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I have a large (N) list of results from a process that is either positive or negative. After examining X of them and receiving only positive results, how certain can I be that the list only contains positive results (with probability P)?

Context: I'm processing the results (between several thousand and several billion) of a process and am given a list of values that take a few seconds each to evaluate as passing/failing. I only need to be reasonably certain that everything passed to pass the batch for most jobs. For some jobs, 100% certainty is necessary, and they'll all need to be checked. For the others, how many do I need to check to be P% certain that there are no fails?

gung - Reinstate Monica
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user20238
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  • I think this answer (specifically the second bullet point for $\hat{p}=0$) gives you a 95% confidence interval that answers your question - as well as a literature reference: http://stats.stackexchange.com/a/6184/1352 – Stephan Kolassa Jan 29 '13 at 19:03
  • You'd need some assumptions about the time-dependence and how the process changes over time. Without some model, you can't really do it. – Glen_b Jan 29 '13 at 22:58
  • For an answer to a question that is formally similar to yours, see: http://stats.stackexchange.com/questions/47286/determining-the-probability-that-two-functions-produce-the-same-outputs-when-no/47338#47338 – Arthur Small Jan 30 '13 at 02:35

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