Fully Sequential Selection Procedures with Parabolic Boundary

We present two fully sequential indifference-zone procedures to select the best sys-tem from a number of competing simulated systems when best is defined by maximum or minimum expected performance. These two procedures have parabola shaped con-tinuation regions rather than triangular continuation regions employed in several pa-pers. 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.