Optimal designs with different risk criteria in attribute acceptance sampling

Abstract

In this paper, a study was conducted on the optimal design of acceptance sampling by attributes as a sample survey method for quality control of the manufacturing industry. Acceptance sampling by attributes is a sampling method in which when a products are produced in units of lots, a sample is taken from each lot, examined, and then a lot is judged to be accepted or rejected according to the number of defective products detected. Traditionally, the optimal design was found using producer's risk and consumer's risk defined by fixing the fraction defective to a specific value, but it has the disadvantage that the number of samples required becomes very large when the fraction defective is very low. Therefore, in this study, an optimal design was based on the average risk and Bayesian risk defined by assuming uncertainty in the fraction defective, and the sensitivity according to the prior distribution was investigated. The optimal design with the new risk has the advantage of controlling the same level of risk with a smaller number of samples, and Bayesian risk has resulted in more inelastic results for prior distributions.