EA-4/02

Summary

EA-4/02 — Expression of the Uncertainty of Measurement in Calibration — is published by European co-operation for Accreditation (EA, the body ILAC member accreditation bodies in Europe belong to). Unlike JCGM 100:2008 (GUM), which lays out general uncertainty theory for any field of measurement, EA-4/02 is GUM specialized into a single mandatory policy for calibration laboratories accredited by an EA member: it fixes the specific choices GUM leaves open (which coverage factor to use by default, exactly what sentence a certificate must contain, how many significant figures to round to) so that certificates from different EA-accredited labs are directly comparable. It's freely available and not commercially licensed, unlike the ISO standards in this section.

Sections 2–4 (definitions, Type A/B evaluation, combining uncertainties) restate GUM directly — see ISO/IEC 17025 §7.6 and Standards & glossary for how Open Gauge implements that shared foundation; this page covers only what EA-4/02 adds on top: the specific coverage-factor policy (§5) and the mandatory certificate statement (§6), plus the Best Measurement Capability concept (Appendix A) that's specific to accreditation scopes.

Compliance

Detail

Combining uncertainties

"4.1 For uncorrelated input quantities the square of the standard uncertainty associated with the output estimate y is given by $u^2(y) = \sum_i u_i^2(y)$... If input quantities are known to be correlated, apply the procedure given in Annex D."

Independent Type A (fit residuals) and Type B (reference standard, resolution, sensor spec) contributions are combined by root-sum-square, matching §4.1 directly. The one place Open Gauge tracks a correlation term explicitly is the polynomial fit's own coefficient covariance matrix (poly_coefficients_covariance, per GUM-6 Annex H.3) — needed when the fitted slope and intercept are later used together. What isn't handled is the more general Annex D case: two different input quantities that happen to share a common source (e.g. the same reference standard reused to determine two separate corrections in one calibration) — Open Gauge has no mechanism to declare "these two Type B entries are correlated with coefficient r," so such cases are implicitly (and incorrectly, per Annex D) treated as independent.

Coverage factor policy

"5.1 ...the standard coverage factor k = 2 shall be used [when a normal distribution can be attributed to the measurand and the standard uncertainty...has sufficient reliability]... 5.3 The reliability...is determined by its effective degrees of freedom... the reliability criterion is always met if none of the uncertainty contributions is obtained from a Type A evaluation based on less than ten repeated observations. 5.4 If one of these conditions...is not fulfilled, ...other procedures have to be followed [see Annex E: a t-distribution on the effective degrees of freedom]."

A calibration's distribution_type can be normal (the default — computes the exact normal-ppf factor for the chosen confidence_level, e.g. k≈1.96 at 95%, rather than EA's rounded k=2 shortcut — a stricter, not looser, application of the same ≈95% target), t (uses the Welch-Satterthwaite effective degrees of freedom to pick a Student-t factor — the exact mechanism EA-4/02's Annex E describes for the low-reliability case), or chi_squared. Open Gauge doesn't auto-select between these based on the "fewer than ten observations" rule in §5.3 the way EA-4/02 describes — the operator chooses the distribution — but the underlying math for either branch is implemented correctly.

Certificate statement

"6.1 ...the estimate y of the measurand and the associated expanded uncertainty U shall be given in the form (y ± U). To this an explanatory note must be added...'The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k = 2, which for a normal distribution corresponds to a coverage probability of approximately 95%.' ... 6.3 The numerical value of the uncertainty of measurement should be given to at most two significant figures."

format_expanded_uncertainty_statement() builds the equivalent full-sentence statement — value, combined uncertainty, coverage factor, the distribution basis (normal or t with its effective degrees of freedom), and the resulting confidence level — printed on every certificate that has an uncertainty result, with both $U$ and $u_c$ rounded to two significant figures via round_to_sig_figs() per this clause (and GUM §7.2.6, the same rule).

Best measurement capability

"A1 Best measurement capability...is one of the parameters that is used to define the scope of an accredited calibration laboratory... A10 The best measurement capability should normally be stated numerically."

Gap. Best Measurement Capability (BMC) — the smallest uncertainty a lab can achieve for a given quantity/method/range under routine "nearly ideal" conditions — is an accreditation-scope concept, published by the accreditation body per lab, not computed per calibration. Open Gauge has no structured place to record or display a declared BMC per physical quantity/procedure, distinct from the uncertainty actually achieved on any individual calibration. A lab using Open Gauge would need to track and publish its BMC outside the system today.

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Verified against EA-4/02 (December 1999, rev00) and the Open Gauge codebase (apps/api/app/services/calibration_analysis.py, apps/api/app/utils/uncertainty_format.py, apps/api/app/models/calibration.py) on 2026-07-29.