失效单调关联系统的条件存活元件数量

The Number of Working Components in a Conditional Coherent Failed System

单调关联系统在可靠性,生存分析和其他生命科学中扮演着非常重要的角色.在本文中,我们考虑了n中取(n-k+1)系统中存活元件的数量,假设在时刻t时存活的元件至少有(n-m+1)个,且系统在时刻t处于失效状态.在此条件下,我们计算系统中存活元件数量为i(i=n-m+1,…,n-k)的概率,从而获得了其可靠性与几个随机性质.此外,我们将结果扩展到具有绝对连续可交换元件的一般单调关联系统.

Coherent systems are very important in reliability,survival analysis and other life sciences.In this paper,we consider the number of working components in an(n-k+ 1)-out-of-n system,given that at least(n-m+ 1) components are working at time t,and the system has failed at time t.In this condition,we compute the probability that there are exactly i working components.First the reliability and several stochastic properties are obtained.Furthermore,we extend the results to general coherent systems with absolutely continuous and exchangeable components.