The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and $k$-ou-of-$n$ systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. In this paper we study them by assuming a Time Transformed Exponential (TTE) model for the joint distribution of the component lifetimes. This model is equivalent to the frailty model which assumes that they are conditionally independent given a common risk parameter (which represents the common environment risk). Under this model, we obtain explicit expressions for the system reliability functions and comparison results for the main stochastic orders. The system residual lifetime (under different assumptions) is studied as well.

翻译：相干系统是可靠性理论与生存分析中的基本概念，其特例包括常见的串联系统、并联系统及$k$-out-of-$n$系统（次序统计量）。在假设部件寿命相互独立的前提下，学界已取得诸多研究成果。然而在许多实际场景中，该假设并不符合现实。本文基于部件寿命联合分布的时间变换指数模型展开研究，该模型等价于脆弱模型——即假设在给定共同风险参数（表征公共环境风险）的条件下部件寿命条件独立。在此模型框架下，我们推导出系统可靠性函数的显式表达式，并获得主要随机序的比较结果。同时研究了不同假设条件下的系统剩余寿命问题。