What ISO/IEC 17025 requires
- Clause 7.6.1: the laboratory identifies the contributions to measurement uncertainty, including those arising from sampling where relevant.
- Clause 7.6.2: calibration laboratories evaluate the uncertainty for all calibrations, including their own equipment.
- Clause 7.6.3: testing laboratories evaluate measurement uncertainty. Where the test method precludes rigorous evaluation, an estimate is made based on an understanding of the theoretical principles or practical experience of the method's performance.
- Where a well-recognised test method specifies limits for the major sources of uncertainty and the form in which results are presented, following the method satisfies the requirement.
- Clause 7.8.3.1 c): the uncertainty is reported when it is relevant to the validity or application of the result, when the customer requests it, or when it affects conformity with a specification limit.
Important for testing laboratories: the standard distinguishes clearly between calibration and testing. A testing laboratory does not have to produce a full mathematical model for every test, but it must be able to show that it knows its main uncertainty sources and has quantified them in a justified way.
The key terms
| Term | Meaning |
|---|---|
| Standard uncertainty u | Uncertainty of one contribution, expressed as a standard deviation. |
| Type A evaluation | Determined statistically from repeated measurements, e.g. standard deviation of the mean. |
| Type B evaluation | Determined from other information: calibration certificates, specifications, resolution, experience. |
| Combined standard uncertainty uc | All contributions combined, usually as the square root of the sum of squared (sensitivity-weighted) contributions. |
| Coverage factor k | Multiplier for the confidence level; k = 2 corresponds to roughly 95 % for a normal distribution. |
| Expanded uncertainty U | U = k × uc — the value that appears in the report, e.g. 12.4 V ± 0.3 V (k = 2). |
Building an uncertainty budget in six steps
- 1
Define the measurand
State exactly what is measured, under which conditions and with which method — "insulation resistance at 500 V DC after 60 s at 23 °C", not just "resistance".
- 2
Set up the model
Write down how the result is calculated from the input quantities, including corrections. For direct readings the model is simple: reading plus corrections.
- 3
Identify the sources
Typical sources: calibration of the instrument, resolution, drift since the last calibration, repeatability, environmental conditions, operator, item under test, reference standards. A cause-and-effect diagram helps not to forget any.
- 4
Quantify each contribution
Convert every source into a standard uncertainty. A calibration certificate stating U with k = 2 gives u = U / 2. A tolerance limit ±a with no further information is treated as a rectangular distribution: u = a / √3. Resolution d gives u = d / (2√3).
- 5
Combine
Multiply each contribution by its sensitivity coefficient and combine as root sum of squares. Check which contributions dominate — often one or two sources account for most of the total.
- 6
Expand and report
Multiply by the coverage factor (usually k = 2), round to at most two significant digits and state k and the confidence level in the report.
Example: voltage measurement with a digital multimeter
A simplified budget for a DC voltage of about 12 V, measured ten times with a calibrated multimeter. The values are illustrative.
| Contribution | Standard uncertainty |
|---|---|
| Calibration of the multimeter (certificate: U = 6 mV, k = 2) | 6 mV / 2 = 3.0 mV |
| Drift since calibration (manufacturer: ±5 mV, rectangular) | 5 mV / √3 ≈ 2.9 mV |
| Resolution (1 mV, rectangular) | 1 mV / (2√3) ≈ 0.3 mV |
| Repeatability (s = 4 mV, n = 10, Type A) | 4 mV / √10 ≈ 1.3 mV |
| Combined standard uncertainty uc | √(3.0² + 2.9² + 0.3² + 1.3²) ≈ 4.4 mV |
| Expanded uncertainty U (k = 2) | ≈ 9 mV |
The budget shows immediately where improvement pays off: calibration and drift dominate. More repetitions would hardly reduce the total; a shorter calibration interval or a better-specified instrument would.
Top-down approaches: when a full model is not practical
For many tests — mechanical, environmental, chemical or durability tests — a complete GUM model is disproportionate. Recognised alternatives use data the laboratory already has:
- Validation data: intermediate precision (different days, operators, instruments) plus bias from reference materials or recovery.
- Interlaboratory comparisons and proficiency tests: reproducibility standard deviations according to ISO 5725 and ISO 21748.
- Quality control data: long-term control charts of reference samples as an estimate of within-lab reproducibility.
- Standard methods that specify their own uncertainty or limits for the major sources — here following the method is sufficient.
Uncertainty in the report and in conformity statements
If you state conformity with a specification ("pass/fail"), uncertainty becomes directly relevant: clause 7.1.3 requires a documented decision rule that takes the uncertainty into account, and the report must state which rule was applied. The most widely used reference is ILAC-G8. A result close to a limit can be a "pass" under simple acceptance but a "not decidable" under guarded acceptance — the customer should agree the rule before the test.
In practice uncertainty budgets fail less often on mathematics than on data: the calibration certificate value is outdated, the instrument used is not recorded with the result, or repeatability data are scattered across spreadsheets. When every result is stored with instrument, calibration status and conditions, the budget can be reviewed and updated with little effort.