























This paper considers the joint distribution of elements of a random sample and an order statistic of the same sample. \ The motivation for this work stems from the important problem in reliability analysis, to estimate the number of inspections we need in order to detect failed components in a coherent system. We consider an $(n-r+1)$-out-of-$n$ system, which is intact until at least $n-r+1$ of the components are alive, and it fails if the number of failed components exceeds $r$. The life time of the system is the $% r$th order statistic. Assuming that some of the components failed but the system \ is still functioning, \ using the results presented in this paper it is possible to find an expected value of the number of inspections we need to do for detecting certain number of failed components.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。