Optimal attribute sampling plans in closed-forms

Abstract

Lot sampling inspection based on the number of defective units observed in selected random samples is widely used in reliability and quality control. An integer nonlinear programming problem is formulated to determine the most powerful binomial sampling plan for the disposition of large lots with limited producer and consumer risks. An appealing approximation of the optimal test plan is then explicitly deduced. The minimum number of units to be tested per lot in order to achieve the desired protections for manufacturers and customers, as well as the best decision rule for lot sentencing, is derived in closed-form. The procedure is simple, quick and accurate in most practical cases, and clearly improves the classical normal approximation. The suggested perspective allows the practitioners to greatly simplify the determination of the best attribute inspection scheme. In addition, it can be used to find the optimal reliability demonstration test plan based on the number of observed failures in a given time period. The developed methodology is applied to some examples in industrial manufacturing for illustrative and comparative purposes. A useful approximation of the optimal attribute sampling plan with given expected risks is also provided.