Producer's and Consumer's Risk When Proportion Defective Is a Random Variable

Abstract

ABSTRACTIn acceptance sampling, producer's and consumer's risk are traditionally based on assumed fixed values of p, the proportion of the lot which is defective. A more useful definition of producer's risk would be the probability of rejecting a lot in which the proportion defective falls within some range of acceptable values. Similarly, a more useful definition of consumer's risk would be the probability of accepting a lot in which the proportion defective falls within some range of unacceptable values. In this paper, we construct measures of these more useful definitions of risk by assuming that p follows either a uniform or triangular probability distribution. The proposed measure yields consumer's risk values, β', which are smaller than the traditionally computed values by a factor of up to twenty times. The proposed measure of producer's risk, α', gives values smaller than traditional values by a factor of two to four times. Decision makers who adopt the proposed measures may be able to reduce sample sizes substantially while maintaining given risk levels.