  We consider the indifference-zone (IZ) formulation of the ranking and
selection problem in which the goal is to choose an alternative with the
largest mean with guaranteed probability, as long as the difference between
this mean and the second largest exceeds a threshold. Conservatism leads
classical IZ procedures to take too many samples in problems with many
alternatives. The Bayes-inspired Indifference Zone (BIZ) procedure, proposed in
Frazier (2014), is less conservative than previous procedures, but its proof of
validity requires strong assumptions, specifically that samples are normal, and
variances are known with an integer multiple structure. In this paper, we show
asymptotic validity of a slight modification of the original BIZ procedure as
the difference between the best alternative and the second best goes to
zero,when the variances are known and finite, and samples are independent and
identically distributed, but not necessarily normal.
