MEASUREMENT UNCERTAINTY / 05
From measurement model to uncertainty
Use sensitivity, correlation and model behaviour to choose the calculation.
Start with the equation
Write y = f(x₁, x₂, …), including relevant corrections, constants and units. For a locally linear model with independent inputs, u²(y) ≈ Σ[cᵢ²u²(xᵢ)], where cᵢ is the local sensitivity of the output to input i. Correlated inputs require covariance terms.
Same units do not mean equal sensitivity
For y = 2x, the sensitivity coefficient is 2, even if x and y use the same unit. For a ratio, the effect of each input depends on its value and on any shared sources of variation. Unit checking helps, but cannot replace a model.
Analytical propagation
Use derivatives when the model is tractable and a first-order approximation is adequate.
Numerical sensitivity
Perturb inputs to estimate sensitivity. Check the step size and local linearity; a spreadsheet is not a proof of validity.
Where Kragten-style calculations fit
A perturbation spreadsheet is useful for simple models, but a basic implementation assumes independent inputs and approximates local response. Keep the baseline result, input standard uncertainties, perturbations and output changes visible. Check the result against a simple case that can be calculated by hand.
When Monte Carlo helps
Sampling specified joint input distributions can reveal asymmetry and nonlinear behaviour. Correlation must be represented in the sampling; arbitrary independent draws can give a misleading answer. Check numerical stability and report how the coverage interval was obtained.
A current point worth noticing
The 2026 JCGM amendment emphasises that significant nonlinearity can affect the estimate of the output as well as its uncertainty. A more elaborate uncertainty calculation does not rescue an unsuitable central estimate.
Convert inputs consistently
For a rectangular distribution with half-width a, standard uncertainty is a/√3; for a symmetric triangular distribution it is a/√6. State that a is the half-width. Type A and Type B describe evaluation methods—not synonyms for random and systematic effects.
Sources & further reading
- JCGM 100:2008 — Guide to the Expression of Uncertainty in Measurement
- JCGM GUM-6:2020 — Developing and using measurement models
- JCGM 101:2008 — Propagation of distributions using Monte Carlo
- JCGM 2026 amendment — Nonlinearity and the GUM
Educational guidance, not a substitute for a locally approved procedure. Worked examples are synthetic. Reviewed against the sources indicated; licensed standards must be consulted for their full requirements.
Take the next step
Use a short explanation or visual example when the terminology gets in the way.
- Laboratory Quality A–Z — Look up terms such as standard uncertainty, correlation and coverage factor.
- Distribution viewer — Explore distribution shapes and spread with a guided example.
- Documenting uncertainty guide — Read how to record the model, assumptions and limits of the estimate.