Test point: spec to certificate

a = Σ terms (or the largest group total for "whichever is greater"); % of X = p/100 × X; ppm of X = q × 10⁻⁶ × X; counts = n × resolution; limits = reading ± a; u = a/√3 (rectangular) or a/k (stated coverage factor)

Term arithmetic from the definitions of each spec term (no standard defines spec notation; read the manufacturer’s datasheet for the basis, period and confidence). Standard uncertainty per JCGM 100:2008 (GUM) §4.3.7 (rectangular bounds) and §4.3.3 (stated coverage factor).

U as entered; no calculation.

Entered by the user from the calibration process uncertainty budget.

TUR = (upper − lower) / (2 × U95); one-sided: TUR = |limit − nominal| / U95; required U95 = (upper − lower) / (2 × target); TAR = tolerance half-width / reference accuracy

TUR as defined in ANSI/NCSL Z540.3-2006 §3.11 (withdrawn by NCSLI in October 2020; still used in contracts and in ANAB’s Z540.3 supplemental accreditation). One-sided handling is Metrology Bench’s stated convention: the distance from nominal to the single limit is used as the half-span, which reduces to §3.11 for a symmetric tolerance. TAR is the older accuracy-spec ratio (MIL-STD-45662A era) and ignores the full calibration process uncertainty.

AL = TL + w, AU = TU − w, w = r·U (simple acceptance: w = 0; specific-risk: w solved so P(out) at the acceptance limit equals the target)

Decision rules and guard bands as described in ILAC G8:09/2019 (§1.7 guard band; §4.1–4.2 simple and guarded acceptance; §5.2 Table 1, w = r·U) and ASME B89.7.3.1; specific risk from a measured value with a normal distribution as in JCGM 106:2012 (cite the documents, do not reproduce them).

P(out) = Φ((TL − y)/u) + Φ((y − TU)/u), u = U/k; conforms per the rule when AL ≤ y ≤ AU

Decision rules and guard bands as described in ILAC G8:09/2019 (§1.7 guard band; §4.1–4.2 simple and guarded acceptance; §5.2 Table 1, w = r·U) and ASME B89.7.3.1; specific risk from a measured value with a normal distribution as in JCGM 106:2012 (cite the documents, do not reproduce them).

PFA = 2∫_T^∞ φ(x; σ_uut)[Φ((A − x)/u) − Φ((−A − x)/u)]dx, PFR = 2∫_0^T φ(x; σ_uut)[Φ((x − A)/u) + Φ((−A − x)/u)]dx; σ_uut = T/Φ⁻¹((1 + EOPR)/2), U = T/TUR, u = U/k, A = T − r·U

Global consumer and producer risk with normal distributions for the UUT error and the measurement error, as in JCGM 106:2012 and the ANSI/NCSL Z540.3 Handbook. 2 % PFA target from ANSI/NCSL Z540.3-2006 §5.3b (withdrawn 2020; still used in contracts and ANAB supplements). Integrals evaluated by adaptive 15-point Gauss–Legendre quadrature; managed guard band solved by bisection.

U rounded to 2 (or 1) significant figures; result rounded to the same decimal place as U; reported U not smaller than the scope CMC.

Reporting policy per ILAC P14:09/2020 (ILAC Policy for Measurement Uncertainty in Calibration) §5.3 (expanded uncertainty to at most two significant digits, usual rounding rules subject to GUM section 7) and §5.5 (reported uncertainty not smaller than the CMC), and JCGM 100:2008 (GUM) §7.2.6 (at most two significant digits; the estimate rounded to match its uncertainty; rounding uncertainty up rather than to nearest is sometimes appropriate). In the superseded ILAC P14:01/2013 these were §6.3 and §6.5. Default rounds U to nearest (half up); rounding U up is an option. Rounding arithmetic is decimal and deterministic.