SELECTING EFFICIENT SINGLE STAGE AND DOUBLE STAGE ATTRIBUTE SAMPLING PLANS OF A GIVEN POWER

WAYNE ALVA TAYLOR, Purdue University

Abstract

The classical problem of selecting single and double sampling plans satisfying P((theta)(,1)) (GREATERTHEQ) 1-(alpha) and P((theta)(,2)) (LESSTHEQ) (beta) is solved for the binomial and hypergeometric distributions with integer sample sizes and for the Poisson distribution with both integer and real-valued sample sizes. For single sampling, it is proved that a single sampling plan exists satisfying the above conditions which is uniformly most efficient regardless of the method of curtailing. For double sampling plans, a method is given for generating the set of admissible double sampling plans satisfying the above conditions. This method is modified so as to determine the double sampling plan satisfying the above conditions and minimizing a weighted function of the ASN curve. This method works for all methods of curtailing, does not place any restrictions on the five parameters describing the double sampling plans, and is exact. Comparison of the double sampling plans selected by the methods given in this thesis and those found in Mil-Std-105D shows that double sampling plans in Mil-Std-105D generally obtain about only one half of the reduction in sample size that is possible. In fact, double sampling plans selected by the methods given in this thesis obtain 70% to 100% of the reduction in sample size obtained by the best sequential sampling plan and are more efficient than the Wald SPRT for most (theta) < (theta)(,1).

Degree

Ph.D.

Subject Area

Statistics

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