Optimal selection of thet best of a sequence with sampling cost

Abstract

This article deals with the problem of selecting the t best of n independent and identically distributed random variables which are observed sequentially with sampling cost c per unit. Assume that a decision for acceptance or rejection must be made after each sampling and that the reward for each observation with value x is given by px - c, where p is 1 if the observation is accepted, or 0 otherwise. The optimal decision procedure (strategy) for maximizing the total expected reward is obtained. The critical numbers which are necessary to carry out the optimal decision procedure is presented by two recursive equations. The limit values of the critical numbers and the expected sample size are also studied.