Measurement Uncertainty Calculator

What it does

Turns a measurement result into an auditable uncertainty budget ready for accredited reporting. Five frameworks are applied in sequence:

1. GUM — JCGM 100:2008 (backbone). A measurement model Y = f(X₁…Xₙ) is built; each input's standard uncertainty u(xᵢ) and sensitivity coefficient cᵢ = ∂f/∂Xᵢ feed the combined standard uncertainty via the GUF (first-order Taylor): u_c²(y) = Σ(cᵢ·u(xᵢ))² (+ covariance term if correlated).
2. Type A vs Type B (GUM §4.2-4.3). Type A = statistics of repeated observations (u = s/√n); Type B = certificate, spec, resolution, handbook. The correct bin is the #1 determinant of budget accuracy.
3. VIM — JCGM 200:2012. Terminology anchor (measurand, traceability, trueness vs precision) — catches the "error ≠ uncertainty" traps.
4. Welch-Satterthwaite (GUM Annex G). Effective degrees of freedom ν_eff → coverage factor k. k=2 is never automatic; for low ν it is corrected from the Student-t table. U = k·u_c.
5. Decision rule — ILAC-G8:2019 / ISO 14253-1. Conformity statement using guard band w = r·U and PFA (false-accept target ~2-5%); ISO/IEC 17025 §7.8.6 makes this mandatory.

Output: the uncertainty budget table (with a %-contribution Pareto surfacing the dominant source), y ± U (k, ≈95%), traceability + correlation audit, a PASS/CONDITIONAL conformity statement and a 0-100 Compliance/Reliability score. Optional Monte Carlo (JCGM 101) cross-check for non-linear models.

When to use

• When a calibration/test result needs an uncertainty budget (to print x ± U (k=2) on a certificate).
• When auditing an existing budget (missing source, wrong distribution, wrong k, conformity stated without U).
• Before an accreditation application / CAB assessment, in the CMC (Calibration & Measurement Capability) check.

Method / frameworks

GUM (JCGM 100:2008 / ISO/IEC Guide 98-3), GUM Supplement 1 (JCGM 101, Monte Carlo), VIM (JCGM 200:2012), ISO/IEC 17025:2017 §7.6/§7.8.3/§7.8.6, EA-4/02 M:2022 (worked-example canon, CMC), ILAC-G8:2019 and ISO 14253-1 (guard band, shared/non-shared risk), the Welch-Satterthwaite equation. Distribution divisors are standard (normal→k, rectangular→√3, triangular→√6, U-shaped→√2) and justified per row. Approximate figures are flagged as "typical range"; missing data (U_ref, n, resolution) is never invented — it is written to gaps and requested.