Selecting the Best Exponential Populations in Terms of Reliability: Empirical Bayes Approach

Suppose that there are k(k ≥ 2) populations (equipments) π1,…, πk. Of them, πi(i=1,…,k ) is exponentially distributed with unknown parameter θi. Suppose R0 is a scheduled minimum reliability (survival rate). From the qualified subsets, we intend to select which has the maximum reliability, the so-called best population. The qualified subsets refer to the standard deviation is no greater than σ0 in the k populations, and its reliability is no less than R0. Apparently, this study is to explore the selection issue of multiple criteria.Based on the Bayes framework, we adopt conjugate prior distribution. Then we employ empirical Bayes approach to solve the issue of selection. So, what we concern mainly is: from the k populations taking gamma distribution as its conjugate prior. Related empirical Bayes selection rule has been submitted, and its asymptotic optimality has also been proven. At the same time, a simulation study is carried out for the performance of the proposed procedure and it is found satisfactory.

並列關鍵字

reliability ； ranking and selection ； loss function ； Bayes risk ； empirical Bayes selection rule ； asymptotic optimality

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