On a Selection Problem in Reliability Theory.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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In this paper, the methodology of subset selection is applied to a reliability problem of choosing units for the series system and the 1-out-of-2 system from k available brands pi1, pi2,..., pik. The problem is treated from a decision-theoretic Bayesian point of view. It is assumed that units from the i-th brand have exponentially distributed lifelengths with mean lifelength 1lambda 1, and that there are n independent observations from each of pi1, pi2,..., pik. The loss functions are assumed to be inversely proportional to the expected lifelength of the corresponding action. For the series system, the natural rule, which selects all the units from the population associated with the largest sample mean life, is shown to be uniformly best within the class of permutation invariant decision rules, admissible and minimax. For the 1-out-of-2 system the Bayes rule w.r.t. the natural independent conjugate Gamma-2 prior is given, and is shown to be admissible. Also the Bayes rule w.r.t. the same prior when the loss function is the relative regret in terms of the expected lifelength, is also given. Author
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems