The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems, where the components are subject to probabilistic failures. Our goal is to understand the reliability of the global system. The reliability evaluation of an SBS belongs to the class of NP-Hard problems, and the combinatorics of SBS imposes several challenges. In a previous work by the same authors, a special sub-class of SBSs called "separable systems" was introduced. These systems accept an efficient representation by a linear inequality on the binary states of the components. However, the reliability evaluation of separable systems is still hard. A theoretical contribution in the understanding of separable systems is given. We fully characterize separable systems under the all-terminal reliability model, finding that they admit efficient reliability evaluation in this relevant context.

翻译：一个系统,如车辆、通信网络或自动过程的运行,在很大程度上取决于其部件的正确运行。一个小二进制系统(SBS)数学模型模拟了机上系统的行为,这些部件可能会发生概率性故障。我们的目标是了解全球系统的可靠性。一个系统(SBS)的可靠性评估属于NP-合成问题的类别,而SBS的组合法则带来了若干挑战。在同一作者以前的工作中,引入了一个称为“可分离系统”的特殊的SBS子类。这些系统接受各部件的二进制状态上以线性不平等为一种有效代表。然而,对可分离系统的可靠性评估仍然很困难。在理解可分离系统方面提供了理论上的贡献。我们充分定性了所有期可靠性模型下的可分离系统,发现它们承认在相关情况下的有效可靠性评估。