Gage R&R Calculator — Crossed Study

About the Gage R&R Calculator — Crossed Study

Analyze a balanced crossed study in which every operator measures every part repeatedly. Crossed ANOVA tests the part-by-operator interaction at your chosen significance level, includes it when significant and otherwise pools it with repeatability. A range-based method provides a separate comparison when you deliberately use that approach. Inspect variance components, percent contribution, study variation, tolerance consumption, distinct categories and the operator range and Xbar charts. No readings are invented to fill an incomplete study.

Variance components

For a parts × operators × trials crossed model, SS(part) = operators × trials × sum((part mean − grand mean)²). SS(operator) is analogous. SS(interaction) = trials × sum((cell mean − part mean − operator mean + grand mean)²), and SS(error) = sum((reading − cell mean)²). Divide each sum by its degrees of freedom.

With interaction retained: repeatability variance = MS(error); interaction variance = (MS(interaction) − MS(error)) / trials; operator variance = (MS(operator) − MS(interaction)) / (parts × trials); part variance = (MS(part) − MS(interaction)) / (operators × trials). Without interaction, its SS and df join the residual and the pooled MS replaces the denominator. Negative estimated components are set to zero and reported. Refer to NIST gauge R&R.

Percentages and discrimination

Total gage R&R variance = repeatability + operator + retained interaction. Total study variance adds part-to-part variance. Percent contribution uses variance/total variance; percent study variation uses component SD/total SD. Tolerance consumption = study multiplier × SD / tolerance width. Distinct categories = floor(1.41 × part SD / gage SD), with a minimum reported value of one. Zero estimated gage variation does not establish a perfect instrument.

Average-and-range estimates repeatability from average cell ranges, operator variation from the range of operator means with a repeatability subtraction, and part variation from the range of part means. The finite-range correction is d2* = sqrt(d2² + d3²/g), for g averaged ranges. It is an approximation without an interaction test.

Limitations

• Estimate — not a professional design or a gage acceptance certificate. Study parts must represent process variation and trials should be randomized.
• Only balanced crossed designs are accepted. Nested studies, missing cells, unequal repetitions and destructive measurements require an appropriate different model.
• The operator range charts and range method use normal-range constants for trial counts 2–25. The range method also requires 2–25 parts and operators.
• The usual under-10%, 10–30% and over-30% study-variation bands are reference guidance, not automatic accept/reject rules. Your customer and intended use decide suitability.
• PDF pages are raster reports. Use Excel or text for selectable text.

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