precision balance,

There are many different activities that your laboratory could perform. You just need to briefly describe what you are doing.

Then, you will summarize the process in just a few words. Using the list above, some common names that you could use would be;

- DC Voltage Measure,
- DC Voltage Generate,
- Temperature Measure,
- Frequency Measure,
- Volume Measure

Additionally, you can describe what you are testing or calibrating. For example, you can specify your measurement function as;

- Scales,
- Pipettes,
- PRT Thermometers,
- Gage Blocks,
- Flowmeters

For inspiration, you should look at other laboratory’s scopes of accreditation to see what they are naming measurement functions.

This will ensure that you are using function names and descriptions that have been approved by your accreditation body.

Another good piece of advice would be to use names and descriptions that your customers will recognize.

Your scope of accreditation is an advertising document. It provides your customers with information about your laboratory’s capabilities. Make sure that your customers can understand what your laboratory does and how it can meet their requirements.

Therefore, start every uncertainty analysis by creating an outline and specifying your measurement function so you know where to focus the attention.

The next thing that you want to do is select your measurement range.

This will help you determine the range of values that your uncertainty analysis will cover so your focus is kept between these two values.

It’s about setting boundaries.

For example, your measurement functions could have one of the following ranges;

- (0 to 100) V,
- (0 to 250) °C,
- (1 to 100) Hz,
- (100 to 1,000) µL,
- (0.1 to 1) in

If you are having a hard time determining the measurement range, try looking the equipment manufacturer’s specifications. You should be able to find this information in manufacturer’s manuals and datasheets.

Typically, the specification sheets will list all of the ranges of the equipment’s measurement capability.

To determine the equipment’s measurement range;

- Find the smallest value of the range,
- Find the largest value of the range, and
- List of the range from smallest to largest.

Look at the image above, you should be able to identify the following ranges;

- (0 to 200) mV
- (0 to 2) V
- (0 to 20) V
- (0 to 200) V
- (0 to 1000) V

Alternatively, you can list the measurement ranges similar to how they will be presented in your scope of accreditation;

- (0 to 200) mV
- (0.2 to 2) V
- (2 to 20) V
- (20 to 200) V
- (200 to 1000) V

In this example, you are listing your measurement ranges where they are typically used and crossover to the next range.

The key takeaway is to make sure that you cover your system’s measurement capability.

However, use common sense when listing your measurement range. Your estimated uncertainty in measurement may not adequately represent equipment’s measurement capability below 5% of the range.

For example, your measurement equipment may not perform well at 0.1% of the measurement range in comparison to 100% of the range.

Typically, measurement equipment is recommended to be used from 10% or 20% of the measurement range to 100% of the range. Therefore, using equipment at 1% or less of the measurement range may not be desirable.

Make sure that you read manufacturer’s specifications and instructions.

Now that you have identified your measurement function and range, it is time to select the test points that you will use to estimate measurement uncertainty.

To select test points for estimating measurement uncertainty;

- Select a test point at the low end of the range,
- Select a test point at the high end of the range, and
- If necessary, select a test point in the middle of the range.

As a minimum, you will need to select two test points, one low and one high.

It is quite common to select test points at 10% and 100% of the range or 20% and 100% of the range.

The best practice is to select test points where your equipment is calibrated. Take a look at your calibration reports and find two points per range (i.e. one low and one high).

If your equipment is not calibrated at two points per measurement range, then you may need to estimate uncertainty at your cross-over points. This is where one measurement range overlaps with the next measurement range.

For example, a digital multimeter has five measurement ranges (e.g. 0.1V, 1V, 10V, 100V, and 1,000V) and is only calibrated at one point per range.

In this situation, it is best to estimate uncertainty at each calibration point and use the data from the previous range to calculate CMC uncertainty equations.

To estimate uncertainty for the 10V range, you would use the uncertainty at 10V and at 1V to develop a cmc uncertainty equation. This would allow you to estimate uncertainty at two points across the measurement range by using crossover or overlapping test points.

To estimate measurement uncertainty for a test or calibration process, you need to know the process.

Therefore, you need to select the method or procedure that will be used to perform the process.

With the method, you can review the process to find sources of uncertainty from the;

- List of recommended equipment,
- Recommended environmental conditions,
- Steps of the process,
- Equations used to obtain results, and/or
- Precautionary notes to avoid errors.

Reading the test method or calibration procedure can be very beneficial to your uncertainty analysis and help you avoid mistakes in your estimation.

You should select your test equipment before beginning an uncertainty analysis. This will ensure that you choose the right equipment to adequately estimate uncertainty in measurement.

It is a good idea to select your best equipment or the equipment that you would typically use.

Selecting inferior or substandard equipment can significantly affect your uncertainty analysis results.

If your goal is to report less uncertainty and you are measuring DC Voltage, selecting a Keysight 3458A multimeter may be a better choice than a 34401A multimeter.

If you are measuring length and have similar goals, selecting a grade 1 gauge block may be a better choice than a grade 3 gauge block.

So, make sure to pick the right test equipment for your uncertainty analysis.

Another task that you should perform is finding the mathematical equation or formula that represents your measurement process.

It is a step that many people often overlook when estimating uncertainty. However, using the mathematical equation can significantly help you.

When available, I recommend that you use the mathematical equation when estimating uncertainty in measurement.

Mathematical equations are like a map. They can;

- Give you sources of uncertainty,
- Reduce the time you spend conducting research,
- Help you calculate sensitivity coefficients, and
- Ensure that you are appropriately estimating uncertainty.

With an equation, you should be able to find what components contribute to measurement uncertainty and determine how each variable contributes to the uncertainty of the test or measurement result.

Additionally, you can use the equation to perform simulations and a calculate sensitivity coefficients.

I highly recommend that you use equations when they are available.

For example, if you are estimating uncertainty for a dead weight tester, you can use the mathematical equation below.

As you can see, this equation has a lot of variables. However, if you quantify the uncertainty for each variable, you can estimate uncertainty for the calculated pressure.

Furthermore, you do not have to worry (as much) about understating uncertainty because you have considered all of the sources of uncertainty included in the equation.

So, make sure to spend some time to find and use the mathematical equation (if available).

After establishing **what** you will be estimating uncertainty for, you need to prepare yourself to begin a new uncertainty analysis.

Before you start, you need to collect information and data that will help you estimate measurement uncertainty.

I recommend that you gather the following items listed below;

- Last 3 calibration reports,
- Repeatability and reproducibility test results,
- Test method or calibration procedure,
- Equipment manuals and datasheets.

This should not be a difficult task. You should have all of these items readily available to you with little or no research.

The purpose of this task is to give you a process that will help you prepare to estimate uncertainty in measurement.

Instead of ending this guide here, I want to give you some examples of this process so you can see how to implement it when you perform uncertainty analysis.

For this example, imagine that you want to estimate uncertainty for your Fluke 8508A digital multimeter.

To outline your uncertainty analysis, you need to:

- Identify the measurement function,
- Identify the measurement range,
- Identify the test points,
- Identify the method,
- Identify the equipment,
- Record your results

Which measurement function of the multimeter will you be using?

Additionally, you will want to whether you are sourcing, generating, or measuring.

For this example, you will be measuring DC Voltage. Therefore, your measurement function would be title: **DC Voltage Measure**.

Which measurement range do you want to evaluate?

Even though you want to estimate uncertainty each range, you should only pick one at a time.

For this example, let’s pick the 200mV range.

To specify the measurement range from beginning to end, identify the lowest and highest points of the range.

Some examples that you can use may include;

- Up to 200mV
- 1mV to 200mV
- 0.000001mV to 200mV

However, be realistic. List the measurement range that you actually intend to use.

What test points will you use to estimate uncertainty?

At a minimum, pick two test points across the range. I would recommend one low test point and one high test point.

Look at your calibration reports. I would recommend using test points that have calibration results. It will be much easier to estimate uncertainty at these points.

For this example, the multimeter is only calibrated at 100mV. Therefore, I would estimate uncertainty at 0mV and 100mV.

Otherwise, I recommend that you pick test points that are close to 10% of the range and 100% of the range.

For the next range (i.e. 2V), I would use your uncertainty at 100mV for the low test point and estimate uncertainty at 1V for your high test point.

Which method do you use to measure DC Voltage?

Select the method that best represents your typical workload or laboratory activities.

For this example, the manufacturer’s calibration procedure was chosen for measuring DC Voltage from a multifunction calibrator.

What equipment will you use?

Select the equipment that will provide your best measurement capability or your most common measurement capability.

I recommend that you select equipment that will provide your best measurement capability because you cannot report uncertainty that is smaller than advertised in your scope of accreditation.

For this example, a Fluke 8508A Multimeter was selected since it provides the best measurement capability for our hypothetical laboratory.

Additionally, I have selected a multifunction calibrator to act as the unit under test since it will help provide smaller uncertainties for repeatability and reproducibility.

If I had selected to use a power supply as my UUT, the results of repeatability and reproducibility testing would have been much larger which would lead to a larger uncertainty estimate.

So, make sure to select equipment (i.e. STD and UUT) with the best measurement capability. It will help achieve smaller uncertainties.

Now, that you have completed the previous five steps, you can record the results in your uncertainty budgets.

I recommend that you list the following information;

- Measurement function,
- Equipment or system description,
- Equipment identification or serial numbers,
- Measurement range, and
- Test-point

Take a look at the image below to see an example. This is the way that I present information in every uncertainty budget that I create.

It gives you a great outline for your uncertainty analysis.

Using this format provides all of the important information that you or your assessor need to understand what section of your scope of accreditation is related to this uncertainty budget.

Furthermore, it will help you keep your focus and attention on the one analysis at a time.

Here are some more examples of specifying your measurement function and outlining your uncertainty analysis.

As you can see, the format for outlining each uncertainty analysis is quite consistent. It contains the following information (in order);

- Measurement Function/Parameter,
- Equipment or System Description,
- Measurement Range, and
- Test-Point or Nominal Value

Therefore, I recommend that you use a similar format when outlining your uncertainty analyses.

Outline each uncertainty analysis when you begin to estimate uncertainty. It will help you focus your analysis on the right function, system, and data. Additionally, it will prevent you from making mistakes.

When you identify the key elements of your uncertainty analysis, it will help you narrow your scope of work and eliminate information and data that is not relevant.

Another benefit of outlining your analysis is it will allow you and others (e.g. assessors) to understand which measurement function is associated with each uncertainty budget. Plus, it will make it easier to organize your budgets in relation to your scope of accreditation.

Outlining your analysis and specifying a measurement function may not make sense to you today, but it is helpful when you look at your uncertainty budgets a year or two from now.

Whether you are updating your budgets or trying to answer an assessor’s question about your results, you will be glad you outlined your uncertainty analysis.

Therefore, make sure you start every uncertainty analysis with an outline of your measurement function. You will not regret it.

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Reporting measurement uncertainty in test and calibration certificates is a common practice for ISO/IEC 17025 accredited laboratories. It is also a common problem for a lot of laboratories.

Many struggle to do it right.

Most accredited laboratories are required to include uncertainty in their certificates. However, many of them do not know how to report uncertainty correctly.

Some of the most common deficiencies laboratories get cited for are;

- Not reporting uncertainty in certificates,
- Not reporting uncertainty correctly,
- Not reporting uncertainty to two significant figures,
- Not rounding uncertainty correctly,
- Reporting uncertainty smaller than their scope of accreditation.

Many of these deficiencies are easily avoidable. However, so much focus is put into learning how to estimate measurement uncertainty that many forget to learn how to report uncertainty.

The good news is the rules for reporting uncertainty have become much clearer over the last 10 years; and, today, we are going to cover them all!

In this guide, you will learn the requirements, the process, and the skills to report uncertainty in measurement.

Plus, I am going to give you plenty of examples from major laboratories that you can use to report uncertainty in your own certificates.

We are going to cover;

- Requirements for Reporting Uncertainty
- How to Report Uncertainty
- What are Significant Figures
- Rules for Rounding Uncertainty
- Reporting Uncertainty Examples

If you have questions about reporting measurement uncertainty in your certificates, then you are going to like this guide.

Let’s get started.

Whether you know it or not, there are rules to reporting uncertainty in your test and calibration certificates.

However, these rules have not always been around.

In the beginning, the GUM only provided recommendations, not rules. These recommendations were not heavily enforced, so laboratories used a variety of methods to report uncertainty.

Within the last decade, the recommendations from the GUM have started to become published in policies and standards.

As a result, accreditation bodies are starting to enforce these requirements. This means that you should become familiar with them and make sure they are implemented in your test or calibration certificates.

Therefore, we are going to cover the recommendations, policies, and requirements published in;

In section 7.2.3, the GUM states that you should include the following information when reporting the expanded measurement uncertainty;

- A full description the of the measurand Y,
- The measurement result, the measurement uncertainty, and the units of measure,
- Include the relative expanded uncertainty (e.g. percent) when appropriate,
- Give the value of the coverage factor (k),
- Give the confidence level associated with the reported uncertainty,
- Give a copy of your uncertainty budget or refer to a document that contains it (see sections 7.2.7 and 7.1.4).

In section 7.2.4, the GUM states that you should report measurement results, for maximum clarity, similar to the example below;

In section 7.2.6, the GUM states that you should not report an excessive number of digits and recommends to round measurement uncertainty to two significant figures.

In section 6.1, the ILAC P14 policy states that a calibration laboratory should report uncertainty;

- In the calibration report,
- With the measurement result

Additionally, section 6.1 provides exceptions to reporting uncertainty as long as you obtain an agreement with the customer and meet the listed criteria.

In section 6.2, the policy states that you should report the measured value and the measurement uncertainty together, and include the associated units of measure for both.

Optionally, you can present the results in a table or provide the measurement uncertainty as relative expanded uncertainty (e.g. percent).

Finally, you will need to add a note or statement explaining the coverage factor and coverage probability of your reported measurement uncertainty values.

In section 6.3, the policy states that you should round measurement uncertainty to two significant figures and use the rounding method provided in section 7 of the GUM.

In section 6.4, the policy states that you include the following sources of uncertainty when estimating measurement uncertainty for your calibration reports;

- CMC Uncertainty,
- UUT Resolution, and
- UUT Repeatability.

