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Aug 2 at 20:56 answer added jginestet timeline score: 1
Aug 2 at 13:25 comment added EdM There is an extensive literature on statistical aspects of quality control. The US National Institute of Standards and Technology has a useful summary here. Without more details about what you are measuring (e.g., a dimension that needs to be within specifications versus a yes/no failure) and the expected characteristics from pilot studies (as @Glen_b suggested), it will be hard to provide useful help. Please edit the question to make the situation more specific.
Aug 2 at 8:50 comment added Glen_b It might be useful to search for sample size and confidence interval to get an initial sense of the kind of information that would be needed.
Aug 2 at 8:31 comment added Glen_b If you want the standard error of the mean to be smaller than some specific amount, you'd sample $n$ such that $\frac{\sigma}{\sqrt{n}}$ is less than that amount. If you don't know the population standard deviation, $\sigma$ or some good bound for it, but do have some information on the standard deviation from a random sample, you can get a large-sample value for the sample size $n$ that would achieve a kind of probabilistic bound. Similarly you can get confidence intervals of specified width, or a specific margin of error, involving a specific long run probability (across multiple samples)
Aug 2 at 8:15 history asked lincoln80 CC BY-SA 4.0