On optimal policy in the group testing with incomplete identification
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Malinovsky, Yaakov. “On Optimal Policy in the Group Testing with Incomplete Identification.” Statistics & Probability Letters 140 (September 1, 2018): 44–47. https://doi.org/10.1016/j.spl.2018.04.015.
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Abstract
Consider a very large (infinite) population of items, where each item independent from the others is defective with probability p, or good with probability q=1?p. The goal is to identify N good items as quickly as possible. The following group testing policy (policy A) is considered: test items together in the groups, if the test outcome of group i of size ni is negative, then accept all items in this group as good, otherwise discard the group. Then, move to the next group and continue until exact N good items are found. The goal is to find an optimal testing configuration, i.e., group sizes, under policy A, such that the expected waiting time to obtain N good items is minimal. Recently, Gusev (2012) found an optimal group testing configuration under the assumptions of constant group size and N=?. In this note, an optimal solution under policy A for finite N is provided.