Subset selection procedures

Selection procedures have been widely studied and applied in determining the required sample size (ie, the number of replications or batches) for selecting the best of k systems and for selecting a subset. The Enhanced Two-Stage Selection procedure is a heuristic two-stage selection procedure that takes into account not only the variance of samples but also the difference of sample means when determining sample sizes. This paper discusses the use of the same technique to select a subset of size m containing at least c of the v best of k normal populations with unknown means and unknown variances. The procedure can be used when the unknown variances across populations are unequal. We derive the probability of correct selection lower bound of determining a subset based on the distribution of order statistics with a clear and concise manner. Numerical experiments indicate that the proposed sample size allocation strategy is superior to other methods in the literature.