  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.
