Algorithm for Calculating the Initial Sample Size in a Fully Sequential Ranking and Selection Procedure

In some fully sequential ranking and selection procedures, such as the KN procedure and Rinott's procedure, some initial samples must be taken to estimate the variance. We analyze the impact of the initial sample size (ISS) on the total sample size and propose an algorithm to calculate the ISS in this type of procedure. To better illustrate our approach, we implement this algorithm on the KN procedure and propose the KN-ISS procedure. Comprehensive numerical experiments reveal that this procedure can significantly improve the efficiency compared with the KN procedure and still deliver the desired probability of correct selection.