Selecting the normal population with the smallest variance: A restricted subset selection rule

Consider k(>= 2) normal populations whose means are all known or unknown and whose variances are unknown. Let sigma(2)([1]) <= ... <= sigma(2)([k]) denote the ordered variances. Our goal is to select a non empty subset of the k populations whose size is at most m (1 <= m <= k - 1) so that the population associated with the smallest variance (called the best population) is included in the selected subset with a guaranteed minimum probability P* whenever sigma(2)([2])/sigma(2)([1]) >= delta* > 1, where P* and delta* are specified in advance of the experiment. Based on samples of size n from each of the populations, we propose and investigate a procedure called R-BCP. We also derive some asymptotic results for our procedure. Some comparisons with an earlier available procedure are presented in terms of the average sub-set sizes for selected slippage configurations based on simulations. The results are illustrated by an example.