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My problem fits well in an analogy of auto manufacturing: There are hundreds of populations (different component) with varying population sizes (say only a few hundred for the wheels for a supercar, to hundreds of thousands for the gas tank that is used in every model). We would like to classify the parts into defective or not-defective. The defect rate will be low, varying maybe from $0\%-10\%$ depending on the part.

Knowing this, how many parts should you sample before you can conclude

  1. $\text{x}\%$ probability that this component population is defect-free? or
  2. $\text{x}\%$ probability that this component's population defect rate falls within some (small) range?

What distribution should be used?

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  • $\begingroup$ I don't think it makes much sense to ask "what is the probability that this part is defect-free" unless your measuring equipment is imprecise. Is it not the case after a measurement is taken, that it will be determined if the individual unit is defect free? $\endgroup$
    – StatsStudent
    Commented Dec 21, 2018 at 0:31
  • $\begingroup$ You are correct, I have edited for clarity - for population, rather than individual part. Measuring equipment would be 100% accurate for all intents and purposes in determining whether a unit is defective or not. $\endgroup$
    – tuxtuxtux
    Commented Dec 21, 2018 at 0:38
  • $\begingroup$ I think you are referring to the binomial distribution. $\endgroup$
    – user2974951
    Commented Dec 21, 2018 at 9:03
  • $\begingroup$ Looking at this: statisticshowto.datasciencecentral.com/… it looks like I should use a Poisson distribution to model? I could use a normal approximation only if both n * p and n * (1-p) are large, which does not hold true since I have few defects. $\endgroup$
    – tuxtuxtux
    Commented Dec 21, 2018 at 16:45

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I used Wilson Score with Continuity Correction to model, using the Rule of Three to account for samples without a defect.

Links here:

Wilson Score

Rule of 3

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