In section 6.5, the policy states that you should not report measurement uncertainty values that are smaller or less than the CMC Uncertainty listed in your scope of accreditation.

Overall, the requirements in the ISO/IEC 17025 standard for reporting uncertainty in measurement are very straightforward.

In section 7.8.3.1c, the ISO/IEC 17025:2017 states that you should report uncertainty in your test reports when;

- It is relevant to the validity of the test results,
- A customer requests it, or
- It affects conformity to a specification limit.

Additionally, when you report uncertainty, it should be reported in the same unit of measurement as the result or in a unit relative (e.g percent) to the result.

In section 7.8.4.1a, the ISO/IEC 17025:2017 states that you should report uncertainty in your calibration reports;

- In the same unit as the measurement result, or
- In a term relative to the measurement result (e.g. percent).

Unlike test reports, the standard does not give you the option to omit reporting uncertainty. Therefore, you should always report uncertainty in calibration reports.

In section 7.8.5f, the ISO/IEC 17025:2017 states that you should include information needed to evaluate measurement uncertainty in subsequent tests or calibrations.

When reporting uncertainty in measurement, follow this five-step process;

- Record the measurement result
- Estimate the uncertainty in measurement
- Round uncertainty to two significant figures
- Round the measurement result to match the uncertainty
- Report the results
- Include an uncertainty statement

The first step to reporting uncertainty is to know the value of the measurement result. Therefore, you must start the process by performing a measurement and recording the result.

Using the example in the GUM, imagine that measure the resistance of a resistor and find it’s value to be 10.05762 Ohms.

Record the resistance value as the measurement result.

After recording your measurement result, you can estimate the uncertainty in measurement.

Following the recommendations of the ILAC P14, estimate your uncertainty in measurement including these three factors;

- CMC Uncertainty
- UUT Resolution
- UUT Repeatability

After combining these three factors and calculating the expanded uncertainty to 95% where k=2, you should have a value for calibration uncertainty.

Now that uncertainty has been estimated for the measurement result, it is time to round uncertainty to two significant figures.

To do this, find your first two significant figures. Then, use conventional rounding to round up or down to the nearest number.

Next, round the measurement result to be consistent with the measurement uncertainty.

Since the estimated uncertainty does not give you enough accuracy to justify the value of the measurement result, round the measurement result to match the accuracy of the uncertainty.

There is no point in reporting a measurement result beyond the number of digits given in the estimated uncertainty. So, just round your measurement result to match the number of digits given in your estimated uncertainty.

Report the results in your test or calibration certificate.

There several ways that you can report uncertainty in your test or calibration reports. You can report the results;

- Alongside your test or measurement results,
- In a sentence or statement, or
- In a table or uncertainty budget.

Choose the method that works best for you.

Finally, provide a statement that explains how your customers should interpret the reported measurement uncertainty.

Your certificate must include a statement that gives;

- Information about uncertainty statements,
- The coverage factor, and
- The coverage probability.

To give you an idea, here is a general statement that you could use in your certificates.

*“Reported uncertainties were estimated in accordance with the [insert method here] **expressed to a 95% confidence interval where k=2.”*

Significant figures is an important concept that confuses many people. Therefore, I am going to try to simplify it for you.

According to the Oxford Advanced Learner’s Dictionary, significant figures are each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

Now, the definition may not make sense to you at first. However, it will become much clearer after you review the rules for determining significant figures.

To determine which figures are significant, follow the rules listed below.

- Any digit that is not zero is significant;
- Zeros between nonzero digits are significant;
- Zeros to the left of the first nonzero digit are not significant;
- Numbers that contain a decimal point; all trailing zeros count as significant figures;
- Numbers that do not contain a decimal point; all trailing zeros may or may not be significant.

In the image below, you will see examples of these rules in use so you can learn how to determine the number of significant figures.

Are you still confused by significant figures?

Try using scientific notation. It will make it easier for you report uncertainty to two significant figures.

Significant figures are much easier and less confusing when you use scientific notation and it will help you avoid making mistakes.

Take a look at the example below. Fluke Calibration uses scientific notation in many of their calibration reports.

As you can see, they report only two significant figures using scientific notation.

It is not the easiest way to provide information to your customers, but it is the easiest way for your laboratory to comply with ISO/IEC 17025 requirements.

When you need to round uncertainty, keep it simple and use conventional rounding.

Despite other recommendations to round up or to even numbers, I recommend that you simply use conventional rounding. This will help you reduce confusion in the laboratory and ensure that everyone provides consistent results.

In fact, conventional rounding is the method recommended by the GUM (JCGM 100:2008). According to section 7.2.6, the GUM states;

“In reporting final results, it may sometimes be appropriate to round uncertainties up rather than to the nearest digit… However, common sense should prevail…”

To do this, just follow the rules for conventional rounding;

- Round up if a number is greater than or equal to 5,
- Round down if a number is less than 5.

For example, if you follow the rules above, you will round 10.5mV up to 11mV and round 10.4mV down to 10mV.

- Round 10.5mV up to 11mV
- Round 10.4mV down to 10mV

**PRO TIP:** To make rounding and reporting uncertainty easy, use scientific notation.

Using scientific notation makes it easy for laboratories to meet requirements and minimize mistakes. However, reporting results in scientific notation it makes it more difficult for your customers to read and understand the results.

From my own experience, it takes me longer to evaluate reports that use scientific notation. Typically, I have to convert the result back to a number and convert it again to match the magnitude of the measurement result.

These are extra steps that I do not like to take to evaluate results. It wastes time and hurts user experience. Therefore, I do not use scientific notation.

If you are looking for ideas to report uncertainty in your test or calibration certificates, get inspiration from looking at other laboratories reports.

It’s a fast and efficient way to find a solution that meets requirements. Just follow this simple three step process;

- look at test and calibration certificates from accredited laboratories,
- choose the format that you like best, and
- implement it in your own certificates.

It’s that easy!

As a result, you will know that you are issuing certificates that meet requirements without having to spend a lot of time on research and design.

To give you inspiration, I have a few examples to share with you from some of the biggest brand laboratories in the US.

Below is an exert of a calibration report issued by Fluke. Notice that they report an uncertainty next to every measurement result.

Additionally, Fluke typically reports measurement uncertainty in scientific notation.

In the image below, take a look at the statement Fluke uses to explain how you should interpret their reported estimates of uncertainty in measurement.

Below is an exert of a calibration report issued by NIST. Notice that they report an uncertainty next to every measurement result.

Additionally, NIST typically reports measurement uncertainty in the same units of measure as the measurement results.

In the image below, take a look at the statement NIST uses to explain how you should interpret their reported estimates of uncertainty in measurement.

Below is an exert of a calibration report issued by Tektronix. Notice that they report an uncertainty next to every measurement result.

Additionally, Tektronix typically reports measurement uncertainty in the same units of measure as the measurement results.

In the image below, take a look at the statement Tektronix uses to explain how you should interpret their reported estimates of uncertainty in measurement.

Below is an exert of a calibration report issued by Keysight. Notice that they report an uncertainty next to every measurement result.

Additionally, Keysight typically reports measurement uncertainty in the same units of measure as the measurement results.

In the image below, take a look at the statement Keysight uses to explain how you should interpret their reported estimates of uncertainty in measurement.

Below is an exert of a calibration report issued by Mitutoyo. Notice that they do not report an uncertainty next to every measurement result. They list it separately.

Additionally, Mitutoyo typically reports measurement uncertainty in the same units of measure as the measurement results.

Finally, take a look at the statement Mitutoyo uses to explain how you should interpret their reported estimates of uncertainty in measurement.

Reporting measurement uncertainty in your test or calibration certificates can be a challenge. There are a lot of rules to follow for ISO/IEC 17025 accreditation.

In this guide, you should have learned;

- The requirements for reporting uncertainty,
- The 6 step process to reporting uncertainty,
- What are significant figures,
- How to round uncertainty, and
- How to present uncertainty in your certificates.

Overall, we have covered a lot of information that should help you easily report measurement uncertainty and meet ISO/IEC 17025 requirements.

If your certificates are not currently meeting these requirements, then give this process a try and let me know if you have any questions.

Also, feel free to leave a comment below telling us how you report uncertainty.

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]]>The post How to Perform a Repeatability Test for Estimating Uncertainty in Measurement appeared first on isobudgets.

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Performing a repeatability test is an essential part of estimating uncertainty in measurement. It is the most common experiment performed to collect Type A Uncertainty data.

Additionally, most accreditation bodies require that you include repeatability data in your uncertainty budgets. However, many people have trouble with performing a repeatability test. They do not know how to conduct the experiment, collect the data, or analyze the results.

In this guide, you are going to learn everything that you need to know about repeatability testing;

- What is a repeatability test,
- How to perform a repeatability test, and
- How to calculate repeatability.

Plus, I have created some great tools to help you perform a repeatability test and analyze the results next time you need to estimate measurement uncertainty.

Every day, I work with clients who need my help to estimate uncertainty in measurement. During the process, I typically ask clients to perform repeatability and reproducibility testing.

However, many of my clients do not know how to conduct a repeatability test. So, they ask for procedures, checklists, and consultation.

After years of continually helping clients perform a repeatability test, I noticed that I had not written a formal guide to help these clients; nor automate the process.

Therefore, I decided to create a guide dedicated to repeatability testing in order to answer all of the questions that I have been asked.

In this guide you will learn;

1. What is Type A Uncertainty

2. What is A Repeatability Test

3. How to Perform a Repeatability Test

4. How Many Samples You Should Collect

5. How to Collect Repeated Samples

6. How to Calculate Repeatability (Single Test)

7. How to Calculate Repeatability (Multiple Tests)

8. How to Add Repeatability to Your Uncertainty Budgets

**Click here to download the repeatability test cheatsheet & calculator for free!**

Type A Uncertainty is a component of uncertainty where data is collected from a series of observations and evaluated using statistical methods associated with the analysis of variance (ANOVA).

Commonly referred to as Type A Data, Type A Uncertainty is typically associated with the results of Repeatability and Reproducibility Testing. However, it can also be associated with stability testing.

According to the Vocabulary in International Metrology (VIM), Type A Evaluation of measurement uncertainty is a component of measurement uncertainty evaluated by a statistical analysis of measured quantity values that were obtained under defined measurement conditions.

A repeatability test is an experiment performed to evaluate how repeatable your results are under a set of similar conditions.

When performing a repeatability test, you will want to collect data using the;

- Same method,
- Same operator,
- Same equipment,
- Same environmental conditions,
- Same location, and
- Same item or unit under test.

Essentially, you want to collect repeatable results over a short period of time without changing anything (if possible).

According to the Vocabulary in International Metrology (VIM), measurement repeatability is measurement precision under a set of repeatable conditions of measurement.

Furthermore, the VIM defines a repeatability condition of measurement as a condition of measurement, out of a set of conditions that includes the same measurement procedure, same operators, same measuring system, same operating conditions, same location, and same replicate measurement on the same or similar objects over a short period of time.

Therefore, you need to define your measurement conditions and collect repeatable results over a short period time so you can evaluate the precision of your process.

In the next section, you will learn step by step how to perform a repeatability test.

To calculate repeatability, you need to have a procedure.

Similar to every test or measurement performed in your laboratory, you must have a method or procedure to guide you through the process and ensure consistency in your results.

In this section, you will learn to perform a repeatability test step by step. Follow the instructions below to add repeatability test data to your uncertainty budgets.

Here is a list of the steps in this process;

1. Select the measurement function to test,

2. Select the measurement range,

3. Select the test-point(s),

4. Select the method,

5. Select the equipment,

6. Select the operator,

7. Perform the test,

8. Collect the number n of repeated samples,

9. Analyze your results,

10. Save a record of your results (recommended),

11. Add the result to your uncertainty budget.

Before you begin performing a repeatability test, it is a good idea to determine what you are going to test.

Start by selecting the measurement function that will be tested.

The measurement function will be the category that best describes your measurement or test result, such as;

- DC Voltage Generate/Measure
- Length
- Pressure Generate/Measure
- Torque Generate/Measure
- Temperature Source/Measure

If you are having trouble, take a look at your scope of accreditation (or another laboratory’s scope of accreditation) and pick the measurement function that you would like to test.

After selecting the measurement function, pick a measurement range to test. This should consist of a chosen starting measurement value and an ending measurement value; typically low to high.

I recommend that you pick a measurement range listed in your scope of accreditation or in the equipment manufacturer’s specifications.

Now that you have specified a measurement range, it is time to select the test-points for your repeatability test.

If you assume that your measurement function is linear, you will need to select two test-points along the measurement range. Typically, it should be a low value and a high value.

Some common practices are to select test points that are at 10% and 90% of the measurement range or at 20% and 100% of the measurement range. For best results, I recommend that you select two calibration points along the measurement range (if available).

If you assume that your measurement function is non-linear, you may want to select three of more test points to evaluate. This will help you prevent errors due to the curvature of the measurement function.

Should you decide to perform a repeatability test at three of more test points, try to select evenly spaced test points to prevent modeling errors in your CMC Uncertainty prediction equation.

The next step to performing a repeatability test is to select the measurement method or procedure. You will want to select a method or procedure that best represents the how the measurement process is performed.

A good place to start is to use a test method or calibration procedure that best represents your measurement process. This will help you make sure that you are evaluating a measurement process that you would normally perform in your laboratory.

If you do not have a procedure, try writing one for your process. Even if the procedure minimally covers the steps of the process, it is still better than nothing. Additionally, it will help you get consistent results.

Following the chosen method, select the equipment recommended to perform your measurement process. Make sure that your equipment is calibrated and functioning properly before use.

For best results, select the most accurate equipment available to you. The equipment you choose will affect the results. So, select your best equipment.

Select an operator to perform the repeatability test. Pick an operator that is qualified and experienced at performing the test or measurement.

Typically, your most experienced or qualified operators will yield the best results.

Your goal should be to achieve consistent repeatable results. Therefore, choose an operator that you will help you achieve it.

Now that you have established all of your conditions, it is time to perform a repeatability test for the measurement function, range, and test-points that you selected using the method, equipment, and operator that you selected.

Perform steps eight through eleven to conduct a repeatability test.

