I took some stats in college, and this is a tip-of-the-tongue problem that I just can't think how to search. If there is an answer to this already, please point me in the right direction.

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

What distribution should be used?

Thanks for all your help!

  • $\begingroup$ 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? $\endgroup$ 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
    Dec 21, 2018 at 0:38
  • $\begingroup$ I think you are referring to the binomial distribution. $\endgroup$ 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
    Dec 21, 2018 at 16:45

1 Answer 1


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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