Gage R&R: ANOVA vs average and range method
Short answer
The average and range method (X̄ & R) estimates repeatability from the ranges of repeated measurements and reproducibility from the differences between operator averages, using d₂-type constants. It is simple to calculate by hand. The ANOVA method uses an analysis of variance on the same data, gives more precise estimates and also shows the operator × part interaction, for example when one operator measures small parts differently. AIAG accepts both; ANOVA is preferred when software is available.
Side by side
| Aspect | Average and range (X̄ & R) | ANOVA |
|---|---|---|
| Calculation | Ranges, averages and constants (K1, K2, K3) | Two-way analysis of variance |
| Interaction operator × part | Not detected, hidden in the other terms | Estimated and tested |
| Precision | Lower, ranges use less information | Higher |
| Effort | Possible on paper or in a simple spreadsheet | Needs software |
| Typical results | %GRR, %EV, %AV, ndc | The same plus interaction p-value and variance components |
Will the results differ?
For most studies the two methods give similar %GRR. They differ when there is a significant operator × part interaction, or when the number of operators is small. If ANOVA shows a significant interaction, look at the interaction plot before accepting the gauge: it usually points to a method problem, such as different clamping or reading of the part.