Gage R&R

Keep the crossed study balanced

Enter the same number of repeated readings for every operator and part combination. Use consistent part and operator identifiers and one measurement unit. The specification width is the full distance between upper and lower limits, not the plus-or-minus tolerance on one side.

Interpret the variation components

The crossed analysis separates components using the implemented ANOVA model, retaining interaction and setting negative variance estimates to zero. A single repeatability percentage is not a complete assessment of bias, linearity, stability, or measurement traceability. Study design and representative parts matter as much as the arithmetic.

Designing readings that answer the question

A repeatability study holds the part and operator fixed so repeated readings can show measurement scatter under those conditions. A crossed study deliberately varies parts and operators while retaining repeated readings for every combination. Missing combinations or unequal repeat counts do not meet this implementation's balanced-study requirement, even if the total number of readings is large.

Choose parts that represent the variation relevant to the measurement task rather than only nearly identical samples. Keep measurement order and operating conditions under control so an unrecorded change is not mistaken for an operator or part effect. The reported percentage relative to tolerance uses the full specification width. A plus-or-minus tolerance must therefore be converted to its complete lower-to-upper span before entry. Variation components estimated as negative are set to zero by the stated model; that is a statistical handling rule, not proof that a source has no variation. Review study design, sample size, bias, and stability alongside the numeric summary.

Formula

Uses a balanced two-factor random-effects ANOVA. σ²repeat = MSE, σ²interaction = (MSinteraction − MSE)/repeats.