Order Statistics and Optimal Allocation Problems
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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Order statistics play an important role reliability. The life time of any coherent system is the first order statistic of the, generally dependent, lives of its cut sets. For the important class of k-out-of-n systems, the lifetime of the system is the n-k 1th order statistic of the lives of its components, which are often assumed to be independent. Therefore the reliability of many systems can be easily stated as a probability concerning an order statistic. A system is called a second order r-out-of-k system if it is a r-out- of-k system based on k modules, without common components, and where each module is an ai-out-of-ni system. Two features of such systems are of interest, namely the probability that a particular module is among the modules that failed before the failure of the system and the number of failed components at the time of the failure of the system. In this paper, we review results regarding these features for some special cases of second order r-out-of-k systems, emphasizing their applications to optimal allocation problems.
- Statistics and Probability