If you are an ISO/IEC 17025 accredited laboratory, you have probably heard the acronym CMC before. It is commonly used on a calibration laboratory’s scope of accreditation to express the laboratory’s measurement capability. If you are a testing laboratory, you are probably less familiar with this acronym; but, you shouldn’t be. Many testing laboratories are required to calculate the uncertainty in measurement results similar to calibration laboratories although your CMCs are not published in your scope of accreditation. Therefore, let’s discuss what a CMC is, how to estimate it’s value, and how to use it.

**What is a CMC?**

CMC is the abbreviation for ‘Calibration and Measurement Capability.’ It is defined by BIPM and ILAC as the calibration and measurement capability available to customers under normal conditions. When claiming a CMC, the measurement or calibration should be performed in accordance with a documented method or procedure and have an uncertainty budget associated with the process. Additionally, the process should be performed on a regular basis, whether scheduled or on demand, and the CMC should be made available to all clients.

To keep it simple, your CMC should publically express your calibration and measurement capability via a statement of uncertainty that follows a documented process and has an associated uncertainty budget.

**Estimating a CMC**

Your CMCs should be estimated using methods that comply with the Guide to the Expression of Uncertainty in Measurement (GUM). The estimation should be evidenced with an uncertainty budget which takes into account factors that significantly influence the measurement result. However, contributions caused by the unit under test (UUT) should normally be excluded from the CMC statement. These factors should be included in the estimation of the calibration or measurement uncertainty.

Some CMC Contributors;

- Repeatability
- Reproducibility
- Resolution
- Bias
- Drift
- Reference Standard Uncertainty
- Reference Standard Stability
- Environmental Factors
- Significant factors that influence the measurement result

**Expressing a CMC**

Once you have estimated your CMCs, there are typically four acceptable ways to express your CMCs; using a range, an equation, a fixed value, or a matrix. If you were to observe several scopes of accreditation, you will find the use of an equation or a fixed value to be the most common way to express a CMC uncertainty statement.

If you are expressing a CMC across the range of a function (i.e. DC Voltage Measure), I would recommend using an equation. Using an equation (typically) allows you to more adequately express that the uncertainty is directly proportional with range; uncertainty increases and the measured value increases or vice-versa. If you are expressing a CMC for a fixed value of a measurement function (i.e. Mass Measure), then it is typically best to use a fixed value for your CMC. However, sometimes it is acceptable to use a fixed value to express CMC uncertainty where the range of the measurement function is narrow and variance in the estimated uncertainty is low.

1 | Range

2 | Equation

3 | Fixed Value

4 | Matrix

Some Examples

Fluke – Everett Service Center

Henry Troemner LLC

**Conclusion**

CMCs should not be confused with the measurement uncertainty published in your calibration and test reports. The values expressed in your reports require some additional evaluation to include the influences introduced the unit under test. Your CMCs should only quantitatively express the measurement capability of your process minus the UUT.

Dear Sir,

Could you explain and give the example. How to calculate CMC

value 16 micro volt/volt + 1.0 micro volt=?

Hi Syed,

Yes. Let’s use an equation: y = B1 * x1 + B0, where B1 is your gain coefficient, B0 is your offset, x is your input variable, and y is your output variable. Now, let’s estimate that our measured value or “x” is 10 Volts. The equation now becomes:

y = 16uV/V * 10V + 1uV = 161uV

If we switch up and measure 1V instead:

y = 16uV/V * 1V + 1uV = 17uV

I hope this helps. I will write a new blog post on this topic; it will be available in January. Subscribe to my blog for updates.

Hi Sir,

I need help in calculating CMC on my balance and Mass cause its my first time to do this

I need help in calculating CMC on my pressure balance cause its my first time to do this.

Hi Munteha,

I will be glad to help you. Please email me at rhogan@isobudgets.com

Rick

Dear sir pls mail me CMC Calculation Calculator. star_calibration@yahoo.com

Hi Rakesh,

If you are trying to calculate CMC Uncertainty, you can buy the CMC Uncertainty Calculator here:

Easy Uncertainty Calculator

If you trying to calculate a linear equation for two CMC Uncertainties across a measurement range, you can buy the CMC Uncertainty Equation Calculator here:

CMC Uncertainty Equation Calculator

If you have any questions, please let me know.

I hope this helps.

Best regards,

Rick

Sir.

I have been given a project of getting the volume and mass laboratory accreditation.

I’m not sure of how/what determines the CMC. I know it has to with the type of equipments you are going to use as reference/standards but I am not sure how to relate them.

Kindly assist

Hi Matome,

I will be glad to help you. Please email me at rhogan@isobudgets.com.

Rick

A very good article. Thank you! I just want to mention that contributions caused by the unit under test (UUT) should normally NOT be excluded from the CMC statement, but contributions from “best existing device” shall be considered. I want to clarify this as many laboratories leaves this out, and therefore easily underestimates their CMCs. More about CMCs can be read at http://www.bipm.org/en/cipm-mra/cipm-mra-documents/#cmcs .

Hi RJ,

You brought up a good point, but you are not entirely accurate.

The ILAC P14 recommends that your include a “best existing device” in your CMC Uncertainty statements, but allows you to omit it from your uncertainty analysis as long as it is identified in the scope of accreditation.

Many times, it is best for most labs to omit UUT contributions in their CMC Uncertainty statements because it will not best represent the actual calibration workload. Furthermore, when you add the actual UUT contributions, you will actually overstate your estimate of uncertainty in measurement.

It is a highly debated topic. However, I have always omitted the UUT contributions in my CMC Uncertainty calculations and only add them in at the time of calibration.

Including the UUT contribution in the CMC Uncertainty works best for laboratories that routinely calibrate similar devices. For example, If your lab only calibrated 4-digit multimeters, then including a best existing or typical device would have its advantages; but, if the laboratory calibrates 4, 5, 6.5, 7.5, and 8.5-digit multimeters, including a best existing or typical device may not be good for the lab.

Refer to section 5.4 of the ILAC P14:01/2013;

“5.4 Calibration laboratories shall provide evidence that they can provide calibrations tocustomers in compliance with 5.1 b) so that measurement uncertainties equal those

covered by the CMC. In the formulation of CMC, laboratories shall take notice of the

performance of the “best existing device” which is available for a specific category of

calibrations.

A reasonable amount of contribution to uncertainty from repeatability shall be

included and contributions due to reproducibility should be included in the CMC

uncertainty component, when available. There should, on the other hand, be no

significant contribution to the CMC uncertainty component attributable to physical

effects that can be ascribed to imperfections of even the best existing device under

calibration or measurement.

It is recognized that for some calibrations a “best existing device” does not exist

and/or contributions to the uncertainty attributed to the device significantly affect the

uncertainty. If such contributions to uncertainty from the device can be separated from

other contributions, then the contributions from the device may be excluded from the

CMC statement. For such a case, however, the scope of accreditation shall clearly

identify that the contributions to the uncertainty from the device are not included.

NOTE: The term “best existing device” is understood as a device to be calibrated thatis commercially or otherwise available for customers, even if it has a special

performance (stability) or has a long history of calibration.”

I hope this helps.

Hi sir

I need help in calculating CMC of Ranges to calibration for calibrator and multimeter

Hi Wedad,

I would be glad to help you. Please email me at rhogan@isobudgets.com