Measurement Uncertainty in GMP Laboratories: Practical Interpretation and Use

Measurement uncertainty describes what remains undetermined about the value attributed to a quantity, based on the available information. It is neither a defect to conceal nor a number to copy automatically from a calibration certificate. In a GMP laboratory, it helps establish measurement capability and interpret the result in the context of the intended decision.

This guide develops a simplified budget and an original numerical case. Its purpose is to make assumptions, contributions and consequences understandable, not to replace a specific metrological assessment or the rules of the applicable method. The case is simulated, does not concern a batch and does not generate a “GMP PASS”. JCGM and ILAC guidance must be used within its scope, without turning it into identical requirements for every pharmaceutical activity.

Uncertainty, error, tolerance, resolution and accuracy

The VIM distinguishes concepts often confused in technical specifications. Measurement error is the measured value minus a reference value and can have a sign. Uncertainty instead characterises the dispersion of values attributable to the measurand, given the information used, and is non-negative. Knowing a correction does not remove the uncertainty with which that correction was determined. [1]

Tolerance defines values permitted by a specification; it does not arise from the uncertainty budget. Resolution concerns the ability to distinguish changes in the indication: more display digits do not automatically demonstrate lower overall uncertainty. In VIM terminology, accuracy expresses closeness to the true value and is not a quantity to which a number can directly be assigned. When a specification states “accuracy ±…”, clarify which performance characteristic is actually being specified. [1]

These distinctions affect everyday work. A result may be repeatable yet influenced by a systematic effect; an instrument may have fine resolution but poorly controlled operating conditions. Uncertainty should not be enlarged to make a known error acceptable, or subtracted from an out-of-specification result to manufacture conformity.

Define exactly what is being measured

Before calculating, write down the measurand: which quantity, of which object, under which conditions, and at which time or over which interval. “Incubator temperature” may mean air temperature at one location, a time average there, distribution throughout the chamber or temperature inside the material. These are different results requiring different information.

Describe the model linking inputs to the result. It may be a simple relationship between an indication and corrections, or include weighing, dilution, instrumental response and method factors. The model must represent the actual activity and significant effects, not merely what is convenient to enter in a spreadsheet. Even an apparently direct reading can depend on several influences. [2,3]

Clarify whether a single observation or a mean is being reported. The dispersion of individual readings and the uncertainty of their mean are not interchangeable. Reduction by the square root of the number of observations requires appropriate assumptions, including independence and a relevant, stable process; it does not justify opportunistic repetition until the result looks favourable.

Identify contributions without double counting

Start from the path followed by the sample and the measurement. Where relevant, consider the reference and calibration, repeatability, resolution, drift, environmental conditions, preparation, recovery, matrix and operator. A long list is not necessarily complete; a short one can be complete only if exclusions are justified. Uncertainty concerns the defined result, not an abstract inventory of possible problems. [3]

For each entry, ask which evidence supports it, which range it covers and whether it is already included in another estimate. Precision data incorporating environmental variation should not automatically be added to an identical environmental contribution. Similarly, a resolution component may already be represented by experimental data: examine the case before adding it.

Known significant corrections belong in the model; their associated uncertainty still needs evaluation. A correction estimated as zero does not mean zero uncertainty. Also distinguish an effect demonstrated to be negligible from an effect not investigated: missing data are a gap to resolve, not proof of irrelevance.

Type A and Type B: how the estimate is obtained

Type A and Type B classify the method of uncertainty evaluation; they do not automatically separate random and systematic errors. Type A uses statistical analysis of observations. Type B uses other information, such as certificates, previous data, technical knowledge or justified bounds. Both can contribute to the same result and require competent judgement. [2,3]

Before combining, express contributions as standard uncertainties. If a certificate reports expanded uncertainty U and its factor k, the corresponding standard component is obtained as U/k within the context to which the data apply. Assuming equally probable values within symmetric bounds ±a gives a/√3 under a rectangular model. The distribution must be justified, not selected to produce a smaller number.

The sensitivity coefficient describes how a change in an input affects the output and converts contributions into the result’s unit. If inputs are correlated, their combination must include covariances: the square root of a sum of squares is not a universal recipe. The 2026 GUM amendment also addresses appropriate treatment of significant nonlinearity, including Monte Carlo methods where suitable. [2,4]

Original budget: a simulated temperature measurement

Consider temperature at one defined point and instant, estimated from a single indication of 25.9 °C with a correction of +0.02 °C applied: the corrected result is 25.92 °C. The teaching model includes four independent, additive residual contributions, each with a sensitivity coefficient of 1. It represents neither chamber mapping nor an actual calibration procedure.

Assume that a sufficiently large, relevant historical series provides a repeatability standard deviation of 0.03 °C for a single measurement. For this example, that component is separate from rounding of the current reading: absence of double counting is explicitly assumed. The reference contribution to the correction comes from U = 0.04 °C with k = 2. Other significant effects are assumed absent or negligible only within this simulation.

The table rounds values for readability; the calculation retains intermediate digits. Under the stated assumptions, the combined variance is 0.003333… °C² and the combined standard uncertainty is u_c = 0.057735… °C. The environmental term represents a residual influence on the result, not an additional permitted operating range for the room.

