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Sufficient conditions for optimality of a (z, c−, c+)-sampling plan in multistage Bayesian acceptance sampling

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Summary

A (z, c−, c+)-sampling plan is based on the following rule: Having observedy defectives in a cumulative sample of sizen, then, in case of y⩽c−(n)[y⩾c+(n)] accept (reject) the lot; otherwise take a further sample of sizez(n, y). This type of sampling plan is shown to be optimal (within the set ofall sampling plans) with respect to the expected total cost in multistage Bayesian acceptance sampling and, thus, improves a single, double or multiple sampling plan in a natural way. Furthermore, some additional structure of an optimal (z, c−, c+)-sampling is obtained; in particular c±(n)⩽c±(n + 1)⩽ c±(n)+1.

Zusammenfassung

Bei Anwendung eines (z, c−, c+)-Stichprobenplanes ergibt sich folgende Entscheidungsvorschrift: Liegt eine Gesamtstichprobe vom Umfangn vor, diey schlechte Stücke enthält, so nehme man das Los im Falle y⩽c−(n) an, lehne es im Falle y⩾c+(n) ab und ziehe ansonsten eine weitere Stichprobe vom Umfang z(n, y). Unter natürlichen Voraussetzungen wird gezeigt, daß ein solcher Stichprobenplan bzgl. der erwarteten Gesamtkosten in der Menge aller Bayesschen Stichprobenpläne optimal ist und somit einen einfachen, doppelten oder multiplen Prüfplan auf natürliche Weise verallgemeinert. Darüber hinaus wird gezeigt, daß die kritischen Funktionen c±(n) eines optimalen (z, c−, c+)-Planes die Eigenschaften c±(n)⩽c±(n + 1)⩽c±(n) + 1 besitzen.

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Authors and Affiliations

  1. Institut für Quantitative Ökonomik und Statistik, Freie Universität Berlin, Garystraße 21, D-1000, Berlin 33, Germany

    K. -H. Waldmann

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  1. K. -H. Waldmann
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Waldmann, K.H. Sufficient conditions for optimality of a (z, c−, c+)-sampling plan in multistage Bayesian acceptance sampling. OR Spektrum 9, 23–31 (1987). https://doi.org/10.1007/BF01720794

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  • DOI: https://doi.org/10.1007/BF01720794

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