Diagnosing ANOVA‐Based Gauge R&R Models: Why Raw Measurements and Model Residuals Provide Different Information

ABSTRACT Gauge Repeatability and Reproducibility (Gauge R&R) studies are widely used to quantify measurement system variability. When variance components are estimated using Analysis of Variance (ANOVA), the validity of the results depends on assumptions concerning the fitted model and its error term. However, many practical implementations rely on the raw measurements, which contain the combined effects of parts, operators, interactions, and measurement error. Consequently, diagnostics performed on raw measurements do not necessarily provide direct evidence regarding ANOVA assumptions. This study investigates how diagnostic conclusions depend on whether analyses are performed on raw measurements or on ANOVA residuals. Monte Carlo simulations evaluate seven normality tests under different experimental designs, variance‐component scenarios, and residual distributions. Two illustrative datasets complement the simulations and demonstrate situations in which raw‐data and residual‐based diagnostics lead to different conclusions. Graphical methods, including Q–Q plots, boxplots, control charts, and an exploratory GLRAM‐based biplot, are also examined. The results show that normality tests applied to raw measurements characterize the marginal distribution of observed responses, which includes part, operator, interaction, and measurement‐error effects, whereas residual‐based diagnostics directly assess model assumptions. The study supports a two‐stage diagnostic strategy: raw measurements should be explored to understand measurement‐system behavior, while model residuals should be analyzed to assess the adequacy of the fitted ANOVA model.