Efficient Fully Sequential Indifference-Zone Procedures Using Properties of Multi-dimensional Brownian Motion Exiting a Sphere

We consider a ranking and selection (R&S) problem to select a system that has either the smallest or largest expected performance measure among several simulated systems. Traditional fully sequential procedures collect one observation from each surviving system and eliminate those found to be statistically inferior, based on sample performances in pairwise comparisons. These procedures often rely on the boundary-crossing properties of univariate Brownian motion for decision-making. Our paper introduces new approaches that make elimination decisions based on the performances of all competing systems, rather than just pairs. By utilizing the properties of multi-dimensional Brownian motion exiting a sphere, we derive heuristics to achieve a predetermined target probability of correct selection. Although our proposal is heuristic, its derivation is nontrivial. This approach allows us to bypass the use of the Bonferroni bound on the worst-case probability of incorrect selection, which frequently leads to inefficiencies in existing R&S procedures. In this experimental study, we demonstrate that our new procedures bring the probability of correct selection closer to the nominal value and also reduce sampling costs compared to widely used fully sequential procedures.