BAYESIAN SINGLE SAMPLING ATTRIBUTE PLANS FOR DISCRETE PRIOR DISTRIBUTIONS

Abstract

Abstract : The main purpose of the paper was to give a rather complete tabulation and discussion of properties of a system of single sampling attribute plans obtained by minimizing average costs under the assumptions that costs are linear in p, the fraction defective, and that the distribution of lot quality is a double binomial distribution. Starting from a cost function containing 6 parameters and a mixed binomial prior distribution it was shown how the average costs may be written in a standard form containing only two parameters, p sub r and p sub s, besides the parameters defining the prior distribution. The one parameter, p sub r, is the economic break-even quality and depends on the costs of acceptance and rejection only, whereas the second parameter, p sub s also depends on the costs of sampling inspection and the average quality. In a simple and practically important case p sub r and p sub s denote the costs of rejection and the costs of sampling inspection, respectively, divided by the costs of accepting a defective item.

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