The expanded uncertainty value stated in a calibration certificate is not a footnote. It is the figure that determines whether that calibration is fit for purpose in the operational context in which the instrument is used. Yet, in everyday practice, it is the value most frequently overlooked: the date is checked, the signature of the accredited body is verified, the document is filed. The uncertainty remains a number devoid of context.
This gap has concrete consequences: during an audit, measurement uncertainty is the first technical element that a qualified inspector examines. A certificate that states an uncertainty value not traceable to national or international standards, or that does not declare the coverage factor used to calculate it, is not a valid certificate for regulatory purposes, regardless of who issued it.
What measurement uncertainty represents
The expanded uncertainty is a parameter that quantifies, at a defined level of confidence, the half-width of the interval centred on the measured value within which a significant proportion of the values plausibly attributable to the measurand are assumed to lie.
The normative reference for the evaluation and expression of uncertainty is the GUM — Guide to the Expression of Uncertainty in Measurement (JCGM 100:2008), adopted by all laboratories accredited to ISO/IEC 17025:2017. It is the document that defines the language with which uncertainty is calculated, propagated, and communicated in the certificate.
Standard uncertainty and expanded uncertainty
Calibration certificates issued by accredited laboratories state the expanded uncertainty U, not the standard uncertainty u. The distinction is operational: the standard uncertainty is the experimental standard deviation of the probability distribution associated with the measurement; the expanded uncertainty is obtained by multiplying the standard uncertainty by a coverage factor k, yielding an interval with a defined level of confidence.
The most widely used value is k = 2, which corresponds to a confidence level of 95.45 % for a normal distribution. This means that the true value of the measured quantity lies within the interval [measured value − U, measured value + U] in 95.45 % of cases.
How to read the notation in the certificate
In the calibration certificate, the result is typically expressed as:
Measured value: X [unit of measurement]
Expanded uncertainty: U = ± Y [unit of measurement] (k = 2)
This notation must be read as a whole. The value Y has no independent meaning unless accompanied by the factor k and an indication of the confidence level. A certificate that states only “uncertainty: ±0.5 °C” without specifying k and the confidence level is incomplete and does not comply with the requirements of ISO/IEC 17025:2017.
Measurement uncertainty and process tolerances: the question that matters
The uncertainty figure in the certificate answers a specific question: is this calibration fit for use in my process?
The answer requires a comparison of the expanded uncertainty with the operational tolerances of the instrument in its context of use.
The tolerance-to-uncertainty ratio
The technical reference criterion is the tolerance-to-uncertainty ratio (TUR — Test Uncertainty Ratio). The principle is that the uncertainty of the calibration process must be significantly smaller than the tolerance of the instrument under test. The commonly accepted ratio is 4:1, which means that the expanded uncertainty of the calibration must be at most one quarter of the permissible tolerance of the instrument.
Applied example: a thermometer with a process tolerance of ±2.0 °C requires a calibration with expanded uncertainty U ≤ ±0.5 °C (k = 2) to satisfy the TUR 4:1. If the certificate states U = ±0.8 °C, the calibration does not meet the metrological criterion, regardless of the laboratory’s accreditation.
When process tolerances are not defined
In some operational contexts, process tolerances are not explicitly documented, particularly in environments where regulatory requirements define monitoring limits but do not specify the metrological adequacy criteria for the instruments used. In such cases, the QA manager is required to define tolerances based on applicable regulatory limits and to document the metrological rationale that justifies the selection of instruments employed.
In regulated sectors — pharmaceutical, clean rooms classified to ISO 14644-1:2015, medical devices — this assessment forms part of the quality management system and is subject to verification during audits. The absence of a documented metrological adequacy criterion is a detectable non-conformity.
Metrological traceability: a necessary condition, but not sufficient
A calibration certificate is valid for regulatory purposes only if the stated uncertainty is traceable to the national or international metrological chain. ISO/IEC 17025:2017, clause 6.5, requires accredited laboratories to ensure the traceability of measurement results to SI (International System of Units) standards through an unbroken chain of comparisons with stated uncertainties.
A laboratory accredited by an accreditation body signatory to the ILAC MRA guarantees this traceability by definition. A certificate issued by a non-accredited laboratory does not offer this guarantee and cannot be considered equivalent for regulatory purposes.
Measurement uncertainty during audits: what is verified
GMP inspectors, certification body audit teams, and accreditation body assessors verify measurement uncertainty against precise criteria. The most frequently checked aspects concern:
- the presence of the expanded uncertainty value, with an indication of the coverage factor k and the confidence level;
- the traceability of the reference instruments used by the laboratory;
- the demonstration that the uncertainty is compatible with the process tolerances defined in the quality management system;
In the pharmaceutical GMP environment, EU GMP Annex 1 (2023 revision) and the ISPE Good Practice Guide on Calibration Management both emphasise that the metrological management of measuring instruments must be documented in such a way as to enable the assessment of metrological adequacy at every stage of the instrument’s life cycle. Measurement uncertainty is an integral part of this documentation.
What to do if the uncertainty in the certificate is absent or incomplete
A certificate that does not state the expanded uncertainty, or that states it without specifying the coverage factor, does not comply with the requirements of ISO/IEC 17025:2017. In such cases, the actions to be taken can be clearly defined:
- request a revised, compliant certificate from the issuing laboratory, with explicit indication of U, k, and confidence level;
- verify whether the laboratory is accredited and whether the accreditation covers the type of calibration in question (the scope of accreditation is publicly available on the relevant accreditation body’s website);
- do not use the incomplete certificate as compliance documentation during an audit or instrument qualification;
- document the non-conformity in the quality management system and initiate the selection procedure for an alternative accredited laboratory.
For a technical assessment of the metrological adequacy of calibration certificates currently in use, as well as for the verification of their compliance with the regulatory requirements of the process, the Altiorlab team is available to provide technical consultancy.
