Gage R&R (%P/T)
Turn repeatability and reproducibility standard deviations into %Tolerance and %Study measurement-system metrics.
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The engineering
Gage R&R asks whether your measurement system is good enough to trust. Repeatability (EV) is one operator repeating a reading on one part; reproducibility (AV) is the spread between operators. Combined in quadrature they give the measurement-system standard deviation, which this card scales by k (6σ captures 99.73% of the spread) and compares against the drawing tolerance.
Two acceptance yardsticks: %P/T judges the gage against the part tolerance — under 10% is good, 10–30% conditional, over 30% reject. %Study judges GRR against the observed total process spread, which matters when your process is tight relative to spec. The ndc (distinct categories) should be ≥5 for the gage to resolve real part-to-part differences; ndc of 1 means the gage can only tell 'in' from 'out'.
Gotcha: %P/T and %GRR are not the same number and can disagree — a capable process (small PV) can pass %P/T yet fail %Study. Report which you used, and remember the legacy AIAG 5.15σ multiplier (99%) reads lower than the modern 6σ; pick one and be consistent across a supplier base.
Where this math comes from
Measurement-system analysis grew out of the same World War II statistical-quality push that gave us control charts, but it was the automotive Big Three who forced it into a standard procedure. Through the 1980s Ford, GM, and Chrysler each ran their own supplier gage studies with incompatible rules, so a supplier shipping all three did the same study three ways.
The Automotive Industry Action Group (AIAG) resolved that in 1990 with the first Measurement Systems Analysis (MSA) reference manual, codifying the average-and-range and ANOVA methods, the %tolerance and %study-variation metrics, and Wheeler's number of distinct categories. The manual is now in its 4th edition (2010) and is the document most QA engineers actually cite when a customer asks for a Gage R&R.
- 1931Walter ShewhartEstablishes statistical control theory underpinning measurement variation analysis.
- 1962Grant & LeavenworthPopularize repeatability/reproducibility study methods in industrial texts.
- 1989Donald WheelerFormalizes the number of distinct categories (ndc) as a discrimination metric.
- 1990AIAGPublishes the first MSA reference manual standardizing Gage R&R across the auto industry.
- 2010AIAGMSA 4th edition — the current pin for %P/T and %GRR acceptance criteria.
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