Three Types of Producer's and Consumer's Risks in the Single Sampling Plan

Abstract

The classical producer's risk and the classical consumer's risk are defined in acceptance sampling based on the assumption that the proportion defective of incoming lots is a constant. This assumption has been a focus of much of the criticism of acceptance sampling in recent years. In this paper, we assume that the proportion defective is a random variable that follows a beta distribution, and we derive the modified producer's risk and the modified consumer's risk. We also derive the Bayes producer's risk and the Bayes consumer's risk. In addition, we clarify the relationships of the modified and Bayes risks with the classical risks.