1. Classify the evaluation method, not the effect
Type A uses statistical analysis of observations. Type B uses other information, including certificates, specifications, experience, material data and environmental knowledge. The distinction describes the evaluation method, not whether an influence is random or systematic.
An input quantity can have contributions evaluated by both methods. A calibration correction's uncertainty may include statistical and non-statistical components. Type B is not inherently inferior, and Type A is not automatically objective. In either case, check whether the evidence represents your measurement and whether its assumptions remain valid.
2. Evaluate the mean of independent observations
For n independent observations from a stable process with common variance, calculate the mean and sample standard deviation s using n − 1 in the denominator. If reporting the series mean, its standard uncertainty is s/√n. Estimating s requires at least two observations.
The quantity s describes the spread of individual observations; s/√n describes the estimated mean's uncertainty arising from that spread. Do not divide by √n when reporting a single reading. Repetition also does not automatically reduce uncertainty associated with a shared correction, reference standard or offset affecting every observation.
3. Check independence and stability first
Inspect readings in time order. Temperature trends, drift, setup changes and environmental cycles can undermine the stable, independent-observation model. More readings do not fix these issues; rapid readings from a filtered instrument may be strongly correlated.
With temporal dependence, s/√n can underestimate uncertainty. Use a suitable correlation model, redesign the sampling plan or remove the source of instability and repeat the series. Do not discard observations simply to reduce s: exclusions need a documented criterion and an explanation of what produced the unusual readings.
4. Convert Type B information into a distribution
If a certificate states expanded uncertainty U and coverage factor k, recover standard uncertainty as U/k. Check the declared coverage and basis for k. Do not assume k = 2 or normality without supporting information. An accuracy label alone does not define uncertainty.
For bounds ±a, a rectangular distribution is appropriate when values throughout the interval are equally plausible. A triangular distribution needs evidence favouring the centre. Their standard uncertainties are a/√3 and a/√6. Resolution q gives q/√12 only under a uniform rounding-error model with bounds ±q/2.
5. Combine contributions without duplication
Express all contributions as standard uncertainties of model inputs. A sensitivity coefficient converts each input uncertainty into its effect on the result. Independent inputs combine through the sum of squared contributions. The coefficient's sign becomes particularly important for correlated inputs, where covariance terms must also be included.
Avoid counting the same effect twice because it appears in both a specification and a certificate, or in both repeatability and resolution. Observed variation may already include some quantization effects. Conversely, an unchanging display does not eliminate rounding uncertainty. Examine the information and dependencies instead of mechanically accumulating entries.
6. Consider how reliable the uncertainty estimates are
A simple Type A estimate has n − 1 degrees of freedom. A small sample makes the variance estimate itself less reliable. For independent contributions under suitable assumptions, the Welch–Satterthwaite formula estimates effective degrees of freedom, which can support choosing a coverage factor from the Student t distribution.
Type B does not automatically imply infinite degrees of freedom: this approximation requires reliable uncertainty estimates and bounds. Report how U and k were obtained and the intended coverage. k = 2 is not a universal 95% recipe.
Remember this
Type A and Type B identify evaluation methods. Use s/√n only for an appropriate series mean, and convert Type B information only after checking what it means and which assumptions support it.
Sources and further reading
This guide explains fundamental GUM principles. Always adapt your model to the method and the information available about the measurement.
Practise with your own measurement.
Understanding comes with practice. Training or coaching connects theory with your own method and data.