Accelerated sequential procedure for selecting the best exponential population

Abstract

Abstract From k (⩾2) independent two-parameter exponential populations, we wishto select the one associated with the largest location parameter, assuming that the common scale parameter is unknown. We adopt the ‘indifference zone’ approach of Bechhofer (1954) and propose an accelerated version of Mukhopadhyay's (1986) purely sequential selection procedure, that is we start sampling sequentially and then terminate the process ‘early’ augmented by batch sampling. Asymptotic second order expansions for the probability of correct selection and other characteristics of this modified rule are provided for arbitrary k . We also discuss small and moderate sample comparisons of performances of our new procedure with those of the existing purely sequential and three-stage selection procedures (Mukhopadhyay (1986, 1987)). It is observed that the accelerated version can save considerable amount of sampling operation, and yet it can be very competitive with the existing purely sequential procedure and at the same time it can outperform the three-stage procedure. This seems very clear when one looks at the achieved probability of correct selection and the average sample size values given in Tables 1–5.