ISO/IEC 17025 accredited laboratories and ISO 17034 accredited producers calculate expanded uncertainty to a 95 % confidence interval where the coverage factor is two.
The expanded uncertainty represents the interval y ± U which the actual measurement result is expected to be (y – U ≤ Y ≤ y + U).
Step-by-Step Instructions
Follow the instructions below to calculate the expanded uncertainty.
- Calculate the combined standard measurement uncertainty.
- Determine the level of confidence (typically 95.45 %).
- Calculate the effective degrees of freedom.
- If the effective degrees of freedom are less than 10, use the t-distribution to determine the coverage factor. Otherwise, use a coverage factor of 2.
- Multiply the combined standard measurement uncertainty and the coverage factor.
For more information, refer to the JCGM 100:2008 section 6.
Example
| Description | Symbol | Value | Unit |
|---|---|---|---|
| Combined Uncertainty | uc | 0.25 | mg |
| Coverage Factor | k | 2 | |
| Expanded Uncertainty | U | 0.50 | mg |
Download: ISOBudgets Expanded Uncertainty Calculator – Version 1.0
FAQ
What is Expanded Uncertainty?
Expanded measurement uncertainty is the product of the combined measurement uncertainty (uc) multiplied by a coverage factor (k).
What is Combined Measurement Uncertainty?
Combined standard measurement uncertainty is the result of combining individual standard measurement uncertainties using the square root of the sum of squares (RSS) method.
What is a coverage factor?
A coverage factor is a multiplier larger then one used to expand the combined standard uncertainty to a desired level of confidence (e.g. 95 % confidence where k=2)
What coverage factor is used to calculate expanded uncertainty?
The coverage factor used depends on the following factors:
- desired level of confidence and,
- where appropriate, the effective degrees of freedom.
Specify the desired level of confidence and find the associated coverage factor from JCGM 100:2008 Table G.1. For example, an ISO/IEC 17025 accredited laboratory needs to estimate uncertainty to a 95.45 % level of confidence using a coverage factor of 2 from JCGM 100:2008 Table G.1. The coverage factors in the table are equal to using the t-distribution with infinite degrees of freedom.
When the effective degrees of freedom are less than 10 (JCGM 100:2008, G.6.6), use the t-distribution or JCGM 100:2008 Table G.2 to find the coverage factor. For example, a combined standard uncertainty with 9 effective degrees of freedom would use a coverage factor of 2.32 according to JCGM 100:2008 Table G.2.
Glossary
- Expanded Measurement Uncertainty
- the product of a combined standard measurement uncertainty (uc) and a factor larger than the number one. (Source: JCGM 200:2012, 2.35)
- Combined Standard Measurement Uncertainty
- standard measurement uncertainty that is obtained using the individual standard measurement uncertainties associated with the input quantities in a measurement model. (Source: JCGM 200:2012, 2.31)
- Coverage Factor
- – number larger than one by which a combined standard measurement uncertainty is multiplied to obtain an expanded measurement uncertainty. (Source: JCGM 200:2012, 2.38)
- Effective Degrees of Freedom
- the degrees of freedom of the combined standard measurement uncertainty (uc) obtained from the Welch-Satterthwaite formula and used to determine the coverage factor (k) approximated by a t-distribution. (Source: JCGM 100:2008, G.4)
- Level of Confidence
- the likelihood that a set of measurement values are contained within a specified coverage interval. (Source: JCGM 200:2012, 2.37)