A TWO-STAGE SUBSAMPLING PROCEDURE FOR RANKING MEANS OF FINITE POPULATIONS WITH AN APPLICATION TO BULK SAMPLING PROBLEMS.
CORNELL UNIV ITHACA N Y DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
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It is assumed that there are available k finite populations, each consisting of U primary units, and that each primary unit can be subdivided into T elements. It is further assumed that the populations have a common known variance among primary units, and a common known variance among elements within primary units. The values of the overall population means per element are assumed to be unknown, as is the true pairing of the ranked values of these means with the populations. It is desired to select the population which has the largest overall population mean per element. This selection is to be accomplished by taking a random sample of u U primary units from each population, and then a random sample of t T elements from each primary unit. The pair t,u is to be chosen in such a way as to guarantee that the probability of a correct selection will be equal to or greater than a specified quantity whenever the true difference between the largest and second largest overall population mean per element is equal to or greater than a second specified quantity. In general several different pairs t,u will accomplish the stated objective. It is proposed that a choice be made among these pairs using the criterion of minimum total cost of xampling. This formulation leads to an integer programming problem with a non-linear constraint. An especially simple method of solving this problem is proposed, and this method is contrasted with certain other methods which have been considered in the literature. It is shown how the subsampling ranking procedure described in this paper can be applied to a bulk sampling problem involving the clean content of wool in bales. Author
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems