Comment on: Determining Sample Size When Searching for Rare Items

Reliability and safety engineers must frequently search for rare items, often as part of a compliance sampling program intended to assure a good population of items. In this setting, Madsen & Holstein have provided a formula for approximating the minimum sample size to find at least one nonconforming item. They also indicate that the approximation is conservative in the sense that it may provide slightly larger sample sizes than actually required. This may lead the engineer, especially in situations where sampling costs are high, to wonder by how much the approximation errs on the conservative side. This note presents bounds on the minimum required sample size and shows that, when the number of nonconforming items in a population is small,the Madsen & Holstein approximation is very close.