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 σ² _[1] ⩽ ⋅⋅⋅ ⩽ σ_[k] ² 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 σ² _[2]/σ_[1] ² ⩾ δ* > 1, where P* and δ* 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 subset sizes for selected slippage configurations based on simulations. The results are illustrated by an example.