Optimal lot disposition from Poisson–Lindley count data

Abstract

Optimal sampling plans based on overdispersed defect counts for screening lots of outgoing and incoming goods are derived by minimizing the required sample size. Best inspection schemes provide appropriate protections to customers and manufacturers. The stochastic distribution of the number of defects per sampled unit is described by Poisson–Lindley models. Optimal frequentist and Bayesian decision rules for lot disposition are found by solving mixed integer nonlinear programming problems through simulation. The suggested criteria are based on likelihood and posterior odds ratios. The asymptotic normality of the quality score statistic is used to deduce explicit and reasonably accurate approximations of the optimal acceptance sampling plans. The Bayesian approach allows the practitioners to reduce the needed sample size for sentencing lots of high-quality products. For illustrative purposes, the proposed methods are applied to the manufacturing of copper wire.