When performing a repeatability test, collect a defined number of repeated samples. Typically, it is recommended that you collect at least 20 to 30 samples to obtain statistically significant results.

However, collecting 20 to 30 samples is not always practical for every test or measurement. Instead, collect the number of samples that is most appropriate for your situation and measurement system.

If you can only collect 5 samples because the test or measurement process is time-consuming or labor-intensive, then only collect 5 samples. If you can collect 100 samples because your test or measurement process is quick and automated, then collect 100 samples.

Only collect the number of samples that is most appropriate for your situation.

After collecting samples, you will need to analyze your data using the analysis of variance (ANOVA). Calculate the mean (i.e. average), standard deviation, and the degrees of freedom.

If you are analyzing a single set of data, you will use the calculated standard deviation and degrees of freedom in your uncertainty budget.

If you are analyzing multiple sets of data, you will need to use the method of pooled variance to calculate the pooled standard deviation and degrees of freedom for your uncertainty budget.

Anytime that you collect data, it is a good idea to save a record of your results. It will come in handy if you need to go back and review your results or compare them with other repeatability test data.

I always recommend that you keep files for your repeatability test data. However, you do not have to keep records. Instead, you can just collect Type A data each time you update your uncertainty budgets. The choice is yours.

Finally, add your repeatability test results to your uncertainty budgets. Create a line item for repeatability and include the standard deviation and the degrees of freedom in your budget.

Characterize your repeatability results with a Normal distribution where ‘k’ equals one (i.e. k=1).

For step by step instructions, read the section below: How to Add Repeatability to Your Uncertainty Budget.

A common question people ask when performing a repeatability test is, “How many samples should I collect?”

The answer is, “As many as you practically can.”

As a general rule of thumb, it is typically recommended to collect 20 to 30 samples to be statistically sound. However, this rule is not applicable to every scenario.

If you are using automation and have the capability to collect 100 or more samples over a short period of time, then collect 100 or more samples. It is practical for your test or measurement process.

If you are performing a test or measurement that is difficult or time-consuming, it may be hard to collect 20 to 30 samples. Therefore, you should collect fewer samples. In this situation, it may be more practical to only collect three to five samples.

Make sure to select the number of samples that is appropriate for your measurement process.

Do not over think it. Start with 20 samples and adjust the number of samples collected as needed based on your situation.

If you would like to manipulate your results to achieve a desired margin of error (i.e. standard deviation), use the formula below;

**How to Calculate**

1. Choose your desired confidence level (z).

2. Choose your desired margin of error (MOE).

3. Multiply the result of step 1 by the value by the standard deviation of the sample set.

4. Divide the result by the margin of error selected in step 2.

5. Square the result calculated in step 4.

When performing a repeatability test, some people get confused on how to collect repeated samples. They believe that they must;

1. Set-up a test,

2. Collect a result,

3. Break-down the setup, and

4. Repeat the process ‘n’ number of times.

This is not true.

Conducting a repeatability test following that process would be rigorous and time-consuming.

Instead, think about how you could collect the data easier and faster if you were to follow this process;

1. Set-up a test,

2. Collect a result,

3. Repeat ‘n’ number of times, and

4. Break-down the setup.

If you follow this process, you would be able to complete a repeatability test much faster. So, to make repeatability testing less rigorous, make sure to collect repeated samples back to back over a short period of time.

If your measurement equipment repeatedly samples results and refreshes the display, collect ‘n’ number of displayed results back to back over a short period of time.

Should your measurement equipment require manual sampling, repeat the process over and over again until you collect your desired number of samples.

Do not break down your test set-up each sample and repeat. That process would actually be a form of reproducibility testing, not repeatability testing.

Analyzing the results of a single repeatability test is pretty simple. Just calculate the mean, standard deviation, degrees of freedom.

1. Calculate the Mean,

2. Calculate the Standard Deviation,

3. Calculate the Degrees of Freedom.

In the sections below, you will learn how to perform these calculations in Excel.

**How to Calculate**

1. Select a cell to calculate the mean.

2. Type “=AVERAGE(“ in the cell.

3. Select the cells containing your results.

4. Type “)“ and press the “Enter” key.

**How to Calculate**

1. Select a cell to calculate the standard deviation.

2. Type “=STDEV(“ in the cell.

3. Select the cells containing your results.

4. Type “)“ and press the “Enter” key.

**How to Calculate**

1. Select a cell to calculate the degrees of freedom.

2. Type “=COUNT(“ in the cell.

3. Select the cells containing your results.

4. Type “)-1“ and press the “Enter” key.

Analyzing the results of a several repeatability tests is more complex. You cannot average standard deviation, so you must pool them together using the method of pooled variance.

1. Calculate the Mean,

2. Calculate the Standard Deviation,

3. Calculate the Degrees of Freedom,

4. Calculate the Pooled Standard Deviation.

**How to Calculate**

1. Select a cell to calculate the mean.

2. Type “=AVERAGE(“ in the cell.

3. Select the cells containing your results.

4. Type “)“ and press the “Enter” key.

**How to Calculate**

1. Select a cell to calculate the standard deviation.

2. Type “=STDEV(“ in the cell.

3. Select the cells containing your results.

4. Type “)“ and press the “Enter” key.

**How to Calculate**

1. Select a cell to calculate the degrees of freedom.

2. Type “=COUNT(“ in the cell.

3. Select the cells containing your results.

4. Type “)-1“ and press the “Enter” key.

**How to Calculate**

1. Select a cell to calculate the weighted variance (i.e. SS).

2. Type “=CELL1*CELL2^2“ in the cell.

3. Copy and Paste function into other cells.

**How to Calculate**

1. Select a cell to calculate the total weighted variance.

2. Type “=SUM( “ in the cell.

3. Select the cells containing your results.

4. Type “)“ and press the “Enter” key.

**How to Calculate**

1. Select a cell to calculate the total degrees of freedom.

2. Type “=SUM( “ in the cell.

3. Select the cells containing your results.

4. Type “)“ and press the “Enter” key.

**How to Calculate**

1. Select a cell to calculate the pooled standard deviation.

2. Type “=SQRT( “ in the cell.

3. Select the cell containing the total weighted variance (i.e. ESS).

4. Type “/ “ for the divide function.

5. Select the cell containing the total degrees of freedom (i.e. EDOF).

6. Type “)“ and press the “Enter” key.

The pooled standard deviation will be your value for repeatability, and the total degrees of freedom will be your value for degrees of freedom.

After performing a repeatability test and analyzing your data, you will want to add the results to your uncertainty budget.

To complete this task, just follow the step by step instructions listed below. The instructions should work for any ISOBudgets uncertainty budget calculators and most uncertainty budget calculators offered by other organizations.

If you don’t have an uncertainty budget calculator, you can buy one here.

Are you ready perform a repeatability test?

If so, get the repeatability test checklist and calculator. The checklist will give a summary of all the instructions provided in this guide, and the calculator will help you analyze your results so you can calculate repeatability faster.

Just click the button below to download.

**Click here to download the repeatability test cheatsheet & calculator for free!**

Performing a repeatability test is the most common methods used to collect type A uncertainty data. If your laboratory is ISO/IEC 17025 accredited or plans to get accredited, you will need to perform repeatability testing and include the results in your uncertainty budgets.

In this guide, you should have learned how to perform a repeatability test and analyze the results to calculate measurement repeatability. Plus, you should have learned some additional tips to help you complete the process with more confidence.

Calculating repeatability is not hard, but it is a task that some people find difficult to complete. Use the information and tools provided in this guide to help you estimate uncertainty in measurement faster and get prepared for accreditation.

The post How to Perform a Repeatability Test for Estimating Uncertainty in Measurement appeared first on isobudgets.

]]>The post How to Find Significant Contributors to Measurement Uncertainty and Automate the Process in 5 Steps appeared first on isobudgets.

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Ever wondered what factors are significant contributors to uncertainty in measurement?

Are you performing an uncertainty analysis and wondering what components to include in your uncertainty budget?

Maybe an assessor cited you a deficiency and recommended that you include more sources of uncertainty in your budgets. Afterward, they provided you with a laundry list of significant contributors.

Perhaps, you wanted to reduce your measurement uncertainty by targeting your largest contributors.

If the answer to any of the previous statements was “Yes,” then this guide is for you.

Today, I am going to show you how to find significant contributors by calculating the value of a metric I call “significance.”

Plus, you will learn how to add this calculation to your uncertainty budget in Microsoft Excel, so you automate the calculation every time you estimate uncertainty.

Several years ago, I was at the **A2LA Annual Meeting** in Maryland discussing measurement uncertainty and significant contributors with a group of technical experts (e.g. metrologists, assessors, and consultants).

One of the topics of conversation was about evaluating uncertainty components to find out how much they contribute to measurement uncertainty.

**Dilip Shah, President at E=mc3 Solutions**, mentioned a method for determining the amount of influence an uncertainty component contributes to the total uncertainty.

Specifically, I remember him stating that you cannot calculate a ratio of standard deviations. He said that you must convert the standard deviations to variances before calculating the ratios.

Now, I remember learning about this method in college, but never in relation to uncertainty analysis. However, when Dilip mentioned it, I knew that it would be a great tool to evaluate and validate my estimations of measurement uncertainty.

So, I added the calculation to my uncertainty budget templates that night at the hotel. I wanted to test the function to see what I could learn from using it in **my uncertainty calculator**.

After a few weeks, I realized that it was extremely valuable. It allowed me to quickly;

• find significant contributors,

• find negligible contributors,

• evaluate my results, and

• find errors.

Having this data in my uncertainty budgets helped me validate my results faster. At this point, I couldn’t calculate uncertainty without it.

Therefore, I added it to every uncertainty calculator that I created. Today, I continue to use it and recommend that you give a try.

In this guide, you will learn everything that you need to know about calculating significance and finding significant contributors to measurement uncertainty. I will even show you how to add it your uncertainty budgets.

Here is a list of topics that will be covered in this guide;

1. **What is a Significant Contributor**

2. **What is Significance**

3. **How to Calculate Significance**

4. **How to Calculate it in Excel**

5. **How to Add it to Your Uncertainty Budget**

6. **How to Validate Your Results**

7. **Find the Largest Significant Contributors**

8. **Find the Least Significant Contributors**

9. **Common Evaluations**

A significant contributor is a source of uncertainty in measurement that increases the CMC Uncertainty by five percent or more.

According to A2LA, a it is “a contributor whose contribution increases the CMC by five percent (5%) or greater.”

See the excerpt from the **A2LA R205 Publication** below;

“Significant (A2LA): “significant” further means a contributor whose contribution increases the CMC by five percent (5%) or greater.”

Now, significant contributor is not an official term defined by the **Vocabulary in Metrology**; but, it is a term used repetitively in several key documents;

• The **GUM** states, “… significant component to uncertainty of the measurement result.”

• The **ISO/IEC 17025:2005 standard** states, “… major sources of uncertainty.”

• The **ISO/IEC 17025:2017 standard** states, “… all contributions that are of significance.”

However, none of these documents define “what is” a significant contributor or establish requirements to determine whether or not a component is a significant contributor to uncertainty.

Therefore, I prefer to refer to the definition provided in the A2LA R205 document. It is the only document to establish requirements for significance.

If laboratories’ uncertainty budgets are going to be assessed for the inclusion of significant contributors, it would be best to rely on requirements rather than opinions.

When a technical expert is allowed to make a decision based on subjective opinions rather than requirements and facts, there will be problems.

Now that you know what a significant contributor is, you may be wondering how to find them in your uncertainty analysis.

Well, it is pretty easy. You just need to calculate a parameter that I call “significance.”

Significance is a proportion, in percentage, of the total uncertainty that a component contributes to the CMC Uncertainty.

While this is not an actual statistical term, it is a term that I have used to describe the magnitude of influence when evaluating significant contributors to uncertainty in measurement.

However, it is statistical method derived from the analysis of variance (ANOVA). Specifically, it is based on the analysis of a **proportion of variance** or a **proportion of total variation**.

I love this method!

I use it all of the time to evaluate my uncertainty analyses. In fact, I include it in every **uncertainty budget calculator** that I use.

It is really helpful for evaluating uncertainty budgets to find;

• The most significant contributors,

• The least significant contributors,

• Negligible contributors, and

• Errors.

Calculating the significance of an uncertainty component is not difficult. The process can be completed in only four steps.

To calculate significance, convert your uncertainty components from standard deviations to variances. Next, calculate the sum of squares of all uncertainty components. Then, calculate the ratio of one uncertainty component to the total sum of squares of all the uncertainty components.

Look at the equation below to calculate significance.

To calculate significance, just follow these step-by-step-instructions;

1. Select an uncertainty component,

2. Square the standard uncertainty component to convert it to a variance,

3. Calculate the **Sum of Squares** for all uncertainty components,

4. Divide the result in Step 2 by the result in Step 3.

To show you how to calculate significance, take a look at the example below.

Imagine that you have 3 uncertainty components;

• CMC Uncertainty,

• UUT Resolution, and

• UUT Repeatability.

The value of each component is provided below as a standard uncertainty;

• CMC Uncertainty: 0.16mV

• UUT Resolution: 0.577mV

• UUT Repeatability: 0.55mV

Now, let’s see how much the **UUT Resolution** contributed to the total combined uncertainty.

In case you want to work out the equation for yourself, the significance of each uncertainty component is listed below;

• CMC Uncertainty: 3.9%

• UUT Resolution: 50.4%

• UUT Repeatability: 45.7%

Calculating significance can be performed using Microsoft Excel. It is a fast and easy way to evaluate your estimates of uncertainty in measurement.

If you use Excel to calculate uncertainty, you can easily add this function to your uncertainty calculator. It will automatically calculate the significance of uncertainty components each time you estimate uncertainty.

In the steps below, you will learn how to add this function to your uncertainty calculator.

To calculate the significance of an uncertainty component, you must first square the value of the standard uncertainty component. This will convert the standard deviation to variance of the uncertainty component.

Next, you will calculate the sum of squares for all uncertainty components.

Essentially, you will convert each uncertainty component to a variance and add them all together.

