Fully sequential selection procedures with a parabolic boundary

We present two fully sequential indifference-zone procedures to select the best system from a number of competing simulated systems when best is defined in terms of the maximum or minimum expected performance. These two procedures have parabola shaped continuation regions rather than the triangular continuation regions employed in several papers in the existing literature. The procedures we present accommodate unequal and unknown variances across systems and the use of common random numbers. However, we assume that basic observations are independent and identically normally distributed. We compare the performance of our procedures with those of other fully sequential procedures available in the literature.