Randy,
To be safe, if I were you I would expect to have a ‘part’ for each ‘n’ in the calculation of sigma. Clearly, if n < 15, then Range would be a better estimate of sigma, but the same rule applies: You should expect to choose the Range (Max-Min) from n parts.
When you have a single part and you take multiple measurements, it’s not always safe to assume random independence.
If you agree that your interest is the ‘Form’ of the part, then you could regard this as just another ‘response,’ so your process would comprise two ‘responses,’ the process mean and the process Form (uniformity) of the part. This of course assumes that the process mean bears no relationship to the ‘uniformity,’ which isn’t always the case.
So .. you option is to either use multivariate methods using multiple measurements taken from one part, or use two responses!
Also, you should recall for Shewhart Charts (X-bar and R charts) in order to assess stability, the elements of the subgroup should be taken in the order of production and from a single stream, as this is a condition known as rational subgrouping. If you agree then it is obvious that we should not form subroups from multiple measurements taken from a single part.
This is why Motorola waferfabs used Multi-vari charts in the mid-1980s, much to the chagrin of quality management, Later, when we started using IBM PCs to manufacture 6800 microprocessors for Macintosh, we incoporporated Hotelling’s T-squared into the Multi-vari Chart.
Good luck!
Andy
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