THE CHI-SQUARE APPROXIMATION APPROACH TO RANKING AND SELECTION PROCEDURES UNDER TYPE-II CENSORING

Abstract

In this paper we consider the problem of ranking and selection with respect to the largest scale parameter of gamma populations under Type-II censoring. Shape parameters of the gamma populations are assumed to be known and equal. Under the assumption of common sample size and censoring number, ranking and selection procedures are presented based on the total time on test (TTOT) statistic. Since the exact distribution of the TTOT statistic is not known in general, a two-moment chi-square approximation is used to derive expressions for the probability of correct selection and its infimum for each procedure. Monte Carlo studies are conducted to obtain coefficients for the chi-square approximation. Performances of the proposed approximate procedures are compared with those of existing ones for various legitimate cases.