In this paper, we consider a coherent system composed of components whose lifetimes are independent and identically discretely distributed random variables. We study several aging and stochastic properties of the conditional residual lifetime of the system under the condition that some of its components have failed by time t. Moreover, we compare the conditional residual lifetimes of two coherent systems by using various stochastic orders.

中文翻译：

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关于由具有离散寿命的组件组成的相干系统的条件剩余寿命

在本文中，我们考虑由组件组成的相干系统，这些组件的寿命是独立且相同离散分布的随机变量。我们研究了系统在某些组件在时间t前失效的条件下系统的条件剩余寿命的几个老化和随机特性。此外，我们通过使用各种随机顺序比较了两个相干系统的条件剩余寿命。