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I have a process which produces plastic parts. I have a requirement that states that the weight shall be > x grams. So far I have measured each individual part produced (around 250 pieces) and found that they all lie above the required weight. The distribution seems to be normal with mean µ and standard deviation σ. A cumulative distribution function shows that based on the samples seen 99.9% of the produced parts are expected to have a weight > x grams.

I would now like to move from weighing each individual piece to taking a sample from each batch and measuring that against an acceptance criteria.

I'm having a hard time setting the acceptance criteria and sample size though. I would like to be able to say something along the lines of "There is a > p probability that 99.9% of the population weighs > x grams" based on my sample.

Testing the sample against x does not seem optimal since each sample will give very little information since very few samples if any in the entire batch will fall below it. Intuitively it feels like i should instead test against another limit y which lies higher in weight and were I expect a few in my sample to weigh < y but I haven't been able to find a good paper or instruction on how to set such a limit.

One idea that came to mind was to do a goodness of fit test and see if the sample can be expected to come from the distribution formed by the initial 250 samples but I'm not interested in the actual distribtion. A reduced σ would for example be acceptable. I'm only interested in how many pieces in the population are expected to fall below x grams and with what certainty I can state that.

If anyone could point me in the right direction or suggest a solution to my problem I would be very happy. Thanks in advance!

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  • $\begingroup$ Hi Antti, welcome. This is a well written question. Have you looked into statistical power calculations? en.wikipedia.org/wiki/Power_of_a_test $\endgroup$
    – Fato39
    Commented Oct 13, 2020 at 12:28
  • $\begingroup$ Thank you! I guess one way to phrase my question, if I understand it correctly, is that I want to reject the null-hypothesis "> 0.05% of the population weighs < x grams" with a power of 0.9. But I'm still stumped when it comes to selecting the criteria to test against y, the allowed number of samples with a weight < y and the sample size. I guess one way to look at it is that I want to maximize my efficiency by selecting an appropirate y. $\endgroup$
    – Antti Stålnacke
    Commented Oct 13, 2020 at 12:52

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Further research led me to tolerance intervals described at nist and wikipedia. Tolerance intervals allow me to, based on sampled data, say that p% of the population will have a weight >x with a confidence c which fits my need.

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