Tools › Quality › Measurement › Uncertainty Budget › Example

Calibration of a 10 kg weight against a class F2 standard: EA-4/02 uncertainty budget, U = 59 mg, and the ILAC-G8 conformity decision against the class M1 limits

Tool	Uncertainty Budget
Source	European co-operation for Accreditation (2022). Evaluation of the Uncertainty of Measurement in Calibration. EA-4/02 M:2022, example S2; International Organization of Legal Metrology (2004). OIML R 111-1, Table 1; International Laboratory Accreditation Cooperation (2019). ILAC-G8:09/2019, 4.2.2 and Table 1; Joint Committee for Guides in Metrology (2012). JCGM 106:2012, 7.4 and 7.6.
Level	Professional

Problem

A 10 kg weight of OIML class M1 is calibrated by substitution against a class F2 reference standard (10 000.005 g, U = 45 mg at k = 2) on a mass comparator with a pooled repeatability of 25 mg; the drift of the standard is within ±15 mg, eccentricity and magnetic effects within ±10 mg, air buoyancy within ±1 × 10⁻⁶ of the nominal value, and three ABBA observations give a mean difference of 0.020 g. Set up the budget, state the result and decide whether the weight conforms to its class M1 maximum permissible error of ±500 mg with the ILAC-G8 guard-band rule.

Inputs to Enter

Budget rows: m_S 10000.005 g, 0.045 normal k = 2; δm_D 0.015 rect; δm 0.020 g, pooled s 0.025 with n = 3; δm_C 0.010 rect; δB 0.010 rect (all in g)
Coverage 95.45 % (k = 2 for a normal output), k rule t at ν_eff; measured value blank (the model is the sum of the estimates)
Tolerance 9 999.5 to 10 000.5 g (OIML R 111-1 class M1, ±500 mg), decision rule guard band w = U, standard's ± 0.160 g (class F2)

Open the Uncertainty Budget tool (loaded with this example)

Answers

Standard uncertainties 22.5 / 8.66 / 14.4 / 5.77 / 5.77 mg (EA-4/02 S2.9), u_c(m_X) = 29.3 mg, ν_eff = ∞, k = 2.00
m_X = 10 000.025 g, U = 2 × 29.3 = 58.5 → 59 mg (EA-4/02 6.3 rounding): m_X = 10.000 025 kg ± 59 mg (S2.11)
TUR = T/(2U) = 1.0/(2 × 0.0585) = 8.54 (C_m = 8.54), TAR = 500/160 = 3.13; acceptance limits 9 999.5585 to 10 000.4415 g (w = U)
Conformance probability p_c ≈ 1 (z = 16), specific consumer's risk ≈ 0: PASS; the rule's worst-case false-accept probability at an acceptance limit is 2.3 % (ILAC-G8 Table 1: < 2.5 %)
Largest contribution m_S at 59 % of u_c²; U needed for a 4:1 TUR would be 0.125 g

Notes

The tool's default inputs are this example; press Submit. The 2022 edition corrected the S2 drift row to 8.66 mg (the 1999 print had 8.95); u_c and U are unchanged. The conformity part is the tool's addition: EA-4/02 stops at the statement. test_uncertainty_budget.php also reproduces S3, S4, S5, S6, S7, S9, S10, S11 and S13 row by row, GUM H.1, the JCGM 106 and NASA-HDBK-8739.19-4 risk tables.