How to Estimate Measurement Uncertainty with GUM

What does measurement uncertainty mean under GUM?

Measurement uncertainty is the range within which the true value of a quantity lies with a stated probability. The GUM (Guide to the Expression of Uncertainty in Measurement, ISO/IEC Guide 98‑3) is the internationally accepted framework that defines how this uncertainty is determined and reported.

The GUM distinguishes two ways to evaluate a contribution. Type A uses statistical analysis of repeated measurements (standard deviation), while Type B draws on other sources such as calibration certificates, datasheets or manufacturer data. Both produce a standard uncertainty u that is processed the same way afterwards.

• Type A: standard deviation from n repeats, u = s / √n.
• Type B: converted from limits, e.g. rectangular distribution u = a / √3.
• Every influence quantity (instrument, temperature, operator, part) adds a contribution.

How is the uncertainty budget calculated?

In the uncertainty budget every contribution is converted to the same standard uncertainty and added in quadrature to form the combined standard uncertainty u_c. This is multiplied by the coverage factor k to give the expanded uncertainty U = k · u_c.

The coverage factor k sets the desired confidence level. For an approximately normal combined uncertainty, k = 2 gives about 95 % and k = 3 about 99.7 % coverage. k = 2 is the default on calibration certificates and test reports.

• 1. Define the model equation and the influence quantities.
• 2. Convert each contribution into a standard uncertainty u_i.
• 3. Apply sensitivity coefficients and sum in quadrature: u_c = √(Σ u_i²).
• 4. Multiply by k: U = k · u_c, usually k = 2.

How do you assess conformity against tolerance limits?

Conformity assessment checks whether a measured value lies within the tolerance limits. Under ISO 14253‑1 the expanded uncertainty U is taken into account: the safe acceptance zone shrinks by U at both ends, and the safe rejection zone begins beyond the limit plus U.

Between them lies the uncertainty range, where no clear statement is possible. Charging the uncertainty to the supplier narrows the acceptance zone (strict rule); charging it to the customer widens it. This decision rule must be agreed and documented in advance.

Frequently asked questions