Optimal sequential plans based on prior distributions and costs

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Cornell University, June, 1966 - Business & Economics - 274 pages
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A. Hald in Technometris, Vol. 2, No. 3 proposed a model of sampling inspection by attributes. He postulated certain definite forms for the losses which are associated with the acceptance or rejection of a lot, and for the cost of taking a single observation. He further assumed that there exists an a priori distribution of the number of defectives, the distribution being known to the experimenter. Under these assumptions he derived the associated single sampling plans which minimize the expected costs averaged with respect to the known a priori distribution. J. Pfanzagl in Technometrics, Vol. 5, No. 2 specialized Hald's model by considering a particular type of a priori distribution, and obtained the double sampling plans which are optimal in the same sense. In this paper, Pfanzagl's work has been generalized by extending his results to sequential plans. In particular, the related optimal (Bayes) sequential sampling plans and their operating characteristics are derived. The Bayes risks of the optimal sequential plans are compared with those of the corresponding optimal single sampling plans for certain representative values of the parameters. The limiting behavior for large lots of the optimal boundaries for the sequential sampling plans is studied using a particular normalization due to Chernoff and Ray. (Annals of Math. Stat., Vol. 36, No. 5). (Author).

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