Some Procedures of Selecting the Best Designs with Respect to Quantile

Abstract

Indifference-zone selection procedures have been used to select a design with the minimum or maximum expected performance measure among a finite number of simulated designs. While there have been significant advancements in selection methodologies, the majority of the selection procedures are developed to process the selection when the performance measures are the mean of some output. In some situations, quantiles provide more suitable information. Quantiles are also more robust to outliers than the mean and standard deviation. Moreover, selection procedures are often derived based on the assumption that the input data are independent and identically distributed (i.i.d.) normal. In this paper we state and justify selection procedures when the ranking parameter is quantile. It is our intention for the quantile estimates to play the role of the i.i.d. normal observations that the original versions of selection procedures process. That is, we assume that our quantile estimates are approximately i.i.d. normal. We perform an empirical study of several stochastic processes to evaluate the performance of the procedure.