Re: p-Value(s) for Anova (Crossed) GRR (Gage R&R) Studies
I love this question. This is the first NEW MSA question that I have seen in a long time.
To start, the current MSA methodology as defined by AIAG, endorsed by the automotive industry and codified by the statistical software companies totally ignore the p-values with one exception.
That exception is for the Operator x Part interaction. In Minitab, if the Op x Part interaction p-value is greater than 0.25 (default value), the interaction is then pooled with the ANOVA error term thus becoming part of Repeatability. If it is less than 0.25, it is shown separately as a sub-item under Reproducibility. Why 0.25? Minitab says to stay consistent with AIAG. AIAG wanted to be extremely conservative about pooling the interaction in error.
Technically, if the Reproducibility p-value is greater than alpha (usually 0.05), it also should be pooled into the error term becoming part of Repeatability. It is only when it is less than alpha that Reproducibility can be distinguished from Repeatability. However, AIAG is silent on this matter and the canned MSA routines in software do not allow it. To do it yourself, you would have to run the standard ANOVA routines and manually generate the graphs.
The p-value for Parts also provides information. If the p-value of Parts is greater than alpha, the part variation is indistinguishable from Repeatability variation. If the p-value is less than alpha, the gage can distinguish at least one part as different from the rest. Not definitive that the gage is good (p < alpha), but conclusive that it is not good (p > alpha).
Thank you for this question.