Selecting the best by comparing simulated systems in a group of three when variances are known and unequal

This paper presents a fully sequential procedure for selecting the best system among a finite number of simulated systems with variances that are known but not necessarily equal. Our procedure compares systems in groups of three and is based on exit properties of a bivariate Brownian motion from an ellipse. The procedure is a modification of the one proposed in Kim and Dieker (2011) for the equal-variance case.