A multiplicative decomposition property of the screening-and-selection procedures of Nelson et al

A multiplicative decomposition property of the screening-and-selection procedures of Nelson et al

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Article ID: iaor2003410
Country: United States
Volume: 49
Issue: 6
Start Page Number: 964
End Page Number: 966
Publication Date: Nov 2001
Journal: Operations Research
Authors:
Keywords: simulation
Abstract:

Recently, Nelson et al. formulated a class of combined screening-and-selection procedures for identifying the simulated system with optimal expected response when the number of alternatives is finite, but large enough to render conventional ranking-and-selection procedures impractical. Under a certain key assumption, they derived an additive decomposition lemma that provides a lower bound on the correct-selection probability when either the original or group-screening version of their combined screening-and-selection procedure is applied to randomly sampled normal populations with unknown and unequal variances. For both these procedures, we establish an improved lower bound on the correct-selection probability that is the product of (a) the probability that the best alternative will survive the first-stage screening procedure, and (b) the probability that the second-stage sampling-and-selection procedure will correctly identify the best alternative starting from the full set of alternatives. This multiplicative decomposition property offers a different perspective on the probabilistic structure of the entire class of combined screening-and-selection procedures developed by Nelson et al., and it does not require the key assumption of their additive decomposition lemma.

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