In this paper, we consider two coherent systems having shared components. We assume that in the two systems there are three different types of components; components of type one that just belong to the first system, components of type two that lie only in the second system and components of type three that are shared by the two systems. We use the concept of joint survival signature to assess the joint reliability function of the two systems. Using this concept, some representations for the joint reliability function of the system lifetimes are obtained under two different scenarios of component failures. In the first scenario, we assume that the components of the systems fail according to different counting processes such as non-homogeneous Poisson processes. In the second scenario, it is assumed that the component lifetimes of each type are exchangeable while the three types of component lifetimes can be independent or dependent. To illustrate the theoretical results, two systems with shared components are studied numerically and graphically.

在本文中，我们考虑两个具有共享组件的相干系统。我们假设在两个系统中存在三种不同类型的组件。类型1的组件仅属于第一个系统，类型2的组件仅位于第二个系统中，类型3的组件由两个系统共享。我们使用联合生存签名的概念来评估两个系统的联合可靠性功能。使用此概念，可以在两种不同的组件故障情况下获得系统寿命联合可靠性函数的某些表示形式。在第一种情况下，我们假设系统的组件会根据不同的计数过程（例如非均匀泊松过程）而发生故障。在第二种情况下，假定每种类型的组件寿命是可互换的，而三种类型的组件寿命可以是独立的也可以是从属的。为了说明理论结果，对两个共享组件的系统进行了数值和图形研究。