In Microsoft Excel, you will use the sum of squares function, or ‘SUMSQ,’

Now, divide the functions given in step 1 by the function in step 2. Your function should look similar to the example below;

=Cell1^2/SUMSQ(Cell2:Cell3)

Where,

Cell1 = standard uncertainty component

Cell2 = First standard uncertainty component

Cell3 = Last standard uncertainty component

Every time you calculate significance, it is important to double-check your work and validate your results.

Validating your significance calculations is pretty easy. Just add all of your significance calculations together. The result should be 100%.

If your results do not add up to 100%, then you have a problem and must go back to check your equation for errors.

In the example given earlier, significance was calculated for three uncertainty components. Their values were 3.9%, 50.4%, and 45.7%.

When added together, their sum equals 100%.

Since the values equal 100%, the calculation is validated to be correct.

Adding significance calculations to your **uncertainty budgets** can be a very helpful tool for evaluating your uncertainty components.

In fact, I add the function to every one of my uncertainty budgets. It allows me to quickly evaluate my uncertainty calculations.

In this section, I am going to show you how to add this function to your uncertainty calculator; if you use Microsoft Excel. The process is easy. Just follow the steps listed below;

Find an empty column next to your uncertainty budget or insert a new column in your uncertainty budget. I prefer to use the last column to the right of the uncertainty calculator.

This column will be used to calculate the significance of your uncertainty components.

Select the cell that is on the same row as your first uncertainty component and add the Excel function in the image below.

Next, repeat the process and add the function to each row that contains an uncertainty component.

Next, you want to convert the values to a percentage. It will help you compare and evaluate results.

Select the cells that contain your significance calculations and click on the percentage button in ‘Home’ tab.

You can also press **Ctrl+Shift+%** simultaneously to convert the values to percentage.

Afterward, your results should look similar to those in the image below.

To help identify your calculations, add a header just above the calculation.

Then, add any necessary formatting to help it blend in with your uncertainty budget or calculator.

Validating your results is important. All of your significance calculations should add up to 100 percent.

So, add the following Excel function just below your significance calculations.

Finally, verify the sum of all significance calculation is 100 percent. If it is, you have validated that your calculations are correct.

If the result does not equal 100 percent, you have a mistake. Review each function and fix any errors.

The greatest benefit of calculating significance is to determine which uncertainty components contribute the most to your estimated uncertainty.

When you identify which components have the largest influence on your measurement uncertainty, you can reduce your uncertainty in measurement by minimizing those components.

Additionally, you can evaluate your largest contributors to verify that you didn’t overstate the uncertainty for a particular component.

Some good questions to ask yourself are;

• Is the value of the uncertainty component correct?

• Is the value of the **sensitivity coefficient** correct?

• Did I select the right probability distribution and divisor?

• Is the significance calculated correctly?

• Is this typically considered a significant contributor?

After you evaluate your largest contributors, you should also review your smallest contributors.

They may not be able to help you reduce your uncertainty in measurement, but you can verify that you did not underestimate uncertainty.

It is quite common for laboratories to underestimate uncertainty. If you have an uncertainty component with little or no significance, you can evaluate it to determine if it is negligible or not.

On the other hand, you can evaluate components considered to be significant contributors to determine whether or not they are in your analysis. If a known significant contributor has a small value for significance, you may want to re-evaluate your estimates to verify that there is not an error.

Some good questions to ask yourself are;

• Is the value of the uncertainty component correct?

• Is the value of the sensitivity coefficient correct?

• Did I **select the right probability distribution** and divisor?

• Is the significance calculated correctly?

• Is this typically considered a significant contributor?

After performing thousands of uncertainty analyses, I have noticed some common trends that occur when estimating uncertainty in measurement. By calculating significance, I have been able to identify problems and opportunities for improvement.

Here are some of the most common trends that I have observed.

When laboratories have large or overstated estimates of uncertainty, the most common causes are;

• A Large Reference Standard Uncertainty

• A Large **Type A Uncertainty**

• A Large Bias

When you discover that the **reference standard uncertainty** is the largest contributing factor, it is typically caused by sending your equipment to a calibration laboratory that has large CMC uncertainties.

Worse yet, you may find out that the reference standard uncertainty is larger than the accuracy of your equipment.

I see this quite often.

Large Reference Standard Uncertainty can be a sign of;

• Using improper equipment,

• Using improper methods,

• Using unskilled or poorly trained personnel,

• Undesirable environmental conditions, or

• All the above.

To fix this, send your equipment to a calibration laboratory that has a smaller CMC uncertainty. **Search your accreditation body’s database to find a laboratory** with uncertainties that meet your requirements.

If you are unsure, contact the laboratory and ask questions. Also, you can add statements to your purchase orders to have your equipment calibrated in accordance with uncertainty statements advertised in the laboratory’s scope of accreditation.

Reducing the calibration uncertainty of your equipment can have a significant impact on your estimation of measurement uncertainty.

If you notice that repeatability and(or) reproducibility contribute significantly to your estimated uncertainty, it may be caused by one or more technicians lacking the skill to achieve repeatable measurement results.

To fix this, provide additional training to laboratory personnel to ensure that they are implementing good measurement practices. Train your personnel to perform measurement processes exactly the same way to reduce the amount of variability in their measurement results.

Dedicating 10 to 30 minutes for training can have a big impact on your measurement results.

Additionally, review your measurement methods and(or) procedures for improvement opportunities. One extra step may dramatically improve your measurement results.

Watch your personnel perform a measurement process while following along with the procedure. Look for opportunities to add value and improve the process.

Furthermore, ask your personnel what tips and tricks they use when performing the process and consider adding them to your procedures. If you open a method or procedure and find handwritten notes, it may be a good indicator that you should update your procedures.

By improving operator skills and measurement methods, you can reduce the variability and uncertainty in measurement results.

If you evaluate your uncertainty budgets and discover that **bias is your most significant contributor**, you may have a problem.

Take a look at your calibration reports. You may discover that your measurement equipment is within specifications but performing close to its tolerance limits.

When this happens you not only run the risk of having large uncertainty estimates, you can also be at risk for reporting bad results in subsequent tests and(or) calibrations.

If you are not sure what I am referring to, check this article on **compliance with specifications**.

To fix this, adjust your measurement equipment during calibration to minimize bias.

For in-house calibrations, establish a threshold to perform adjustments. For example, you can establish a threshold to adjust equipment when measurement performance exceed 70% of specifications.

If you send your equipment to another laboratory for calibration, make sure that you request, in writing, that you want your equipment adjusted if it exceeds a defined percentage of the specification.

Talk to the laboratory during to contract review process to see what options they may be able to provide and make sure to that you get your requirements in writing. A good place to have it written is in the laboratory’s quote and in your purchase order.

By reducing bias, you may be able to dramatically reduce you estimations of uncertainty in measurement.

**Disclaimer:** This only pertains to uncertainty analyses that contain estimates of bias. If you use reference values from your certificates of calibration to compare to subsequent measurement results, you should not need to consider bias in your uncertainty analysis. However, if you assume that a nominal value is true and make no correction for error, then you should include an estimate of bias in your uncertainty budgets.

Finding significant contributors to measurement uncertainty is great way to evaluate your uncertainty budgets.

The best way to find significant contributors to calculate a parameter that I call significance. Calculating significance is fairly easy and can help you quickly evaluate your uncertainty calculations.

If you calculate uncertainty using Microsoft Excel, you can add the function to your uncertainty budgets to automatically calculate significance.

Use the instructions and tips in this guide to calculate significance and find significant contributors. It can help you evaluate your calculations and improve your estimates of measurement uncertainty.

Then, leave a comment and let me know if it helped you evaluate your uncertainty analyses. If not, let me know how you evaluate measurement uncertainty.

The post How to Find Significant Contributors to Measurement Uncertainty and Automate the Process in 5 Steps appeared first on isobudgets.

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Type A and Type B uncertainty are two elements that are commonly discussed in estimating measurement uncertainty.

Uncertainty type is covered in most measurement uncertainty guides and uncertainty training courses. Auditors review uncertainty budgets to make sure the components are categorized correctly.

However, have you ever looked at most of the information published on Type A and Type B uncertainty?

It’s very minimal. No one covers the topic of uncertainty type as well as the GUM. There is so much information left out of other guides and training.

It might be the reason why most people only evaluate type B uncertainty with a rectangular distribution when there are so many more realistic options.

Why are other options omitted?

In this guide, I am going to teach you all about Type A and Type B uncertainty as explained in the GUM. However, I am going explain in a manner that doesn’t require you to have a PhD.

So, if you want learn how to calculate uncertainty, make sure to read this guide to learn everything you need to know about Type A and Type B uncertainty.

Before you learn about uncertainty type classifications, it’s a good idea to know more about why they exist and where they came from.

In 1980, the CIPM Recommendation INC-1 suggested that measurement uncertainty components should be grouped into two categories; Type A and Type B.

Below is an exert from the **Vocabulary in Metrology**;

“*In the CIPM Recommendation INC-1 (1980) on the Statement of Uncertainties, it is suggested that the components of measurement uncertainty should be grouped into two categories, Type A and Type B, according to whether they were evaluated by statistical methods or otherwise, and that they be combined to yield a variance according to the rules of mathematical probability theory by also treating the Type B components in terms of variances. The resulting standard deviation is an expression of a measurement uncertainty. A view of the Uncertainty Approach was detailed in the Guide to the expression of uncertainty in measurement (GUM) (1993, corrected and reprinted in 1995) that focused on the mathematical treatment of measurement uncertainty through an explicit measurement model under the assumption that the measurand can be characterized by an essentially unique value. Moreover, in the GUM as well as in IEC documents, guidance is provided on the Uncertainty Approach in the case of a single reading of a calibrated instrument, a situation normally met in industrial metrology.*” – VIM 2012

As you can see, the VIM gives a great explanation and recommends that you read the GUM for more details.

Here is an exert from the **Guide to the Expression of Uncertainty in Measurement**;

“*3.3.4 The purpose of the Type A and Type B classification is to indicate the two different ways of evaluating uncertainty components and is for convenience of discussion only; the classification is not meant to indicate that there is any difference in the nature of the components resulting from the two types of evaluation. Both types of evaluation are based on probability distributions (C.2.3), and the uncertainty components resulting from either type are quantified by variances or standard deviations.*” – JCGM 100

For more information on the CIPM recommendation INC-1 (1980), go to **iso.org**. The text is in French but can be easily translated with tools like **Google Translate**.

Now that you have read the VIM and the GUM, you can understand that the use of uncertainty types (i.e. A & B) are to help you quickly determine how the data was evaluated.

If you continue to read the GUM, it will teach the difference between Type A and Type B uncertainty. See the excerpt below.

“*3.3.5 The estimated variance u2 characterizing an uncertainty component obtained from a Type A evaluation is calculated from series of repeated observations and is the familiar statistically estimated variance s2 (see 4.2). The estimated standard deviation (C.2.12, C.2.21, C.3.3) u, the positive square root of u2, is thus u = s and for convenience is sometimes called a Type A standard uncertainty. For an uncertainty component obtained from a Type B evaluation, the estimated variance u2 is evaluated using available knowledge (see 4.3), and the estimated standard deviation u is sometimes called a Type B standard uncertainty.*” – JCGM 100

From the excerpt above, you can determine two things;

• Type A uncertainty is calculated from a series of observations,

• Type B uncertainty is evaluated using available information.

Furthermore, the GUM provides you with information about the **probability distributions for each uncertainty type**.

“*Thus a Type A standard uncertainty is obtained from a probability density function (C.2.5) derived from an observed frequency distribution (C.2.18), while a Type B standard uncertainty is obtained from an assumed probability density function based on the degree of belief that an event will occur [often called subjective probability (C.2.1)]. Both approaches employ recognized interpretations of probability.*” – JCGM 100

Type A uncertainty is characterized by the observed frequency distribution which means that you should look at the histogram to find the correct probability distribution.

Following the Central Limit Theorem, the more samples that you collect, the more the data will begin to resemble a normal distribution. Here is a link to an **amazing video on the Central Limit Theorem**. I recommend that you watch it.

On the other hand, Type B uncertainty is characterized using an assumed probability distribution based on available information. Without the original data or a histogram, you are left to determine how the data is characterized based on your information sources.

Most of the time, you are not given much information. Therefore, people typically assume a rectangular distribution.

However, there are plenty of other ways for you to evaluate Type B uncertainty data that no one ever references; not even in the best guides to estimating uncertainty.

Today, I am going to cover everything that you need to know about Type A and Type B uncertainty. Look at the list below to see what is covered in this guide.

**1. What is Type A Uncertainty
2. Evaluation of Type A Uncertainty
3. Examples of Evaluating Type A Uncertainty
4. What is Type B Uncertainty
5. Evaluation of Type B Uncertainty
6. Examples of Evaluating Type B Uncertainty
7. Difference Between Type A and Type B Uncertainty
8. How to Choose Type A or Type B**

According to the Vocabulary in Metrology (VIM), Type A Uncertainty is the “evaluation of a component of measurement uncertainty by a statistical analysis of measured quantity values obtained under defined measurement conditions.”

In the **Guide to the Expression of Uncertainty in Measurement (GUM)**, Type A evaluation of uncertainty is defined as the method of evaluation of uncertainty by the statistical analysis of series of observations.

Essentially, Type A Uncertainty is data collected from a series of observations and evaluated using statistical methods associated with the analysis of variance (ANOVA).

So, if you collect repeated samples of similar measurement results and evaluate it by calculating the mean, standard deviation, and degrees of freedom, your uncertainty component would be classified as Type A uncertainty.

For most cases, the best way to evaluate Type A uncertainty data is by calculating the;

• Arithmetic Mean,

• Standard Deviation, and

• Degrees of Freedom

When performing a series of repeated measurements, you will want to know the average value of your sample set.

This is where the arithmetic mean equation can help you evaluate Type A uncertainty. You can use the value later to predict the expected value of future measurement results.

**Definition**

The central number of set of numbers that is calculated by adding quantities together and then dividing the total number of quantities.

**Equation**

**How to Calculate**

1. Add all the values together.

2. Count the number of values.

3. Divide step 1 by step 2.

When performing a series of repeated measurements, you will also want to know the average variance of your sample set.

Here, you will want to calculate the standard deviation. It is most common Type A evaluation used in uncertainty analysis.

