Enhanced Lot Acceptance Testing Based on Defect Counts and Posterior Odds Ratios

Abstract

Optimal defects-per-unit test plans based on posterior odds ratios are developed for the disposition of product lots. The number of nonconformities per unit is modeled by the Conway–Maxwell–Poisson distribution rather than the typical Poisson model. In essence, a submitted batch is conforming if its posterior acceptability is sufficiently large. First, a useful approximation of the optimal test plan is derived in closed form using the asymptotic normality of the log ratio. A mixed-integer nonlinear programming problem is then solved via Monte Carlo simulation to find the smallest number of inspected items per lot and the maximum tolerable posterior odds ratio. The methodology is applied to the manufacturing of paper and glass. The suggested sampling plan for lot sentencing provides the specified protections to both manufacturers and customers and minimizes the needed sample size. In terms of inspection effort and accuracy, the proposed approach is virtually an advantageous extension of the classical frequentist perspective. In many practical cases, it yields more precise assessments of the current consumer and producer risks, as well as more realistic decision rules.

Keywords

• industrial quality control
• acceptance sampling
• Bayesian statistics
• mixed-integer nonlinear programming
• Conway–Maxwell–Poisson distribution
• Monte Carlo simulation