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Single sampling plans for attributes satisfying an arbitrary set of constraints—A graphical approach

Kouikoglou Vasilis

Πλήρης Εγγραφή

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Περίληψη

In this paper we present a solution to the problem of determining a single sampling plan, using Larson's Nomograph of the binomial distribution. The problem consists of deciding whether a lot of items will be accepted or rejected, by inspecting a sample of specified size n drawn from the lot. The lot is rejected if the number of bad iterms in the sample is greater than a specified threshold c, otherwise the lot is accepted. The classical procedure for determining a single sampling plan (n,c) is to specify the maximum acceptable probabilities of Type I and Type II errors. Next one expresses these errors in terms of n and c by using the binomial approximation to the hypergeometric distribution. Finally, the pair (n,c) is read at the intersection of the characteristic lines which correspond to the specified maximum error probabilities in the Nomograph. Here, we show that there is a region of plans in the Nomograph which satisfy the error constraints, rather than a single plan. Then we generalize the procedure to problems with an arbitrary number of constraints involving both error types.

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