So, if there were only one function to learn, this would be the one to focus your attention on.

**Definition**

A measure of the dispersion of a set of data from its mean (i.e. average).

**Equation**

**How to Calculate**

1. Subtract each value from the mean.

2. Square each value in step 1.

3. Add all of the values from step 2.

4. Count the number of values and Subtract it by 1.

5. Divide step 3 by step 4.

6. Calculate the Square Root of step 5.

After calculating the mean and standard deviation, you need to determine the degrees of freedom associated with your sample set.

It is an important value that most people neglect to calculate. Even most guides on measurement uncertainty forget to include it in their text. However, the GUM does not forget to mention it.

In fact, in section 4.2.6, the GUM recommends that you should **always include the degrees of freedom** when documenting Type A uncertainty evaluations.

I agree.

I always include the degrees of freedom when evaluating Type A data and in my uncertainty budgets.

You can also use it to estimate confidence intervals and coverage factors.

**Definition**

The number of values in the final calculation of a statistic that are free to vary.

**Equation**

**How to Calculate**

1. Count the number of values in the sample set.

2. Subtract the value in step 1 by 1.

To give you an example of evaluating Type A uncertainty data, I am going to show you two common scenarios people encounter when estimating measurement uncertainty.

• Single Repeatability Test, and

• Multiple Repeatability Tests

Imagine you are estimating uncertainty in measurement and need to obtain some Type A data. So, you perform a repeatability test and collect a series of repeated measurements.

Now that you have collected data, you need to evaluate it. Therefore, you calculate the mean, standard deviation, and the degrees of freedom.

Next, you add the standard deviation and degrees of freedom to your uncertainty budget for repeatability.

In this scenario, let’s imagine you are estimating measurement uncertainty for a measurement system that is critical to your laboratory. Try to think of a reference standard that you own.

It is so important that you perform a repeatability test for this system every month and document the results.

Your records have the mean, standard deviation, and degrees of freedom listed for each month.

With so much Type A data, you are probably wondering, “Which results do I include in my uncertainty budget?”

The answer is all of them; or, at least, the last twelve months.

To evaluate your Type A uncertainty data, you will want to use the **method of pooled variance**. It is the best way to combine or pool your standard deviations.

After performing this analysis, you will want to the pooled standard deviation to your uncertainty budget for repeatability.

According to the Vocabulary in Metrology (VIM), Type B Uncertainty is the “evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation of measurement uncertainty.”

In the Guide to the Expression of Uncertainty in Measurement (GUM), Type B evaluation of uncertainty is defined as the method of evaluation of uncertainty by means other than the statistical analysis of series of observations.

Essentially, Type B Uncertainty is data collected from anything other than an experiment performed by you.

Even if you can analyze the data statistically, it is not Type A data if you did not collect it from a series of observations.

Most of the Type B data that you will use to estimate uncertainty will come from;

• Calibration reports,

• Proficiency testing reports,

• Manufacturer’s manuals,

• Datasheets,

• Standard methods,

• Calibration procedures,

• Journal articles,

• Conference papers,

• White papers,

• Industry guides,

• Textbooks, and

• Other available information.

Since Type B Uncertainty can come from so many different sources, there are a lot ways that it can be evaluated.

This means that there is a lot of information to cover in this section.

Most of the time, people default to assigning a rectangular distribution to an uncertainty component and using a square root of three divisor to convert quantities to standard uncertainty.

If this describes how you evaluate uncertainty in measurement, go ahead and raise your hand.

The good news is that this will work for 90% of the uncertainty calculations that you will perform in your lifetime. However, there are many more realistic options available for you to use to evaluate Type B uncertainty.

It depends whether or not you want use them or not.

If you are interested, keep reading. I am going to cover the evaluation methods in the GUM that most measurement uncertainty guides tend to leave out.

In section 4.3.3 of the GUM, the guide gives recommendations for evaluating information published in manufacturer’s specifications and calibration reports.

“*4.3.3 If the estimate x _{i} is taken from a manufacturer’s specification, calibration certificate, handbook, or other source and its quoted uncertainty is stated to be a particular multiple of a standard deviation, the standard uncertainty u_{(xi)} is simply the quoted value divided by the multiplier, and the estimated variance u^{2}_{(xi)} is the square of that quotient.*”

Additionally, in section 4.3.4 of the GUM, the guide gives you more information for evaluating manufacture specifications.

“*4.3.4 The quoted uncertainty of x _{i} is not necessarily given as a multiple of a standard deviation as in 4.3.3. Instead, one may find it stated that the quoted uncertainty defines an interval having a 90, 95, or 99 percent level of confidence (see 6.2.2). Unless otherwise indicated, one may assume that a normal distribution (C.2.14) was used to calculate the quoted uncertainty, and recover the standard uncertainty of x_{i} by dividing the quoted uncertainty by the appropriate factor for the normal distribution. The factors corresponding to the above three levels of confidence are 1,64; 1,96; and 2,58 (see also Table G.1 in Annex G).*”

If the uncertainty is reported to a particular confidence interval (e.g. 95%), use the associated coverage factor to convert to standard uncertainty.

In the image below is an excerpt from the Fluke 5700A datasheet. You should notice that the specifications are stated for both 95% and 99% confidence intervals.

Therefore, to find standard uncertainty, simply divided published uncertainty by the coverage factor (k) that associated with the confidence interval given.

If the confidence level is not provided in the specifications (most of the time it is not provided), it is best to assume that it is given to a 95% confidence interval. Only assume a 99% confidence interval if it is stated.

**PRO TIP**: Next time your auditor suggests that you should evaluate manufacturer’s accuracy or uncertainty specifications with a rectangular distribution, please refer them to read sections 4.3.3 and 4.3.4 of the GUM.

In section 4.3.5 of the GUM, the guide tells you how to evaluate type B uncertainty when you believe that there is a 50% chance of occurrence. The guide recommends that you divide the interval by 1.48.

Therefore, you would use the following equation to convert to standard uncertainty.

“*4.3.5 Consider the case where, based on the available information, one can state that “there is a fifty-fifty chance that the value of the input quantity X_{i} lies in the interval a_{−} to a_{+}” (in other words, the probability that X_{i} lies within this interval is 0,5 or 50 percent). If it can be assumed that the distribution of possible values of X_{i} is approximately normal, then the best estimate x_{i} of X_{i} can be taken to be the midpoint of the interval. Further, if the half-width of the interval is denoted by a = (a_{+} − a_{−})/2, one can take u_{(xi)} = 1,48a, because for a normal distribution with expectation μ and standard deviation σ the interval μ ± σ /1,48 encompasses approximately 50 percent of the distribution.*”

If you are confused, do not worry. This is not a common occurrence.

I have never encountered a situation where I have had use this technique to evaluate type B uncertainty. Most likely, you will never use it either unless you are performing measurements that can only have two possible outcomes.

In section 4.3.6 of the GUM, the guide tells you how to evaluate type B uncertainty when you believe that there is approximately a 67% chance of occurrence. The guide recommends that you divide the interval by 1 because it is close to the conference interval covered by one standard deviation, 68.3%.

Therefore, you would use the following equation to convert to standard uncertainty.

“*4.3.6 Consider a case similar to that of 4.3.5 but where, based on the available information, one can state that “there is about a two out of three chance that the value of X_{i} lies in the interval a_{−} to a_{+}” (in other words, the probability that X_{i} lies within this interval is about 0,67). One can then reasonably take u_{(xi)} = a, because for a normal distribution with expectation μ and standard deviation σ the interval μ ± σ encompasses about 68,3 percent of the distribution.*”

Similar to the 50/50 chance of occurrence, this is not a common evaluation.

I have never encountered a situation where I have had use this technique to evaluate type B uncertainty. Most likely, you will never use it either.

In section 4.3.7 of the GUM, the guide tells you how to evaluate type B uncertainty when you believe that there is a 100% chance that the value will be between the upper and lower limit.

“*4.3.7 In other cases, it may be possible to estimate only bounds (upper and lower limits) for X _{i}, in particular, to state that “the probability that the value of Xi lies within the interval a− to a+ for all practical purposes is equal to one and the probability that X_{i} lies outside this interval is essentially zero”. If there is no specific knowledge about the possible values of X_{i} within the interval, one can only assume that it is equally probable for X_{i} to lie anywhere within it (a uniform or rectangular distribution of possible values — see 4.4.5 and Figure 2 a). Then x_{i}, the expectation or expected value of X_{i}, is the midpoint of the interval, x_{i} = (a_{−} + a_{+})/2, with associated variance…*”

In this scenario, the guide recommends that you assign a rectangular distribution and divide the interval by the square-root of 12 or the square root of 3.

If the value of the mean is expected to be the midpoint of the interval, divide by the square root of 12.

If the difference between of the interval limits is equivalent to 2a, divide by the square root of 3.

If you are not sure how to evaluate the interval, use the second equation and divide by the square root of 3. It is more likely to be the correct evaluation method.

Every once in a while, you may encounter specifications or data that is not symmetrically distributed. This means that the limits are not equal for both the upper and lower limits.

“*4.3.8 In 4.3.7, the upper and lower bounds a_{+} and a_{−} for the input quantity X_{i} may not be symmetric with respect to its best estimate x_{i}; more specifically, if the lower bound is written as a_{−} = x_{i} − b_{−} and the upper bound as a_{+} = x_{i} − b_{+}, then b_{−} ≠ b_{+}. Since in this case x_{i} (assumed to be the expectation of X_{i}) is not at the centre of the interval a_{−} to a_{+}, the probability distribution of X_{i} cannot be uniform throughout the interval. However, there may not be enough information available to choose an appropriate distribution; different models will lead to different expressions for the variance. In the absence of such information, the simplest approximation is…*”

For example, the upper limit could be a greater distance from nominal than the lower limit. Look at the image below to see Grade 2 specifications for gage block in accordance with the GGG specification.

If you notice, the upper and lower limits are not equal in magnitude. Therefore, they are asymmetrical.

When you encounter this type of scenario, the GUM recommends the following instructions to evaluate Type B uncertainty;

If your limits are asymmetrical, subtract the upper limit by the lower limit and divide the result by the square root of 12.

Now, if you know a thing or two about statistics, then you know that a rectangular distribution is used when all chances of occurrence are equally probable.

However, you probably did not know that you could also use a trapezoidal distribution.

If you did, great. If not, read section 4.3.9 of the GUM.

“*4.3.9 In 4.3.7, because there was no specific knowledge about the possible values of Xi within its estimated bounds a− to a+, one could only assume that it was equally probable for X _{i} to take any value within those bounds, with zero probability of being outside them. Such step function discontinuities in a probability distribution are often unphysical. In many cases, it is more realistic to expect that values near the bounds are less likely than those near the midpoint. It is then reasonable to replace the symmetric rectangular distribution with a symmetric trapezoidal distribution having equal sloping sides (an isosceles trapezoid), a base of width a_{+} − a_{−} = 2a, and a top of width 2aβ, where 0 < β < 1. As β → 1, this trapezoidal distribution approaches the rectangular distribution of 4.3.7, while for β = 0, it is a triangular distribution [see 4.4.6 and Figure 2 b)]. Assuming such a trapezoidal distribution for X_{i}, one finds that the expectation of X_{i} is x_{i} = (a_{−} + a_{+})/2 and its associated variance is…*”

The GUM explains that a rectangular distribution is not always realistic. If you expect values to occur closer to the midpoint and less likely at the limit, then you should use a trapezoidal distribution.

Furthermore, it even provides some additional insight to recommend the use of a triangular distribution.

I think this evaluation of Type B uncertainty is very interesting. It is realistic and practical for most applications where people typically use a rectangular distribution.

However, I do not see it used very often and don’t expect to see many people switching over from rectangular distributions anytime soon.

For those who do, you may enjoy the benefits of a smaller estimate of uncertainty and the additional questioning by your auditors. So, make sure to refer to this section of the GUM to defend using it in your uncertainty budgets.

Another good resource is **this paper by Howard Castrup**. At the bottom of page 15, Howard gives you a good alternative equation for the trapezoidal distribution.

In uncertainty analysis, there are two common problems; not considering enough sources of uncertainty in your uncertainty budget and double-counting uncertainty components.

Section 4.3.10 of the GUM warns you of double-counting uncertainty to prevent overstated estimates of measurement uncertainty.

“*4.3.10 It is important not to “double-count” uncertainty components. If a component of uncertainty arising from a particular effect is obtained from a Type B evaluation, it should be included as an independent component of uncertainty in the calculation of the combined standard uncertainty of the measurement result only to the extent that the effect does not contribute to the observed variability of the observations. This is because the uncertainty due to that portion of the effect that contributes to the observed variability is already included in the component of uncertainty obtained from the statistical analysis of the observations.*”

I see double-counting uncertainty components a lot in calibration uncertainty estimates.

For example, a laboratory considers an “ideal” unit-under-test (i.e. UUT) for UUT resolution in their CMC Uncertainty analysis, then includes the actual UUT resolution when calculating calibration uncertainty.

That’s double-counting; and, it happens all of the time.

Even auditors are bad about enticing laboratories to double-count uncertainty components in the very scenario given in the example above.

In fact, I spoke with an assessor this week who wanted to know why the UUT resolution wasn’t included in the CMC Uncertainty calculation. I had to happily refer him to read **section 5.4 of the ILAC P14:01/2013**.

Another common example of double-counting is when a laboratory includes uncertainty components that would typically be included in the Type A uncertainty components; repeatability and repeatability.

The bad news is it can be difficult to determine if an uncertainty component is already accounted for in another uncertainty component. This means that it is nearly impossible to prevent double-counting uncertainty.

Evaluating data from your calibration reports is pretty easy as long as you are getting ISO/IEC 17025 accredited calibrations.

Most accredited calibrations report the measurement result and the associated measurement uncertainty. Additionally, the report will tell you the confidence level the estimated uncertainty; typically, 95% where k=2.

Therefore, all you need to do is divide the reported uncertainty by the expansion factor (k).

Using the information shown in the calibration report below and the equation given above, you should be able to convert the expanded uncertainty to standard uncertainty.

Simply divide the expanded uncertainty (U) by the coverage factor (k). Your result will be the standard uncertainty.

