Gauge R&R (Average & Range)
Measurement system study from operators × parts × repeat readings: repeatability, reproducibility, GRR, part and total variation, % of study, ndc.
EV, AV, GRR, PV and TV with their percentages, %GRR against a tolerance when given, ndc, and the operator and part means — the average-and-range method with the constants it uses stated.
Example: Two operators, three parts, two trials: R̄ 0.10, operator spread 0.167, part range 2.6 → EV 0.089, AV 0.143, GRR 0.168 (10.9 % of TV, 33.7 % of a tolerance of 3), ndc 12.
How much of the spread
is the gauge?
The average-and-range method step by step, the constants it uses, and what the percentages mean.
Repeatability and reproducibility
Each operator measures each part several times. Repeatability (EV) comes from the average range of those repeats divided by d2 for the number of trials — the spread of the gauge itself. Reproducibility (AV) comes from how far the operators’ averages sit apart, divided by d2 for the number of operators, with the repeatability share removed under the root. GRR = √(EV² + AV²).
Part variation and the percentages
Part variation (PV) is the range of the part averages ÷ d2 for the number of parts; total variation TV = √(GRR² + PV²). %GRR is GRR ÷ TV (and, when a tolerance is given, GRR × 6 ÷ tolerance). ndc = 1.41 × PV ÷ GRR estimates how many distinct groups the gauge can separate in the parts measured.
Constants and limits
d2 is the range-to-sigma constant for a sample of that size (Duncan / ASTM). AIAG’s MSA manual uses d2*, which depends on how many subgroups fed the range and approaches d2 as that number grows — the difference is a few percent for a small study. Whether a %GRR is acceptable is your customer’s rule; the ANOVA method (with an operator × part term) is a different calculation. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Average-and-range GRR: EV = R̄/d2, AV = √((X̄diff/d2)² − EV²/(n·r)), PV = Rp/d2, TV = √(GRR² + PV²), ndc = 1.41·PV/GRR with the d2 range constants (Duncan / ASTM); no acceptance limit embedded
Last reviewed 21 September 2026. How results are checked: How we verify.