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How can you estimate the confidence interval around the total Gage R&R standard deviation and therefore the % error. I have situation where I have to use a fewer samples and would like to know how to quantify the effects. I also alway get asked the uncertainty of the %error number when stated and am not sure what to say. Many thanks.

As this post has been here for 2 weeks and no one has replied it is clearly a tricky question. None of the mainstream statistics packages, Minitab, JMP etc., that I am aware of address the question. So let me have a go. My approach is the following.

Repeatability is relatively straightforward and comes from the ANOVA table. We have operators x parts x (replicates-1) degrees of freedom, the MSE gives the variance of repeatability and the standard chi squared calculation gives us confidence limits on a variance.

The tricky bit is reproducibility and as this gets summed to repeatability it also affects the whole R&R figure. As we rarely use the more than 3 operators the degrees of freedom on reproducibility is very small and the confidence limits are rather wide. The conversion of numbers of operators into df is not simple apparently but however many parts and replicates you use the calculation never gets very far from the number of operators. Professor Vardeman , Iowa State University, kindly publishes some lecture notes on the web which gives a method of doing this. (A Google search will find them.)

However for the case of reproducibility (and reproducibility only) I don’t think confidence limits get us very far. We are dealing with human operators and when you allow for Fred who has never had his eyesight tested and Joe who thinks the gauge operating instructions are nuts and his way is much better we have to test every operator. I don’t think the ANOVA assumptions are valid when considering the strange ways of humans. You only need one maverick operator and your whole system falls down.

So my suggestion is: Do the gauge R&R and assess the confidence interval from the ANOVA table. This tells you how well this gauge can perform. If the answer is satisfactory then repeat the R&R with every operator on a regular basis to see if they are following the standard method. If you find a really good operator get the other operators to do what he does. If you find a really bad operator retrain him. Once you have tested everyone confidence limits for reproducibility don’t come in to it. We know; we have a 100% sample.