Technical Note—First-Stage Sampling in Ranking and Selection: Beyond Variance Estimation

This study sheds light on a crucial aspect of ranking-and-selection (R&S) procedures—how the first-stage sample size, [Formula: see text], impacts the procedure efficiency beyond the variance estimation. This research demonstrates that the presence of [Formula: see text] helps reduce the probability of incorrect selection (PICS). However, this issue of [Formula: see text] has been traditionally ignored, thereby leading to unnecessarily conservativeness of existing R&S procedures. To address this issue, the authors provide exact formulas for both indifference-zone (IZ) and IZ-free procedures, highlighting how [Formula: see text] influences PICS under worst-case configurations. Based on these formulas, this research further offers new guidelines on the choice of [Formula: see text] for the existing procedures and introduces an improved version of the classic IZ-free procedure. This research provides important insights for further enhancing the efficiency of R&S in various potential applications.