Actual use would require evidence for each assumption: repeatability data, the meaning of the certificate, display behaviour, the environmental influence model and verification of excluded effects. Do not copy these numbers into a company budget. The structure is reusable; the values belong exclusively to the simulated case.

Expanded uncertainty and the meaning of the coverage factor

To illustrate the move to expanded uncertainty, choose k = 2: U = k × u_c = 0.115470… °C, reportable as 0.12 °C with consistent rounding. The result can therefore be expressed as (25.92 ± 0.12) °C, specifying k, the model and the conditions. The ± sign does not mean that every possible error is certainly contained within the interval.

The correspondence between k = 2 and approximately 95% coverage requires appropriate conditions, including the shape of the result’s distribution and adequate degrees of freedom. It is not an identity valid for every budget. In this example, k is a teaching choice: no exact coverage probability is assigned. A real case must justify the factor and the probabilistic statement used. [2]

Do not directly compare two U values without reading k, the measurand, range, conditions and model. A lower value may reflect different conditions or a narrower scope. Uncertainty provides information about the measurement described, not an independent ranking of laboratory quality.

A result near the criterion: what it allows us to say

For this simulated case only, an allowable interval from 25.80 to 26.00 °C is established before assessment, along with an illustrative rule: accept only if y ± U is entirely contained within the limits. These values and this rule are not GMP, pharmacopoeial or incubation requirements and must not be transferred to an actual method.

Using unrounded values, the calculated interval is approximately 25.8045–26.0355 °C. The central value of 25.92 °C is within the limits, but the upper endpoint exceeds 26.00 °C; the case does not meet the preselected acceptance rule. This does not prove that the true value is out of specification and does not authorise a batch release decision.

The result calls for the response defined in the applicable procedure, considering context, risk and further relevant evidence. Do not change the rule after seeing the number or repeat measurements and retain only favourable ones. ILAC G8 addresses different rules and their associated risks; it does not prescribe one guard band for every application. [5]

The calculations were checked using two separate implementations: floating-point arithmetic and rational arithmetic with high decimal precision. Both return the same variance, the same endpoints within rounding and the same non-acceptance under the illustrative rule.

From the certificate to measurement under conditions of use

The uncertainty on a certificate concerns the calibration result under the conditions described. It may be a fundamental input to subsequent use, but it does not automatically include future drift, installation, environment, operator, sample or the laboratory’s method. Identify which influences change and how to evaluate them without duplicating components already included.

The documentation chain must link the instrument, configuration, corrections and range actually used. If another probe, channel, range or an uncovered configuration is used, reassess the data’s relevance. For the connection to recognised references, see the guide to metrological traceability of laboratory results.

Document, review and improve the budget

A useful budget enables another competent person to reconstruct the result. Retain the measurand, model, inputs, units, source data, distributions, sensitivities, correlations, exclusion criteria, coverage factor and decision rule where applicable. Link calculation tool versions, checks performed, author, reviewer and the assessment’s validity date. [2,3]

• Does the described result match the one used in the decision?
• Does the evidence cover the actual range, configuration and conditions?
• Is each component standardised and expressed in the correct unit?
• Are independence, correlations and exclusions justified?
• Are double counting and inappropriate statistical reductions avoided?
• Are coverage factor, rounding and rule explicit?

Review after method changes, repairs, new conditions, significant precision changes or new evidence. Assign responsibilities and update criteria rather than merely changing the date. To reduce uncertainty, first address the dominant contributions and verify the benefit achieved, instead of increasing the number of repetitions indiscriminately.

The BIPM catalogue now includes the 2026 amendment to the GUM and GUM-5:2026 on examples. A new document should not automatically be presented as replacing the entire framework, and a draft should not be adopted as a final text. The Calibration & Laboratory Metrology hub connects these concepts to operational measurement management. [6]

Sources and limitations

1. JCGM/BIPM. JCGM 200:2012 — International Vocabulary of Metrology, VIM3. Entries 2.13, 2.16, 2.26, 4.14 and 4.15.
2. JCGM/BIPM. JCGM 100:2008 — Guide to the expression of uncertainty in measurement, sections 4–8, to be read with the 2026 amendment. Evaluation, combination, coverage and reporting.
3. JCGM/BIPM. JCGM GUM-1:2023 — Introduction, sections 2–5. Model, information and approach selection.
4. JCGM/BIPM. JCGM 100:2008/Amd.1:2026 — Nonlinearity in measurement models. Final amendment consulted; no advanced formula is reproduced.
5. ILAC. ILAC G8:09/2019 — Guidelines on Decision Rules and Statements of Conformity. Guidance for the ISO/IEC 17025 context, not a universal GMP release rule.
6. BIPM. Official Guides in Metrology catalogue. Publication status verified; GUM-5:2026 examples are neither reproduced nor used in the original case.

Sources verified on 30 September 2026. The budget, checklist and case are original GuideGxP contributions. Simulated numbers do not represent experimental data or regulatory limits.