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

We consider a ranking and selection (R&S) problem with the goal to select a system with the largest or smallest expected performance measure among a number of simulated systems with a pre-specified probability of correct selection. Fully sequential procedures take one observation from each survived system and eliminate inferior systems when there is clear statistical evidence that they are inferior. Most fully sequential procedures make elimination decisions based on sample performances of each possible pair of survived systems and exploit the bound crossing properties of a univariate Brownian motion. In this paper, we present new fully sequential procedures with elimination decisions that are based on sample performances of all competing systems. Using properties of a multidimensional Brownian motion exiting a sphere, we derive heuristics that aim to achieve a given target probability of correct selection. We show that in practice the new procedures significantly outperform a widely used fully sequential procedure. Compared to BIZ, a recent fully-sequential procedure that uses statistics inspired by Bayes posterior probabilities, our procedures have better performance under difficult mean or variance configurations but similar performance under easy mean configurations.