The “Coupon Collector's Problem” and Quality Control

This article examines the classical “coupon collector's problem” and applies several key results to certain problems in quality control sampling. It is shown how solutions to the coupon sampling problem are readily adaptable to industrial sampling problems where the intent is to sample at least 1 of k specific product unit types in a well mixed stream of product where the product unit is equally likely to be any of the k specific types. Several variations on this theme are presented. Theoretical formulas are developed and applied to quality control sampling. Additional applications involving Monte Carlo simulation using the freeware programming language “R” are also illustrated.