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

• Published in: Applied statistics 2004-01, Vol.53 (1), p.51-62
• Main Authors: Gasparini, Mauro, Nusser, Harald, Eisele, Jeffrey
• Format: Article
• Language: English
• Subjects: Acceptance sampling; Applications; Bayesian analysis; Bayesian method; Bayesian methods; Binomial distribution; Binomial distributions; Binomials; Biology, psychology, social sciences; Distribution; Distribution theory; Error; Error rates; Exact sciences and technology; False negative errors; False negative results; False positive errors; Inspection error; Inspections; Length bias; Mathematics; Medical sciences; Negative binomial distribution; Pharmaceutical industry; Pharmaceutical preparations; Pharmaceuticals; Pills; Probability; Probability and statistics; Probability theory and stochastic processes; Quality assurance; Quality control; Random variables; Sampling; Sciences and techniques of general use; Sensitivity; Statistical methods; Statistics; Studies
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/j.1467-9876.2004.00425.x

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.