Multi Cavity Sampling Plan
Scott,
First of all, I am not sure why your customer is doing the analysis on just 20 pcs. 30 pcs is the very minimum, without using students-t. The estimate of capability increases with the sample size. This is unless there is something I am not aware of. If so, someone please explain.
Secondly, the process capability can not be evaluated by sampling parts produced off of different manufacturing processes and considering them as one. Each cavity, set when it was cut and limited only to tool wear, produces an unique mean and distribution. Individually, this cavity may produce a capable product over and over again for the long-term. Thats what the customer is interested in - statistical evidence that the process is stable and not outputting nonconforming material. If the capability indices suggest that each cavity individually meets this requirement, then there should be no problem. Data generated from randomly sampled product mixed with different cavities could result in a standard deviation calculation that suggests a process that is not capable. See attached. The resulting distribution could be non-normal for which the statistics are invalid. Using the averages from subgroups may smooth it out and appear to produce a more normal distribution, but I don't think this is correct to do either. It is my understanding that statistics can only be applied to data from the same population or process. Each cavity will produce its own unique distribution or population. Unless I am wrong here, it is my opinion that your customer needs to be shown the data and convinced he is receiving good product. I would not back down from this especially if you believe the parts are good and a number such as 1.33/1.67 is being misunderstood. Looks like an opportunity for an annual visit to the customer.
Regards,
Chemman