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Constructing a Markov process for modelling a reliability system under multiple failures and replacements

机译:构建马尔可夫过程以对多个故障和替换下的可靠性系统进行建模

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We present a reliability system subject to shocks, internal failures, and inspections. Shocks cause damage or failure to several units simultaneously. The units undergo internal failures. After an inspection, the units that have failed are replaced by new and identical ones. The shocks are governed by a Poisson process, the internal failures and the inspection times are exponentially distributed. Under these assumptions a Markov process governing the system is constructed. The states of the system are formed by state-vectors associated to the units of the system. The instantaneous transitions among the states are constructed by using intermediate functions and indicators. A system with three components illustrating the procedure is studied and a numerical application is performed, comparing the performance measures of the k-out-of-3 systems for k = 1, 2, 3. (C) 2018 Elsevier Ltd. All rights reserved.
机译:我们提出了一种受到冲击,内部故障和检查的可靠性系统。震动会同时损坏或损坏多个单元。单元发生内部故障。检查后,将出现故障的单元替换为相同的新单元。冲击由泊松过程控制,内部故障和检查时间呈指数分布。在这些假设下,构建了控制系统的马尔可夫过程。系统的状态由与系统各单元关联的状态向量形成。状态之间的瞬时转换是通过使用中间函数和指示器构建的。研究了一个由三个组成部分组成的系统,对该程序进行了研究,并进行了数值应用,比较了k = 1,2,3的k-out-3系统的性能指标。(C)2018 Elsevier Ltd.保留所有权利。

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