This paper focuses on the reliability analysis of $k$-out-of-$n$ systems which are designed to perform a given mission consisting of several distinct phases. As the phases of the mission change, the reliability characteristics of the system and the system structure vary accordingly. The phase transition probabilities, phase durations, and component failure rates are dependent on the number of operating components. Moreover, the system is allowed to have cold, warm, or hot standby components. We propose computationally tractable methods to compute the system reliability, mean time to failure, and long-run availability for such a general system structure. We also provide a numerical analysis to show the applicability and the empirical computational complexity of the proposed methods.

本文着重于可靠性分析 $ķ$-在......之外-$ñ$旨在执行给定任务的系统，包括几个不同的阶段。随着任务阶段的变化，系统的可靠性特征和系统结构也会随之变化。相变概率，相持续时间和组件故障率取决于运行组件的数量。此外，允许系统具有冷，热或热备用组件。我们提出了一种易于计算的方法来计算这种一般系统结构的系统可靠性，平均故障时间以及长期可用性。我们还提供了数值分析，以显示所提出方法的适用性和经验计算复杂性。