Reevaluating producer's and consumer's risks in acceptance sampling

Abstract

This paper presents improved methods for measuring a consumer's and producer's risk in acceptance sampling. We define Bayesian risks for both the consumer and producer. A Bayesian consumer's risk is defined as the probability that a lot which is accepted will contain more than a designated level of defectives, as opposed to the traditional measure of consumer's risk: the probability that a lot which contains a designated number of defectives will be accepted. A Bayesian producer's risk is defined as the probability that a lot which is rejected will contain less than a specified level of defectives, as opposed to the traditional measure: the probability that a lot which contains a designated number of defectives will be rejected. We conduct sensitivity analyses to examine the response of these risk measures to changes in the probability distribution on the number of defectives in the lot and to the variance of these distributions. We conclude that Bayesian consumer's risk gives better information to the decision maker than does a conventional consumer's risk and should be considered the preferred measure. We give practical equations for assessing these risks.