ISO Compliance Insights & Best Practices
CART
ISO Compliance Insights & Best Practices
Most laboratories can quote their measurement uncertainty. Rather fewer can explain how they arrived at it, and a good number arrived at it by measuring the same sample ten times and calculating a standard deviation. That is one contribution out of eight or nine, and usually not the largest. This guide covers how a budget is actually built, with a worked example, and the three errors that appear most often in assessment.
The measurement uncertainty requirement sits in clause 7.6 of ISO 17025. Calibration laboratories evaluate uncertainty for all calibrations. Testing laboratories evaluate it for all measurements, and where the method precludes rigorous evaluation, an estimate based on theoretical principles or practical experience is acceptable — but an estimate is still an evaluation, not an omission.
A measurement uncertainty budget is a list of everything that could make your result differ from the true value, each converted to a common form, then combined. The common form is the standard uncertainty, written u — an uncertainty expressed as a standard deviation.
Contributions come in two flavours. Type A evaluations come from statistical analysis of repeated observations. Type B evaluations come from everything else: calibration certificates, manufacturer specifications, published data, professional judgement. Neither is superior; the labels describe how you got the number, not how good it is.
Work through the measurement systematically rather than listing what comes to mind. A useful order:
| Source | Typical contributions |
|---|---|
| Sampling | Heterogeneity, sampling method — often the largest of all |
| The item | Instability, inhomogeneity, sub-sampling |
| Reference standards | Certified value uncertainty, drift since certification |
| Equipment | Calibration uncertainty, resolution, drift, non-linearity |
| Environment | Temperature, humidity and pressure effects |
| Method | Bias, recovery, incomplete extraction |
| Operator | Reading, judgement, technique variation |
| Calculation | Rounding, constants, curve fitting |
| Repeatability | Observed scatter under repeat conditions |
You may exclude contributions that are negligible against the dominant ones — but record the reasoning. “We considered it and it was two orders of magnitude smaller” is an answer. Silence is not.
Type A is straightforward: u = s / √n, where s is the standard deviation of n observations.
Type B requires you to assume a distribution and divide by the appropriate factor:
| What you have | Distribution | Standard uncertainty |
|---|---|---|
| Expanded uncertainty U with coverage factor k | Normal | u = U / k |
| Limits ±a, all values equally likely | Rectangular | u = a / √3 |
| Limits ±a, central values more likely | Triangular | u = a / √6 |
| Digital display resolution d | Rectangular | u = d / (2√3) |
Weighing a sample by difference on an analytical balance — two weighings, tare and gross.
| Contribution | Type | Value | Distribution | u (mg) |
|---|---|---|---|---|
| Balance calibration, certificate U = 0.20 mg at k = 2 | B | 0.20 | Normal, k=2 | 0.100 |
| Readability 0.1 mg, two readings | B | 0.1 | Rectangular | 0.041 |
| Drift since calibration, from history ±0.15 mg | B | 0.15 | Rectangular | 0.087 |
| Repeatability, s = 0.12 mg from n = 10 | A | — | Normal | 0.038 |
| Buoyancy correction not applied, ±0.10 mg | B | 0.10 | Rectangular | 0.058 |
Combine in quadrature:
uc = √(0.100² + 0.041² + 0.087² + 0.038² + 0.058²) = √0.0241 = 0.155 mg
Multiply by the coverage factor for the expanded uncertainty. At k = 2, giving approximately 95% confidence:
U = 2 × 0.155 = 0.31 mg, reported as approximately 0.3 mg at k = 2.
Look at what the budget shows. Calibration contributes 41% of the variance and drift another 31%. Repeatability — the contribution most laboratories measure first, and some measure only — contributes 6%. A budget built from replicates alone would have reported roughly 0.08 mg, understating the real measurement uncertainty fourfold.
A certificate says “U = 0.20 mg, k = 2”. That is an expanded uncertainty at roughly 95% confidence. The standard uncertainty is 0.10 mg. Using 0.20 directly double-counts the coverage factor, and then multiplying the combined figure by k at the end double-counts it again. This is the single most common arithmetic error in laboratory budgets, and it inflates the result rather than understating it — which is why it survives so long unnoticed.
Where the laboratory takes the sample, sampling is part of the measurement — and in heterogeneous material it usually dominates everything else combined. A budget that covers only the analysis can understate total uncertainty by an order of magnitude.
If you do not include it, say so on the report: state that the uncertainty relates to the measurement only. A customer making a conformity decision against a limit needs to know which uncertainty they are looking at.
Repeatability is easy to measure, which is why it gets measured. It captures short-term random variation and nothing else — not calibration, not drift, not bias, not matrix effects. As the worked example shows, it is frequently among the smallest contributions.
A measurement uncertainty budget is not written once. Revisit it when the method changes, when equipment changes, when a calibration certificate comes back with materially different uncertainty, when proficiency testing suggests your uncertainty is understated, and on a defined cycle regardless.
Where uncertainty varies across the measurement range — and it usually does — state it as a function or by range rather than a single figure spanning the whole scope. A relative uncertainty at the top of the range is often meaningless at the bottom.
Measurement uncertainty is reported where it is relevant to the validity or application of a result, where the customer asks for it, or where it affects conformity to a specification limit. That last case is where it stops being an academic exercise: when a measured value sits close to a limit, whether the item passes depends on the uncertainty and the decision rule applied to it.
Our ISO 17025 Toolkit includes a measurement uncertainty evaluation procedure and a budget workbook carrying this worked example as live rows — contributions, distributions, divisors, sensitivity coefficients and the expanded result — alongside the other 68 templates covering the standard.
Error is the difference between a measured value and the true value — a single number you can never actually know. Uncertainty describes the range within which the true value is expected to lie. You correct for known errors; you quantify the uncertainty that remains.
k = 2 is conventional, giving approximately 95% confidence for a normal distribution. Some sectors and some accreditation bodies specify otherwise. Whatever you use, state it on the report along with the approximate confidence level.
Clause 7.6 requires testing laboratories to evaluate measurement uncertainty for all measurements. Where the method precludes a rigorous evaluation, an estimate based on theoretical understanding or practical experience of the method’s performance is acceptable — but the reasoning has to be recorded.
Not necessarily. An implausibly small measurement uncertainty usually means contributions were omitted. What matters is whether the uncertainty is fit for the customer’s decision, and whether the budget can be defended contribution by contribution.
August 12, 2026
August 12, 2026
