Bayesian Variables Acceptance-Sampling Plans: Quadratic Loss Function and Step-Loss Function

Abstract

In developing quality-control procedures, a step-loss function has been used implicitly or explicitly to describe consumer perceptions about product quality. A quadratic loss function has been suggested by Taguchi as an alternative to the step-loss function in measuring the loss due to imperfect product quality (cost of acceptance). In this article, Bayesian analyses of the known-standard-deviation acceptance-sampling problem are described for both the step and quadratic loss functions with three cost components—cost of inspection, cost of acceptance, and cost of rejection. A normal prior distribution is used for the lot mean. Efficient procedures for finding minimum expected cost procedures are given. For a particular example, comparisons are made of how optimal sampling plans and costs computed under the two cost structures change as the form of the prior distribution and misspecification of its mean and variance are varied. Sensitivity analyses for both cost functions show that the optimal sampling plan is robust with respect to the form of the prior distribution, as well as to misspecification of its mean and variance, if the tail specification reasonably approximates that of a normal distribution.

KEY WORDS:

• Bayes rule
• Prior distribution
• Quality costs