Evaluating data from manufacturer’s specifications is just as easy as evaluating the data from your calibration reports.

Typically, manufacturer’s specifications can be found in manufacturer manuals, datasheets, catalogs, or other marketing materials.

However, not all manufacturers do their due diligence when publishing specifications. So, you may have to make some assumptions.

Most credible manufacturers publish specifications with an associated confidence interval. In the image below, you will see that Fluke has published specifications for both 95% and 99% confidence intervals.

For this example, let’s focus on the 95% specification to evaluate a 10V signal using the 11V range.

Looking at the 1 Year absolute uncertainty specification for the 11 volt range, the uncertainty for 10 volts is approximately 38 micro-volts.

Using the information shown in the manufacturer’s specification, use the equation given below to convert the expanded uncertainty to standard uncertainty.

Afterward, your evaluation of Type B uncertainty should be approximately 19.4 micro-volts.

Now, you are probably thinking, “What if the manufacture specifications don’t give a confidence interval?”

The answer is, **assume it is stated to a 95% confidence interval** and evaluate it similar to the example given above. Feel free to use the values 2 or 1.96 for the coverage factor, k.

When evaluating Type B uncertainty, you are not always going to have the convenience of using your own data.

Most laboratories do not have the time or resources required to test every factor that contributes to uncertainty in measurement. Therefore, you are going to use data from other laboratories that have already done the work for you.

The biggest challenge is finding the data! You must put some time and effort into conducting research. To make life easier, I have already created a **list of 15 places you can find sources of uncertainty**.

Once you find the data and deem it applicable for your measurement process, you can evaluate it for your uncertainty analysis.

Now, you can evaluate Type B uncertainty data in many ways. However, I will focus on the situation that you are going to encounter 90% of the time.

Typically, you are going to find information in a guide, conference paper, or journal article that gives you data with no background information about it.

Therefore, you are most likely to characterize the data with a rectangular distribution and use the following equation to evaluate the uncertainty component.

For example, imagine that you are estimating uncertainty for measuring voltage with a digital Multimeter. You are performing research and stumble upon a paper published by Keysight Technologies that has really good information that is relatable to the measurement process you are estimating uncertainty for.

So, you decide to include some of the information in your uncertainty budget.

The image below is an excerpt from a paper on **System Cabling Errors and DC Voltage Measurement Errors in Digital Multimeters** published by Keysight Technologies. It contains information on Thermal EMF errors that you want to include in your uncertainty budget.

The table in the image has some great information to help you quantify thermal EMF errors, but provides very little information on the origin of the data. Therefore, it would be best to assume that the data has a rectangular distribution.

For a copper-to-copper junction with a temperature change of 1°C, your thermal EMF error should be approximately 0.3 micro-volts. To convert your uncertainty component to standard uncertainty, you would divide the uncertainty component by the square-root of three.

On the other hand, you may find data in a guide, conference paper, or journal article that is normally distributed or has been already converted to standard uncertainty.

**Don’t assume all Type B data is rectangular, you will overstate your uncertainty estimates. Look for clues to help you find the right method to evaluate it.**

For example, imagine that you are performing research and stumble upon a paper published in the **NIST Journal of Research**. The study you found has information that is relatable to the measurement process you are estimating uncertainty for.

So, you decide to include some of the information in your uncertainty budget.

The image below is an excerpt from an article on **Uncertainty and Dimensional Calibrations** by Ted Doiron published in the NIST Journal of Research. It contains data for the elastic deformation of gage blocks calibrated by mechanical comparison that you want to include in your uncertainty budget.

Notice that the paper states that the data is reported as standard uncertainty where k=1.

Assuming that the data has a normal distribution and a coverage factor of one, use the equation below to evaluate Type B uncertainty.

Therefore, your evaluation of Type B uncertainty should be approximately 2 micro-meters since your coverage factor (k) is one.

There is a lot of misinformation on type A and type B uncertainty.

The VIM definitions are the most accurate. Type A uncertainty is evaluated using statistical means. Type B uncertainty is evaluated using other than statistical means.

**It is all evaluated by statistical methods**. Therefore, the difference is how the data is collected, not how it is evaluated.

Type A uncertainty is collected from a series of observations. Type B data is collected from other sources.

Although Type B uncertainty found in publications may have been collected from a series of observations, it wasn’t collected by you or your laboratory personnel.

Therefore, you are not sure that the data was collected from a series of observations. Furthermore, you do not know how the experiment was conducted.

Experimental results can be manipulated, especially when performed by a group who stands to benefit from the results (e.g. manufacturer, sponsored agency, etc.).

Over the years, many **researchers and laboratories have been caught manipulating experiments** to achieve results that benefit themselves or their mission. So, you need to be careful.

The image below is from phdcomics.com. It was shown to me in grad school when covering the topic of ethics in research. It depicts the realistic manipulation of the scientific method.

Many people have a hard time trying to decide whether their data is a Type A or Type B uncertainty.

However, it doesn’t have to be a difficult process. In fact, I am going to show you a simple two-step process that will help you choose the correct uncertainty type every time.

All you have a to do is ask yourself these two questions;

**Question 1**: Did you collect the data yourself via testing and experimentation?

• If yes, go to question 2.

• If no, choose Type B.

**Question 2**: Is your data older than 1 year?

• If yes, choose Type B

• If no, choose Type A

I even made you a handy flowchart to help you decide whether your data is Type A or Type B uncertainty.

Think about it. If you collected the data yourself, then you are going to evaluate it statistically. Therefore, it is Type A Data.

However, if you performed a repeatability experiment 5 years ago and still want to include it your uncertainty budget, then it is Type B data.

The age of the data is important. Hence, the reason for question two. You need to routinely update your Type A uncertainty data.

If it is older than a year, then it is most likely Type B data and you should collect more data soon.

Now, there are some exceptions. I have read some repeatability procedures over the years that have recommended that two years’ worth of data should be kept on record at all times.

However, the procedure required that new data should be collected each month which means that the test records included 24 independent sampling events. So, new data was constantly being collected and added to the repeatability records.

In this case, I would consider it Type A uncertainty data.

Don’t stress about picking an uncertainty type, use the two questions listed above and your best judgement. It will help you make the right decision.

Type A uncertainty and Type B uncertainty are two classifications commonly used in uncertainty analysis. Typically used for informational purposes only, they let others know how the data is collected and evaluated.

This guide has covered everything that you need to know about Type A and B uncertainty. It should help you distinguish the difference between the two uncertainty types, so you can select the appropriate method of evaluation for your uncertainty analysis.

So, use the information and give some of these evaluation methods a try. They should help you improve your ability to calculate uncertainty.

Now, leave a comment below and tell me how you choose Type A and Type B uncertainty.

The post Type A and Type B Uncertainty: Evaluating Uncertainty Components appeared first on isobudgets.

]]>The post How to Create a Scope of Accreditation for ISO/IEC 17025 Laboratories appeared first on isobudgets.

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A laboratory’s scope of accreditation is a key element of ISO/IEC 17025 accreditation and a vital asset to your customers. It lists all of the activities that your laboratory is accredited perform.

However, many laboratories forget to consider its importance when getting accredited or reaccredited. They just rush to develop a scope of their capabilities and submit it to their accreditation body.

Instead, you need to make sure to develop a scope of accreditation that is functional for both your laboratory and customers.

It is a great marketing tool that make an impact your business.

When a customer looks at your scope, they want to know one or more of the following;

1. Is your laboratory ISO/IEC 17025 accredited,

2. Can you calibrate/test “x,”

3. What is your measurement uncertainty. and(or)

4. What methods are you using to calibrate/test “x?”

If your scope of accreditation does not answer these questions, you may have a problem that could be driving away potential customers.

In this guide, I am going to show you a simple five step process that will help you develop an amazing scope of accreditation for your laboratory. Plus, I have included plenty of important links to valuable resources that will help you meet ISO/IEC 17025 requirements.

So, if you are looking to create or update your scope of accreditation, let’s get started.

When I took over a calibration program for an accredited laboratory, I remember reviewing and updating the scope of accreditation for the first time.

It wasn’t difficult. Most the work had already been done for me.

However, when I needed to add new capabilities, I always had a tough time figuring out the right terminology and format to use.

So, I read the policies, requirements, and guides published by my accreditation body. Yet, I still struggled to get it right. Most of the guides were great for knowing the rules, but did not provide exact match examples that met my needs.

Therefore, I started to look at other laboratories’ scopes of accreditation for inspiration.

It was great! I was able to review several laboratory scopes that were similar to mine and replicate the format that I thought would fit my laboratory’s needs.

But meeting the needs of my laboratory was not enough. I had to learn the hard way that our scope of accreditation was not helping our current and prospective customers.

At the time, we were receiving a ton of phone calls each week with questions about our calibration capabilities. We were helping customers by answering their questions, but we were wasting our valuable time and not pushing out quotes fast enough (because we were constantly on the phone).

Now, most people would recommend that we hire more personnel to handle the volume of work. However, I disagree.

We did not have a personnel problem, we had a communication problem. We were not answering our customers’ questions with our scope of accreditation. Therefore, they had to call us to get answers to their questions.

Luckily, they were interested enough in our services to pick up the phone and call!

How many potential customers do you think we were losing because our scope did not answer their questions?

I am not certain; but, I bet it was a lot!

I am confident that the majority of potential customers looked at our scope, did not find the answer they were looking for, and moved on to look at other laboratories’ scopes of accreditation.

Bummer! Another customer lost.

Then, it dawned on me. I needed to design and format my scope to meet my customers’ needs. So, we spent time documenting customer questions and identifying the questions that we the most repetitive.

With this information, I decided to change the terminology used in our scope of accreditation to meet our customers’ needs (i.e. answering questions).

As a result, we were able to reduce the amount of phone calls related to questions and respond quicker to customer inquiries for quotes.

The content of our telephone conversations changed from “Can you calibrate X” to “Can I get a quote for calibration of X.” Furthermore, we noticed a significant bump in the number of requests for quotes (both via telephone and email).

With this in mind, what are potential customers seeing when they look at your scope of accreditation; Do they find what they are looking for or are they moving on to another laboratory’s scope of accreditation?

Whether you are creating your first scope of accreditation or considering the need to update your current scope, I hope that you find this guide helpful.

In this guide, you will learn;

1. What is a Scope of Accreditation

2. Testing Labs vs Calibration Labs

3. Guides For Creating A Scope of Accreditation

4. How to Create a Scope of Accreditation (Step-by-Step)

5. Scope of Accreditation Examples

According to the ILAC G18, a scope of accreditation is the official and detailed statement of activities for which the laboratory is accredited.

Basically, it is an official list of tests and/or calibrations that your laboratory is accredited to perform.

Look at the image below. It is an excerpt of Fluke’s Everett Service Center’s scope of accreditation. If you notice, the scope of accreditation lists the laboratory’s;

• Name,

• Location,

• Technical or Quality Manager,

• Contact information,

• Certificate number,

• Expiration date, and

• List of accredited activities.

Most laboratories use their scope of accreditation as a marketing tool to showcase their capabilities to current and prospective customers. If you plan to do the same, it is important to ensure that your scope is accurate and up to date.

To provide your customers accredited calibration and test results, the activities must be listed in your scope. If not, you must report the results as non-accredited regardless of capability.

Every ISO/IEC 17025 accredited laboratory has a scope of accreditation. However, there are slight differences in the presentation of information depending on the type of laboratory.

The scope of accreditation for a testing laboratory is not formatted the same way as a calibration laboratory.

According to the ILAC G18, the scope of accreditation must include:

• **Testing Laboratories** – The tests or types of tests performed and materials or products tested and, where appropriate, the methods used.

• **Calibration Laboratories** – the calibrations, including the types of measurements performed, the Calibration and Measurement Capability (CMC) or equivalent.

Look at the image below. You will see a table from the ILAC G18 that lists the typical information included in the scope of accreditation based on laboratory type.

Calibration laboratory scopes typically list the measurement function, range, and CMC Uncertainty for each activity that the lab is accredited to perform. This makes it easy to find and compare laboratory measurement capability and quality.

Testing laboratory scopes typically list only the test activities and methods which they are accredited to perform. Only few testing scopes contain quantitative information about capability and uncertainty.

As a result, the majority of testing laboratory scopes of accreditation do not include statements or estimates of measurement uncertainty. This makes it difficult for customers to compare the capability and quality of testing laboratories.

In an industry of buyer beware, the scope of accreditation should allow customers to confidently find and select laboratories that will meet their requirements; and, provide customers the reassurance that they are conducting business with a laboratory that is ISO/IEC 17025 accredited.

If you are going to create or update your laboratory scope of accreditation, you should make sure that you are meeting ISO/IEC 17025 requirements. Luckily, there are plenty of guides available to help you.

In this section, you will find a list of guides that will help you develop a scope of accreditation.

The first guide that you should read is the ILAC G18. You can access it using the link provided below.

ILAC G18:04/2010 (under revision)

Afterward, you should read your accreditation body’s documents and guides. They will help you meet their specific requirements.

Find your accreditation body from the list below and download the guide relevant to your laboratory type.

**A2LA**

• G117 – Guidance on Scopes of Accreditation for Testing Laboratories Registered with the US Consumer Product Safety Commission (CPSC)

• G118 – Guidance for Defining the Scope of Accreditation for Calibration Laboratories

**ANAB**

• PR 2350, Preparing a Draft Scope of Accreditation for ISO/IEC 17025 Testing Laboratories

• PR 2351, Preparing a Draft Scope of Accreditation for ISO/IEC 17025 Calibration Laboratories

**PJLA**

• Policy on Calibration Scopes of Accreditation PL-4

• Work Instructions for Setting Up Scope of Accreditation Testing WI-8

**IAS**

• Policy on the Expansion of Scope

**NVLAP**

• NIST Handbook 150:2016, NVLAP Procedures and General Requirements (PDF)

Now, that you have some good background information on the scope of accreditation, it is time to get to work and start making one for your laboratory.

All you need to do is follow the five step process listed below to develop your laboratory scope;

1. Contact your Accreditation Body and Get the Draft Template.

2. Read your Accreditation Body’s policies and requirements.

3. Research other laboratory scopes with similar capabilities.

4. Enter your data into the Scope of Accreditation template.

5. Submit it to your accreditation body with your application.

Using this simple five-step process will help you make an amazing laboratory scope for ISO/IEC 17025 accreditation that will benefit both your laboratory and your customers.

