Optimal partitions of finite populations for Dorfman-type group testing
type: Item
instance of: scholarly article
title: Optimal partitions of finite populations for Dorfman-type group testing
zbMATH Open document ID: 0584.62178
DOI: 10.1016/0378-3758(85)90087-4
author: C. Zachary Gilstein
published in: Journal of Statistical Planning and Inference
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62P30
Mathematics Subject Classification ID: 62L99
zbMATH DE Number: 3936337
zbMATH Keywords: group testing models
zbMATH Keywords: optimal partition of a finite population
zbMATH Keywords: Dorfman- type procedures
zbMATH Keywords: binomial model
zbMATH Keywords: modified binomial model
MaRDI profile type: Publication
full work available at URL: 0378-3758(85)90087-4
OpenAlex ID: W1973169820
cites work: Q3331506
cites work: Dorfman and \(R_1\)-type procedures for a generalized group-testing problem
cites work: Dorfman-Type Group Testing for a Modified Binomial Model
cites work: Q3263103
cites work: Q5606373
cites work: On the Detection of Defective Members of Large Populations
cites work: The cutoff point for group testing
description: scientific article; zbMATH DE number 3936337