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Repeated screening with inspection error and no false positive results with application to pharmaceutical pill production
Author(s) -
Gasparini Mauro,
Nusser Harald,
Eisele Jeffrey
Publication year - 2004
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2004.00425.x
Subject(s) - bayesian probability , statistics , mathematics , set (abstract data type) , pill , production (economics) , quality (philosophy) , posterior probability , computer science , medicine , economics , pharmacology , philosophy , epistemology , macroeconomics , programming language
Summary. 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.