Repeated screening with inspection error and no false positive results with application to pharmaceutical pill production

Repeated screening is a 100% sampling inspection of a batch of items followed by removal of the defective items and further iterations of inspection and removal. The reason for repeating the inspection is that the detection of a defective item happens with probability p < 1. A missed defective item is a false negative result. The no false positive result is contemplated in this paper, which is motivated by a problem coming from the production of pharmaceutical pills. Bayesian posterior distributions for the quality of the lot are obtained for the case of both p known and p unknown. Batch rejection and batch acceptance control limits for the number of defective items at subsequent iterations can then be calculated. Theoretical connections to the problem of estimating the number-of-trials parameter of a binomial distribution are drawn.