I am looking at the question of how to sample rare occurances, like a rare defect in a manufacturing line. If I use the standard sample size formula the sample size goes into hundreds, which is unreasonable due to the long waiting times.

My idea s to measure the time intervals between occurences.mThis being continous I can get a much smaller sample size to get the average waiting time between occurences. Knowing the production rate I can even estimate the percentage occurences - thus beating the odds.

Does this make sense?