Bob,
Upon reflection, I agree with you that the X-bar R chart is an inappropriate tool for a tool wear situation. I recalled that when tracking 2 critical dowel hole locations that were done on a multiple station drilling/reaming machine that I used a run chart successfully.
The run chart derived from CMM inspection drove 2 activities:
1) The QC department dictated sampling frequencies since we knew that as tools wore that frequency needed to be increased to stop the process before a bad part was produced and yet minimize needless tool changes and downtime.
2) Having tracked both hole positions on the run chart over time we could accurately predict whether a drill, reamer, bushing, or all 3 needed to be changed which minimized machine downtime.
We never bothered to calculate Cpk as we knew that we were drifting across a tolerance range and were using virtually the entire tolerance through the course of a run. As has been noted in Bill's post that violates the first rules of Cpk as a metric as the data is not identically, independently & normally distributed, and is not in a state of statistical control (trend). However, we were able to predict and steer the process.
Thanks for the very good catch!
