Measurement uncertainty expresses the interval within which the true value of a measurement result may lie, and it must appear on every calibration certificate. A measurement result given without uncertainty is technically incomplete.
What Is the GUM (Guide to the Expression of Uncertainty in Measurement)?
The GUM is the reference guide accepted by the international metrology community for calculating measurement uncertainty. ISO/IEC 17025:2017 requires calibration laboratories to calculate the uncertainty on their certificates according to the GUM method.
Type A Uncertainty Components
Type A uncertainty is calculated by the statistical analysis of repeated measurements, using standard deviation and experimental standard deviation formulas:
- At least 10 repeated measurements are made under the same conditions
- The arithmetic mean is calculated
- The experimental standard deviation s(x) is found
- The standard deviation of the mean u(x̄) = s(x)/√n gives the Type A uncertainty
Type B Uncertainty Components
Type B uncertainty covers all uncertainty sources evaluated by non-statistical means:
- Reference standard uncertainty: taken from its certificate; for k=2, U/2 is used
- Resolution: via the (d/2)/√3 formula (rectangular distribution)
- Drift: based on the change between the last two calibrations
- Ambient temperature effect: thermal expansion coefficient × temperature deviation
Combined Standard Uncertainty
If all components are assumed independent, the square root of the sum of their squares is taken:
Expanded Uncertainty and k=2
The expanded uncertainty stated on calibration certificates is calculated as U = k × uc. For a normal-distribution assumption and a 95.45% coverage probability, the coverage factor k=2 is used. In some special cases (low degrees of freedom), the effective degrees of freedom are calculated with the Welch-Satterthwaite formula and k is taken from the t-distribution.
Practical tip
The largest component of the uncertainty budget is usually the uncertainty of the reference standard. If you want your laboratory to stay competitive, invest in reference instruments with lower uncertainty.
Conclusion
The measurement uncertainty calculation is the most concrete indicator of a calibration laboratory’s technical competence. A detailed uncertainty budget should be prepared for each measured quantity and reviewed annually.