A Multiplicative Decomposition Property of the Screening-and-Selection Procedures of Nelson et al.

Recently, Nelson et al. (2001a, b) 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.