考虑休眠的两部件系统可用度马氏建模方法

Markov modeling method for availability of two-item system under passivation

针对Metric模型中假设备件需求不依赖于可用系统数而导致可用度被低估的问题,考虑部件的休眠状态(即故障系统中无故障部件不产生备件需求的情况),提出一种两部件系统可用度马氏建模方法。利用可用系统数、备件库存以及备件短缺数描述备件状态,根据连续时间马尔可夫链方法,分析不同部件的故障修复过程对状态转移的影响,构建了两组马尔可夫随机过程;随后,分析两种随机过程间的联系,将其合并后建立了备件的马尔可夫状态转移模型;进而利用该模型求解各备件期望短缺数EBO(expected backorders)以及系统可用度的稳态值与瞬时值;最后将模型应用于数值案例,得到了比Metric模型更接近仿真值的备件期望短缺数与系统可用度。

Aiming at the problem that the assumed spare part demand does not depend on the number of available working systems in Metric model, which leads to underestimated availability, considering the passivation state （, where the fault-free parts in the failure system do not generate spare part depend）, this paper proposes a Markov modeling method for availability in two-item systems under passivation. Firstly, the system spare part state is described as a three-dimensional array consisting of the number of available working systems, stock and backorder, then according to the continuous time Markov chain （CTMC） method, the influence of the fault repairing process of different parts on the state transition is analyzed, two groups of Markov random processes are constructed. Furthermore, the relationship between these two kinds of random processes is analyzed; after merging these two random processes, a Markov state transition model of the spare parts is built, and the expected backorders （EBO） of the spare parts and the instantaneous and steady-state values of the system availability are solved with the model. Finally, the proposed model was used in numerical examples, and the result shows that the EBO and availability of the two-item system calculated using CTMC method are closer to the simulation results compared with those using Metric model.