In this situation there is no "correct" way of choosing Xbar-R and Xbar-S, they are both wrong. The variation within subgroups is comprised of three components of variation: short term randomness, "long term" trends and occasional special cause unpredictable spikes. There are no control charts that are correct for this situation. There is only advanced modeling, which in the end might be appropriate. However, in this situation with this product under these conditions, range charts have demonstrated their capability at being better at detecting data having spikes, S charts are too sensitive and cause over-reaction.
I simply wanted to know the math. Had I more skills at JMP help I could have avoided the help forums. I feel offended at having to defend myself just in order to ask a question about how something works. If you look at the responses I got to my question, more than half the people were telling me I was doing something wrong without offering any insight into an answer. That borders on trolling, and is more like Reddit than it is a professional help forum. Only two people contributed something toward answering my actual question.
Try to give someone the benefit of the doubt and don't immediately assume that because I am breaking some guidelines I am therefore incompetent and am some sort of heretic. I wasn't asking an applicaiton question, I was asking a question about the formulas.
There was one person that was curious about why n=475, as opposed to the multitude that said I should do Xbar-S. Xbar-S is also wrong, but in the face of opposition I can't be bothered to elaborate.