If you are ready to get started, just keep reading to learn more about completing each step of the process.

To create a scope of accreditation, you will need a template. If you have selected an accreditation body and are in the application or reaccreditation process, contact your accreditation body and request a template for your Draft Scope of Accreditation.

The easiest way to do this is send an email to your accreditation officer requesting the template. Typically, they will send it to you within 24 hours. However, if you do not receive the template within 24 hours, follow up with a telephone call.

Before you begin completing your draft scope of accreditation, read your accreditation body’s policies and requirements. Each accreditation body has their own preferences for how they like scope to be designed. It will help you create your scope using the correct terminology and format.

Additionally, make sure to read your accreditation body’s guides. They will provide you with insight and guidance to prevent you from making mistakes.

Accessing your accreditation body’s documents is easy. You can download them directly from your accreditation body’s website.

To help you out, I have provided a list of accreditation requirements documents below. Find your accreditation body in the list below and click on the link to access the document(s) relevant to your laboratory.

**A2LA**

• R101 – General Requirements: Accreditation of ISO/IEC 17025 Laboratories

**ANAB**

• MA 2100, Accreditation Manual for Laboratory-Related Activities

**PJLA**

• Accreditation Procedure – General – SOP-1 General

**IAS**

• Accreditation Criteria for Calibration Laboratories (AC204)

• Accreditation Criteria for Testing Laboratories (AC89)

**NVLAP**

• NIST Handbook 150:2016, NVLAP Procedures and General Requirements (PDF)

A great trick to developing your scope of accreditation is to get inspiration from other accredited laboratories. Just look at their scope of accreditation to see how they are listing their activities.

The best part is the information is available online and easy to find. Just search your accreditation body’s search directory. You should be able to find plenty of examples from other laboratories that perform similar activities.

However, do not just look at one scope of accreditation. Try reviewing at least three to five scopes to see how other laboratories list their activities. If you have time, look at ten.

Pay attention to the terminology they use and how they present information. Find examples that you like and replicate it in your scope of accreditation.

While this may seem like a lot of extra work. I promise that it will save you time in the long run. When you are not sure what to do, you can spend a lot of time thinking about how to present the information. Not good!

Always remember that the scope of accreditation should be targeted toward your customers. So, make sure that it answers their questions about your laboratory’s capability.

**PRO-TIP:** Think of words and copy that will resonate best with your customers. After all, your scope of accreditation is a marketing document. Make sure it designed help customer quickly find what they are looking for!

To search your accreditation body’s directory, use the links provided below.

• **A2LA Directory of Accredited Organizations**

• **NVLAP Directory of Accredited Laboratories**

• **ANAB Directory of Accredited Organizations**

• **PJLA Listing of Accredited Labs**

• **IAS Directory of Accredited Organizations**

Now that you have a template and access to helpful information, it is time take your data and add it to your scope of accreditation.

Be sure to focus on one discipline or measurement function at a time. If you do not, it will be easy to get disorganized and make mistakes. This is especially true if you are developing a large scope with a lot of activities.

With all of the work and stress that you will have during an ISO/IEC 17025 audit, the last thing you want to do is stay at work late fixing mistakes in your scope of accreditation.

The worst mistake that you can make is to forget to add a measurement function entirely. Unless you want to pay for an additional audit, you will have to wait until next time to add new activities to your scope.

So, make sure to pay attention and focus on one measurement function or parameter at a time.

Below, you will find guidance to help you enter data into your scope of accreditation. Read and use the information to develop your laboratory scope.

**a. Measurement Function / Parameter / Equipment**

This column defines the measurement functions and disciplines that you are accredited to perform.

You can list functions such as;

• Length,

• Voltage,

• Pressure, and/or

• Temperature.

Or, you can use copy that specifically narrows down your capability to a niche, such as;

• Micrometers.

• Multimeters,

• Pressure Gauges, and/or

• Liquid-in-Glass Thermometers

As you can see, you have some flexibility. However, you will want to check you accreditation body’s requirements to see what type of terminology they will allow.

If you are having trouble deciding, choose the option that will best guide your customer to requesting a quote for calibration services.

**b. Measurement Range**

This column defines the range of your measurement function.

Try to think of the minimum and maximum values of you measurement capability. Then, add this information to your scope.

Make sure that you read your accreditation body’s policies, requirements, and guides. Some accreditation bodies will not allow you to use zero (i.e. 0) in your measurement range.

Instead, they may prefer that you use;

• the minimum resolution of the measurement range,

• the phrase “up to” the max value of the range, or

• the minimum value that you would test, measure, etc.

**c. CMC Uncertainty**

This column is used to define the Calibration and Measurement Capability of your measurement function at a specific measurement range.

Therefore, you will need to list your estimates of uncertainty in measurement for each measurement range included in your scope of accreditation.

When listing your measurement uncertainty, follow the guidance of the ILAC P-14 policy and your accreditation body. Express your CMC Uncertainty as;

• A single value,

• A range of values,

• An equation (typically a linear equation),

• A matrix of values, or

• A graph

**d. Comments / Notes / Remarks**

This column is used to provide additional information relevant to your measurement function, range, and CMC Uncertainty.

Some accreditation bodies may use more than one column (e.g. ANAB, IAS, etc) for comments, notes, remarks, etc.

So make sure to follow your accreditation body’s polices and guides. Also, look at other laboratories’ scope of accreditation to find what information they are providing and how it is expressed.

Information typically provided in these sections may include;

• The method,

• The equipment used,

• The location, and/or

• important notes and comments.

Now that you have completed your draft scope of accreditation. Save the file as a Microsoft Word document and email a copy to your accreditation officer.

They will review your scope of accreditation for errors and submit it to your assessors to further review.

If the assessors approve your scope, it will be submitted to the accreditation board for final review.

Once approved, your scope of accreditation will become an official document.

Your accreditation officer will send you a digital and hardcopy version of your scope. Additionally, it will be posted on the accreditation body website so customers can access it via the online search directory.

In this section, you will see some examples of scopes of accreditation for various accreditation bodies in North America.

Use this information to see how each accreditation body formats their laboratories’ scopes. However, you should still make sure to use your accreditation body’s search directory to look at scopes of accreditation for laboratories that are similar to your laboratory.

**A2LA Accredited Calibration Laboratory**

**A2LA Accredited Testing Laboratory**

**ANAB Accredited Calibration Laboratory**

**ANAB Accredited Testing Laboratory**

**NVLAP Accredited Calibration Laboratory**

**NVLAP Accredited Testing Laboratory**

**PJLA Accredited Calibration Laboratory**

**PJLA Accredited Testing Laboratory**

**IAS Accredited Calibration Laboratory**

**IAS Accredited Testing Laboratory**

Developing a scope of accreditation is a key element required for ISO/IEC 17025 accreditation. It lists all of the activities that your laboratory will be accredited to perform.

However, it is also a key element to your business. It is the document that a majority of your customers (requiring accredited testing/calibration services) are going to refer to before doing business with you.

Therefore, it is important that you dedicate some time and effort to developing a scope of accreditation that is functional for both your laboratory and your customers.

Neglecting to do so may negatively affect your business’s reputation and annual revenue.

In this guide, I have given you a simple five-step process to follow when developing your laboratory scope for ISO/IEC 17025 accreditation. Additionally, I have provided you with a ton links to access helpful guides that you can use to ensure that you are meeting requirements.

Whether you are getting accredited for the first time or preparing for reaccreditation, use the information in this guide to develop you scope of accreditation. I promise that it help you create a better scope for your laboratory.

So, give it try and leave a comment below. Let me know your questions, tips, and feedback.

The post How to Create a Scope of Accreditation for ISO/IEC 17025 Laboratories appeared first on isobudgets.

]]>The post How to Create An Uncertainty Budget in Excel appeared first on isobudgets.

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Estimating uncertainty can be a difficult task, especially if you are a beginner. Tools like an uncertainty budget or calculator can really make a big difference.

However, **software to calculate uncertainty** is typically outdated, expensive, and difficult to learn.

Many people have problems because they do not know what to do or where to begin.

Luckily, there is an easier way!

You don’t need expensive software to estimate uncertainty. All you need is a program named Microsoft Excel.

In fact, you probably have Microsoft Office on your computer. Therefore, the cost for you to begin to calculate uncertainty with Excel is zero.

In this guide, I am going to show you how to create an uncertainty budget in Excel so you can estimate uncertainty in measurement for ISO/IEC 17025 accreditation.

So, keep reading. I am going to show you how to;

1. Create an uncertainty budget in Excel,

2. Add functions to automatically calculate uncertainty, and

3. Validate that your uncertainty calculator functions correctly.

When I first began to estimate uncertainty, I spent months buying and trying all kinds of software that was supposed to help me calculate uncertainty.

It was awful!

I wasted many hours searching for software, buying it, downloading it, installing it, and testing it only to find out that it didn’t calculate uncertainty like I thought it would.

Finally, I stumbled across the **Hewlett Packard’s UnCal 3.2**. It was the best program (at the time) that helped me estimate uncertainty. Best of all, it was free!

I used it to prepare for an ISO/IEC 17025 accreditation audit where I had to estimate uncertainty for the laboratory’s entire 25-page scope of accreditation.

At the time, I inherited a metrology program that had based all of it’s uncertainty statements on manufacturer’s specifications.

Most of the scope of accreditation was not supported with any uncertainty budgets. The few parameters that did have uncertainty budgets were awful and didn’t make much sense.

Every measurement parameter needed an uncertainty budget and I had to start from scratch!

The worst part was, I had three months to get it done and I didn’t have a clue what I was doing.

Needless to say, I got hit hard during the assessment. Most of deficiencies were related to missing uncertainty budgets.

Nearly 70% of my scope of accreditation was marked “TBD.”

It was embarrassing!

As a result, I spent the next 6 months creating uncertainty budgets and living off of scope extensions. It was not fun.

Luckily, A2LA agreed to work with me throughout the process while I created uncertainty budgets for my entire scope of accreditation.

After spending 9 months of my life calculating uncertainty, here is what I learned;

• I learned a lot about estimating uncertainty,

• I learned a lot about my calibration laboratory,

• I hated measurement uncertainty software, and

• I learned Microsoft Excel was great for calculating uncertainty.

Since then, I have used Microsoft Excel (almost exclusively) to create uncertainty budgets for estimating uncertainty.

So, if you are interested in using Excel to calculate uncertainty in measurement, let me show you how to create a powerful uncertainty budget calculator.

According the **Vocabulary in Metrology (VIM)**, an uncertainty budget is a statement of a measurement uncertainty, and of their calculation and combination.

Essentially, it is a document that describes how you estimated uncertainty in measurement including the components and calculations.

For a better understanding, read the note below the definition. It states that an uncertainty budget should include the following information;

1. Measurement model

2. Estimates,

3. Uncertainties for quantities in the measurement model,

4. Covariances,

5. Probability distributions,

6. Degrees of freedom,

7. Type of Evaluation (i.e. Uncertainty Type), and

8. Coverage factor

Following the list above will help you create an uncertainty budget. However, I recommend that you include more information.

Take a look at section 7.1.4 of **The Guide to the Expression of Uncertainty in Measurement (GUM)**. It offers some great advice about creating uncertainty budgets. The last phrase is my favorite!

“

*a) describe clearly the methods used to calculate the measurement result and its uncertainty from the experimental observations and input data;*

*b) list all uncertainty components and document fully how they were evaluated;*

*c) present the data analysis in such a way that each of its important steps can be readily followed and the calculation of the reported result can be independently repeated if necessary;*

*d) give all corrections and constants used in the analysis and their sources.*

*A test of the foregoing list is to ask oneself “Have I provided enough information in a sufficiently clear manner that my result can be updated in the future if new information or data become available?”*

Therefore, to create a great uncertainty budget, make sure that you include enough information to repeat the process in the future.

I recommend that you include as much information as you can in your uncertainty budgets. You can always remove information that is useless or unnecessary later.

It’s more difficult to add important information after the analysis has been completed. Proportionally, the more time that elapses since the analysis, the more difficult it will become to recall how you estimated measurement uncertainty.

Take it from me. It is rather embarrassing when an assessor asks you to explain your uncertainty analysis and you cannot remember how you achieved the results.

Leaving out important details and information about your uncertainty calculations is only setting yourself up for failure.

So, make sure to provide plenty of information in your uncertainty budgets and update them routinely (e.g. every 12 to 24 months) to recall how you estimated uncertainty.

If you need help, I have included a section in this guide that will show you what factors I include in my uncertainty budgets.

Uncertainty budgets are important because they provide detailed information for how you estimate uncertainty.

Additionally, uncertainty budgets are important if you want your laboratory to be ISO/IEC 17025 accredited.

As an accredited laboratory, you are required to estimate uncertainty for the test and measurement functions your organization will be accredited to perform.

An uncertainty budget is the tool that you will use to estimate measurement uncertainty to support your scope of accreditation. Without it, you will have a difficult time getting accredited.

Therefore, you need an uncertainty budget. It will help you convey to others exactly how you estimated uncertainty.

If you want to make the process easier, you will want to make sure that your uncertainty budget can function as an uncertainty calculator. It will save you a lot time that can be better spent elsewhere.

To calculate uncertainty effectively, you should consider including the following elements in your uncertainty budgets.

1. Definition of Measurand

2. Uncertainty Source or Component,

3. Sensitivity Coefficient,

4. Uncertainty Value,

5. Unit of Measure,

6. Uncertainty Type

7. Probability Distribution,

8. Divisor,

9. Standard Uncertainty,

10. Degrees of Freedom,

11. Significance or Influence on Total Combined Uncertainty,

12. Combined Uncertainty,

13. Total Effective Degrees of Freedom,

14. Coverage Factor,

15. Expanded Uncertainty, and

16. Notes, References, and Comments.

I know that this may seem like a lot of information; but, it is important for explaining how you estimated uncertainty. Plus, you can use some of the additional information to help you reduce measurement uncertainty.

In the example below, you will see how I typically include these elements into my uncertainty budgets.

