标题： 混合相干系统与Lévy-frailty Marshall-Olkin失效时间的极限行为 显示英文标题

标题： Limiting behavior of mixed coherent systems with Lévy-frailty Marshall-Olkin failure times

摘要： 在本文中，我们展示了系统可靠性函数的极限结果——即在给定时间后整个系统仍处于运行状态的概率——当系统的组件数量趋于无穷大时。 更具体地说，我们考虑了一类混合相干系统的序列，其组件是同质且不可修复的，故障时间由Lévy-frailty Marshall-Olkin（LFMO）分布支配——一种允许同时组件故障的分布。 我们证明，在可积性条件下，可靠性函数收敛于Lévy子过程的首次通过时间的概率。 据我们所知，这是第一个研究系统组件数量增长时可靠性函数渐近行为的结果。 为了说明我们的方法，我们给出了一个可靠性函数的参数族示例，其中系统故障时间按分布收敛于指数随机变量，并进行了计算实验以测试收敛性。 显示英文摘要

摘要： In this paper we show a limit result for the reliability function of a system -- that is, the probability that the whole system is still operational after a certain given time -- when the number of components of the system grows to infinity. More specifically, we consider a sequence of mixed coherent systems whose components are homogeneous and non-repairable, with failure-times governed by a L\'evy-frailty Marshall-Olkin (LFMO) distribution -- a distribution that allows simultaneous component failures. We show that under integrability conditions the reliability function converges to the probability of a first-passage time of a L\'evy subordinator process. To the best of our knowledge, this is the first result to tackle the asymptotic behavior of the reliability function as the number of components of the system grows. To illustrate our approach, we give an example of a parametric family of reliability functions where the system failure time converges in distribution to an exponential random variable, and give computational experiments testing convergence.