Optimal partitions of finite populations for Dorfman-type group testing
In some group testing models, a group of units may be tested simultaneously to determine that either all units are satisfactory or that at least one unit in the group is defective. In this article, a simple method is given for determining an optimal partition of a finite population into groups for doing group testing by using Dorfman-type procedures for both the usual binomial model and the modified binomial model of \textit{C. G. Pfeifer} and \textit{P. Enis} [J. Am. Stat. Assoc. 73, 588-592 (1978; Zbl 0388.62090)]. It is shown that an optimal partition can be determined by evaluating the expected number of tests for at most two partitions. The given method of determining an optimal partition greatly improves on the method given by Pfeifer and Enis and proves the optimality of the method suggested by \textit{J.-K. Lee} and \textit{M. Sobel} [Dorfman and \(R_ 1\)-type procedures for a generalized group-testing problem. Math. Biosci. 15, 317-340 (1972)] for the usual binomial model.
optimal partition of a finite population
scientific article; zbMATH DE number 3936337