Balancing producer and consumer risks in optimal attribute testing: A unified Bayesian/Frequentist design

Abstract

Unified Bayesian/frequentist approaches for the design of attributes sampling plans are introduced by minimizing and limiting a weighted-average of the classical or expected producer and consumer risks adopted by the decision maker. This change of paradigm in the construction of test plans for lot acceptance provides optimal inspection schemes from both frequentist and Bayesian perspectives. Classes of admissible test plans minimizing the weighted-average risks are first defined. Constrained optimization problems are then solved in order to determine sample sizes with smallest classical or expected weighted-average risks, as well as acceptance test plans with minimal inspection effort and controlled risks. The proposed methodology to determine optimal sample sizes and decision criteria for lot sentencing constitutes a plausible consensus between Frequentists and Bayesians. Moreover, the use of prior information on the fraction defective allows the practitioners to appreciably reduce the required sample size for lot screening. Optimal lot inspection schemes can also be easily updated using past performance of the sampling plans. Besides the advantages the suggested approach has for hypothesis testing, namely large sample consistency and reproducible results, it permits to make a trade-off between the opposite goals of customers and manufacturers. Some applications in reliability demonstration testing and industrial quality control are presented for illustrative purposes.