Gage R&R by ANOVA: Two-Way Crossed Design
What is the Difference Between ANOVA and Xbar-R?
The ANOVA (analysis of variance) method is based on a two-way crossed design in which parts and operators are the two factors and repeated measurements fill each cell. It decomposes total variation into part-to-part variation PV, operator variation AV, the part-by-operator interaction and repeatability EV. Compared with the Xbar-R method, ANOVA estimates the interaction separately, handles unbalanced data, and is the complete method recommended by AIAG MSA 4th edition.
When to Use It
Use ANOVA when a full MSA study is required, when the part-by-operator interaction must be estimated, or when the data are unbalanced. It is also preferred when results will be audited and a complete variance component table is expected. For destructive measurements where parts cannot be remeasured, use a nested GRR design instead of the crossed design.
How to Use It (Step by Step)
Prepare the data in three columns: part number, operator and measurement, with the typical 10 parts × 3 operators × 3 trials layout or any unbalanced repeat counts. Paste the data and the tool outputs the variance component table, interaction F-test, %GRR, %P/T and ndc. The tool also interprets the significance of the interaction and whether the model can be simplified.
Key Formulas / Example
Total variation decomposes as TV² = PV² + AV² + Interaction² + EV², and GRR² = AV² + Interaction² + EV², with interaction counted into reproducibility per AIAG practice. ndc = 1.41 × (PV/GRR) should be 5 or more. Acceptance follows the same %GRR thresholds as the Xbar-R method: below 10% acceptable, 10-30% conditional, above 30% unacceptable.