Some recent findings in bayesian attribute single and double sampling

Abstract

Abstract This article deals with several items, including theoretical and applied results. Specific topics include (1) a discrete, economically based, attributes acceptance sampling model and its adaptations, (2) relevant costs, (3) relevant prior distributions, (4) comparison of single‐ and double‐sampling results, and (5) reasons for marginal implementation success following excellent implementation efforts. The basic model used is one developed by Guthrie and Johns; adaptations include provisions for fixed costs as well as modifications to permit double sampling. Optimization is exact, rather than approximate. Costs incorporated into the model are for sampling inspection, lot acceptance, and lot rejection. For each of these three categories a fixed cost is included as well as two variable costs, one for each item and the other for each defective item. Discrete prior distributions for the number of defectives in a lot are used exclusively. These include the mixed binomial and Polya distributions. Single‐ and double‐sampling results are compared. Double sampling regularly performs at only slightly lower cost per lot than single sampling. Also, some cost and prior distribution sensitivity results are presented. Comments are provided regarding actual implementation experiences in industry. Practical deficiencies with the Bayesian approach are described, and a recommendation for future research is offered.

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