空间相依圆形马尔可夫可修系统可靠性分析

Reliability Analysis of Circular Markov Repairable Systems with Spatial Dependence

针对具有一定拓扑结构的元件相依复杂系统的可靠性分析问题,提出了一类新的元件相依系统——空间相依圆形可修系统。该系统由若干个排列成圆形的元件组成,并且每个元件的运行依赖于空间上与之相邻的元件("邻居")。采用马尔可夫过程描述系统的运行过程,定义了四元件和五元件空间相依圆形可修系统的状态,得到了系统的状态转移率矩阵。运用Laplace变换方法,给出了系统的可用度。通过数值示例说明了结论的应用,并把上述2个系统的可用度与元件独立马尔可夫可修系统的可用度进行了对比。

Aim.The introduction of the full paper reviews a number of papers on reliability models with dependent units in the open literature and proposes what we believe to be a new model mentioned in the title.The core of Sec-tion 1 consists of：（ 1） we present the assumptions of the circular Markov repairable systems with spatial depend-ence;（ 2） we put forward the Markov processes associated with the 4-unit and 5-unit circular Markov repairable systems with spatial dependence and define their states as indicated in Fig.1 and Fig.2.Section 2 analyzes the state transitions of the 4-unit and 5-unit systems and obtains the state transition rate matrices corresponding to them.Sec-tion 3 discusses the instantaneous and asymptotic availabilities of the 4-unit and 5-unit systems, which are given by equations （3）-（5）.Section 4 presents the numerical examples of the 4-unit and 5-unit systems.The curves of in-stantaneous availabilities are shown in Fig.5 and Fig.6.We obtain the conclusions that：（1） the system with inde-pendent units is more reliable than the circular Markov repairable system with spatial dependence;（2） the 5-unit circular Markov repairable system is more reliable than the 4-unit system.