Pardon my comments and please ignore if you prefer. Perhaps I don't understand your situation, but doesn't your situation (CPV) call for analytical statistical thinking, not enumerative (see Deming, W. Edwards (1975), On Probability As a Basis For Action. The American Statistician, 29(4), 1975, p. 146-152)? I suppose your concern for normality is because you want to use the appropriate estimates for central tendency and variation? I would think what you want is a sample that appropriately represents the central tendency and variation of the API of the process for the period of time you are assessing (over the variables in the process that change during that time period). How you sample the process can have a huge effect on conclusions you draw about the process central tendency and variation. I realize I may be in the minority here, but a sample size of 30 seems quite arbitrary. Consider these possible hypothetical situations:
- 30 samples randomly taken from the process making batches over multiple shifts and lots of raw material
- 30 samples from 1 batch, 1 shift and 1 lot of raw material
- 30 samples, 3 samples from 10 batches and 1 shift
- 30 samples, 1 sample from 30 consecutive batches over 3 shifts
- 30 samples, 1 from 30 batches, 10 batches from each of 3 lots of raw materials
- 30 samples, each sample measured 3 times for 10 batches
Each may give completely different estimates of mean and variation. Each will confound or separate different components of variation.
From the above referenced paper:
“Analysis of variance, t-test, confidence intervals, and other statistical techniques taught in the books, however interesting, are inappropriate because they provide no basis for prediction and because they bury the information contained in the order of production. Most if not all computer packages for analysis of data, as they are called, provide flagrant examples of inefficiency.”
"All models are wrong, some are useful" G.E.P. Box