**DISCLAIMER:** The uncertainty budget examples shown in this guide are for reference only and do not represent an actual measurement uncertainty analysis for the identified item.

While there are several formats that can be used, most people tend to use a table format to demonstrate how they calculate uncertainty.

In fact, I prefer to use a table format to present the information in a clean and simple way that makes my analyses easy to read and understand.

Look at the image below to see how I format my uncertainty budgets.

If you notice, I use rows to list each uncertainty contributor and columns to provide important details about each contributor. This makes it easy to keep an uncertainty budget organized and consistent.

Additionally, I prefer to use lines to only separate important information. This minimizes distractions, eye strain, and reduces the amount of ink required for printing.

With a clean and simple format (like the example above), you can make your uncertainty budgets easy to read and understand how uncertainty is calculated. Additionally, a minimalist design will keep your file sizes small and reduce your printing costs.

However, I have seen amazing uncertainty budgets that use borders and colors in their design. The format is entirely up to you. Just make sure that you can quickly read and understand the information when needed. That’s what is really important.

Creating an uncertainty budget is actually pretty simple if you are using Microsoft Excel. However, most people seem to have trouble using Excel’s functions.

If you are not familiar with Excel, adding formulas and functions can seem like an overwhelming task.

Luckily for you, I have outlined the process below with step by step instructions. Follow them and you can create a fully functional uncertainty calculator in less than 20 minutes.

After creating your uncertainty budget, you should save the file as a template that you can use each time you need to calculate uncertainty. This will ensure that your process is repeatable and prevent you from making mistakes and miscalculations.

If you are ready to create an uncertainty budget, let’s begin.

To create an uncertainty budget, get started by opening Microsoft Excel and creating a ‘New’ workbook.

When you first open the Excel program, you should see a screen that looks like this.

There will be several options to choose from, but you simply want to start with a blank workbook.

Select “Blank Workbook” to open a new spreadsheet like in the image below.

This is a great time to create a name and title for your uncertainty budget.

I recommend that you use this opportunity to define your measurement function or test method.

For example, I always use the first four rows to define;

• Measurement Function,

• Description of the equipment or method used.

• Measurement Range, and

• The Measurement Value

To see how I define the measurement function, look at the image below.

Now, before you do anything else, save your file. Use a unique file name that will help you identify your uncertainty budget later on. I recommend keeping it simple and naming your file, “uncertainty-budget-template.xlsx.”

You will not understand how important this step is until you need to find your file again.

It is really frustrating when you are not able to find your uncertainty budgets during an ISO/IEC 17025 audit.

To take it a step further, I recommend that you create a unique file architecture system for your computers and servers. This will save you plenty of headaches over the course of your lifetime.

In this step, create a table that you will use to perform uncertainty calculations. This will become your uncertainty budget.

When developing your table, make sure to include the following parameters;

• Uncertainty Sources or Components

• Sensitivity Coefficients

• Uncertainty Values

• Units of Measure

• Probability Distributions

• Divisors

• Standard Uncertainty

• Degrees of Freedom

• Significance or Influence on Total Combined Uncertainty

• Combined Uncertainty

• Total Effective Degrees of Freedom

• Coverage Factor

• Expanded Uncertainty

• Notes, References, and Comments

In my uncertainty budgets, I like to use rows to list my sources of uncertainty and columns to define the parameters of each uncertainty source.

Refer to the image below for an example.

However, fell free to use any type of format that you wish. You want to make sure that you and your assessors are able to understand your uncertainty budgets and calculations.

It is always best to be consistent. So, choose a format that works best for you and stick to it. Remember, you are the one who has to defend it.

Now that you have created a table for your uncertainty budgets, you will want to add functions and formulas to help you calculate uncertainty.

The benefit to adding formulas and functions is to add automation to your process for estimating uncertainty. Your uncertainty budget will become a calculator that will automatically calculate uncertainty based on your input values.

The five functions that I recommend you add are;

• Calculate standard uncertainty,

• Calculate combined uncertainty,

• Calculate expanded uncertainty,

• Calculate effective degrees of freedom, and

• Calculate the significance of your uncertainty components

Calculating standard uncertainty is pretty easy to do, and you can add this function to your uncertainty calculator in no time.

All you need to do is multiply the value of your uncertainty component by it’s respective sensitivity coefficient and divide it by it’s respective divisor (which is based on the probability distribution assigned to the uncertainty component).

To calculate standard uncertainty, follow these simple steps;

1. Select the standard uncertainty cell,

2. Press the equals (=) key to start a new function,

3. Select the sensitivity coefficient cell,

4. Type the asterisk(*) key (i.e. Shift+8) for the multiplication function,

5. Select the Uncertainty Value cell,

6. Type the forward-slash (/) key for the division function,

7. Select the Divisor cell,

8. Hit the ‘Enter’ key.

If you followed the steps above, your formula should look similar to the image below and your uncertainty budget calculator will now calculate standard uncertainty.

To calculate combined uncertainty, you will need to use the Root Sum of Square method as directed by the **Guide to the Expression of Uncertainty in Measurement (i.e. GUM)**.

Over the years I have seen people perform this calculation in Excel the hard way by creating a very long formula to square each uncertainty component and add them together.

Well, I am going to show you the easy way to calculate combined uncertainty with just two Excel functions;

• sum of squares (i.e. SUMSQ), and

• square root (i.e. SQRT).

All you need to do is follow these simple steps;

1. Select the combined uncertainty cell,

2. Press the equals (=) key to start a new function,

3. Type the square root function (i.e. SQRT),

4. Press the open parenthesis key (i.e. Shift+9),

5. Inside the SQRT parenthesis, type the sum of squares function (i.e. SUMSQ),

6. Press the open parenthesis key (i.e. Shift+9),

7. Inside the SUMSQ parenthesis, select or type in the range of values,

8. Press the close parenthesis key (i.e. Shift+0) twice, and

9. Hit the ‘Enter’ key.

If you followed the steps above, your formula should look similar to the image below and your uncertainty budget calculator will now calculate combined uncertainty.

The last step to estimating uncertainty in measurement is to calculate the expanded uncertainty.

This is where you multiply your combined uncertainty by a coverage factor (i.e. expansion coefficient) to achieve a desired confidence interval.

Typically, most people aim to calculate uncertainty with a 95% confidence level. To accomplish this, you will want to use a coverage factor of 1.96 (i.e. 95%) or 2 (i.e. 95.45%).

If you wish to use a different coverage factor, you can **learn about choosing a coverage factor here**.

To calculate expanded uncertainty, follow these simple steps;

1. Select the expanded uncertainty cell,

2. Press the equals(=) key to start a new function,

3. Select the coverage factor cell,

4. Type the asterisk(*) key (i.e. Shift+8) for the multiplication function,

5. Select the combined uncertainty cell, and

6. Hit the ‘Enter’ key.

Your function should look similar to the example in the image below. Now, your uncertainty budget should calculate the expanded uncertainty automatically.

If you do not care to calculate effective degrees of freedom or the significance each uncertainty component contributes to the total combined uncertainty, you can skip the next two sections.

However, if you would like to have these functions in your uncertainty budget, keep reading. I am going to show you how, step by step.

To **calculate the effective degrees of freedom**, you will need to use the Welch-Satterthwaite approximation equation.

However, calculating this value in a single cell requires a very long string of functions that can cause you plenty of headaches if you have errors or need to update the function.

For many years, I used to perform this calculation in a single cell which required me to constantly update the function every time I wanted to add or delete a row from my uncertainty budget.

The worst part is most the function had to be entered by hand. It was time consuming.

So, I decided to split the function into sub-functions to help minimize the level of effort required to calculate effective degrees of freedom.

First, I calculate the first half of the equation in each row associated with it’s respective source of uncertainty. This allowed to me to perform a majority of the calculations with a simple function that I could copy and paste.

To calculate the first half of the Welch-Satterthwaite equation, follow these simple steps;

1. Select a cell in the same row as the first uncertainty component,

2. Press the equals(=) key to start a new function,

3. Press the open parenthesis key (i.e. Shift+9) twice,

4. Select the sensitivity coefficient cell,

5. Raise it to the power of 4 by pressing the carrot key (i.e. Shift+6) and 4,

6. Press the close parenthesis key (i.e. Shift+0),

7. Type the asterisk(*) key (i.e. Shift+8) for the multiplication function,

8. Press the open parenthesis key (i.e. Shift+9),

9. Select the standard uncertainty cell,

10. Raise it to the power of 4 by pressing the carrot key (i.e. Shift+6) and 4,

11. Press the close parenthesis key (i.e. Shift+0) twice,

12. Press the forward slash key ( / ) for the divide function,

13. Select the degrees of freedom cell,

14. Hit the ‘Enter’ key.

If you followed the steps listed above then your function look similar to the example in the image below.

Next, double check the function to make sure that it performs a calculation and that there are no errors. Then, copy the cell and paste the function for each additional source of uncertainty in your uncertainty budget.

Now, let’s add the second half of the equation to your uncertainty budget and calculate effective degrees of freedom.

To calculate the last half of the Welch-Satterthwaite equation, follow these simple steps;

1. Select the cell designated for effective degrees of freedom,

2. Press the equals(=) key to start a new function,

3. Press the open parenthesis key (i.e. Shift+9),

4. Select the combined uncertainty cell,

5. Raise it to the power of 4 by pressing the carrot key (i.e. Shift+6) and 4,

6. Press the close parenthesis key (i.e. Shift+0),

7. Press the forward slash key ( / ) for the divide function,

8. Press the open parenthesis key (i.e. Shift+9),

9. Type ‘SUM’ for the summation function,

10. Press the open parenthesis key (i.e. Shift+9),

11. Select the range of cells for the first half of the Welch-Satterthwaite equation,

12. Press the close parenthesis key (i.e. Shift+0) twice,

13. Hit the ‘Enter’ key.

If you followed the steps listed above then your function look similar to the example in the image below, and your result will be the calculation of effective degrees of freedom.

Knowing the significance or the amount of influence each source of uncertainty has on your measurement results is important.

Calculating significance can show you;

• how much each source contributes to the total uncertainty,

• which factors have the greatest influence, and

• help you reduce your estimated measurement uncertainty.

When you know which uncertainty components contribute the most, you can take action to target and reduce the magnitude of the largest contributors.

This approach will have the biggest impact and help you improve your CMC Uncertainty estimates.

To calculate the significance of each source of uncertainty, follow these simple steps;

1. Select a cell in the same row as the first uncertainty component,

2. Press the equals(=) key to start a new function,

3. Select the standard uncertainty cell for that row,

4. Raise it to the power of 2 by pressing the carrot key (i.e. Shift+6) and 2,

5. Press the forward slash key ( / ) for the divide function,

6. Type ‘SUMSQ’ for the sum of squares function,

7. Press the open parenthesis key (i.e. Shift+9),

8. Select the range of cells for standard uncertainty,

9. Press the F4 key once to fix these reference cells (should add $ symbols to the formula),

10. Press the close parenthesis key (i.e. Shift+0),

11. Hit the ‘Enter’ key.

Now, copy and paste this function for each uncertainty component in your uncertainty budget. Then, format the values to display as percentages (%).

If you followed the steps listed above then your function look similar to the example in the image below.

Additionally, the sum of all the significance calculations should equal 100%. This is a great way to verify that calculations are correct.

To check, follow the steps below to calculate the sum of all of your significance calculations;

1. Select a cell in the same column as the significance calculations,

2. Press the equals(=) key to start a new function,

3. Type ‘SUM’ for the summation function,

4. Press the open parenthesis key (i.e. Shift+9),

5. Select the range of cells for significance,

6. Press the close parenthesis key (i.e. Shift+0),

7. Hit the ‘Enter’ key.

If you followed the steps listed above then your function look similar to the example in the image below and the summation value should equal 100%. If not, something was miscalculated and you should double check your functions to find the error.

By now, you should have a functional uncertainty calculator that can be used to create uncertainty budgets for ISO/IEC 17025 accreditation.

However, you need add a section for notes.

Adding notes to your uncertainty budgets is important. It will help you and your assessor better understand how you estimated uncertainty in measurement.

You should add notes to explain;

1. How you identified your sources of uncertainty,

2. How you quantified them,

3. What reference material (e.g. reports, books, guides, etc.) was used, and

4. Other important information that supports your estimate.

Most people forget to add notes to their uncertainty budgets which is a big mistake.

You may remember how you estimated uncertainty in measurement today, but it is harder to recall the details several months later when you need to explain the results to an auditor or update your calculations.

To avoid headaches and audit deficiencies, make sure that you are recording notes. I promise that you will thank me later.

This is important for validation. It’s not just for your own sanity, it helps when assessors question whether or not you have validated your uncertainty calculator.

Some assessors like to assert that it is required as part of validation of software. However, it is not.

You are not creating measurement uncertainty software. Instead, you are using Microsoft Excel as a calculator. No different than a scientific or graphing calculator.

However, this does not mean that you should not validate that your uncertainty budget calculator works properly.

So, try one of more of these methods to verify that your uncertainty budget calculates measurement uncertainty correctly. Compare your results to;

1. hand-written uncertainty calculations,

2. calculations performed with a scientific or graphing calculator,

3. measurement uncertainty software,

4. another Excel uncertainty calculator, and(or)

5. results estimated by a third-party.

Any of the methods listed above should help you validate that your uncertainty budget calculator works correctly.

If your comparison yields similar results, consider your uncertainty budget to function properly. If not, review your functions for errors. Then, correct the errors and repeat the verification process.

Once you verify that your uncertainty budget calculates measurement uncertainty correctly, it is safe to use for developing your scope of accreditation.

Uncertainty budgets are a useful tool for estimating uncertainty. They will help you clearly explain how you calculated uncertainty in measurement.

The number one thing to remember is to include enough information that you can easily recall how you calculated uncertainty and repeat the process when you need to update your estimates.

In this guide, I have given you step by step instructions to create your own uncertainty budgets in Microsoft Excel. Use the information to help you calculate uncertainty for ISO/IEC 17025 accreditation.

If you want an uncertainty budget template but don’t want to build it yourself, try my uncertainty calculator for Excel. You can **get it for only $29 and download it now**.

Leave a comment below if you find this guide helpful, and let me know if you have any questions.

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