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Selecting the best exponential population under Type-II progressive censoring scheme via empirical Bayes approach

ABSTRACT The problem of selecting a population according to “selection and ranking” is an important statistical problem. The ideas in selecting the best populations with some demands having optimal criterion have been suggested originally by Bechhofer (1954) and Gupta (1956, 1965). In the area of ranking and selection, the large part of literature is connected with a single criterion. However, this may not satisfy the experimenter’s demand. We follow methodology of Huang and Lai (1999) and the main focus of this article is to select a best population under Type-II progressively censored data for the case of right tail exponential distributions with a bounded and unbounded supports for μi. We formulate the problem and develop a Bayesian setup with two kinds of bounded and unbounded prior for μi. We introduce an empirical Bayes procedure and study the large sample behavior of the proposed rule. It is shown that the proposed empirical Bayes selection rule is asymptotically optimal.