基于CTMC族的多部件装备群稳态可用度建模方法

针对复杂可修装备群稳态可用度解析计算困难的问题,提出一种通过构建多个相关连续时间马尔可夫链(continuous time Markov chain,CTMC)来求解稳态可用度的方法。通过分析装备群的使用与维修特点,采用可用装备数、备件库存数、备件短缺数来刻画部件的状态,分别建立各类部件库存状态的CTMC,进而建立用于分析装备群稳态可用度的CTMC族模型;并根据各类部件的状态转移关系及转移率矩阵,在求解各类部件CTMC模型稳态概率的基础上,给出各类部件的期望备件短缺数和装备群稳态可用度算法。最后通过构建数值案例,将提出的CTMC族模型结果分别与仿真分析和多级可修产品库存控制模型的结果进行对比,验证了提出模型和算法的有效性。

Steady state availability modeling method for multi component equipment group based on CTMC family

Aiming at the problem that the conventional method is difficult to calculate the steady state availability for complex repairable equipment group, a method of constructing multiple continuous time Markov chain (CTMC) is proposed to solve its steady state availability. With consideration of the features of the use and maintenance- of the equipment group, three parameters, which are the number of equipment, spare parts inventory and expected backorder respectively, are proposed to represent the inventory state of components. Then, the CTMC for each component is established, forming a CTMC family to analyze the steady state availability of the equipment group. Based on the state transition relations and the transfer rate matrix of each component, the algorithms for each component expected backorder and the steady state availability of the equipment group are given. Finally, a numerical analysis case is constructed, which shows that the result of the CTMC family model proposed is closer to the simulation results than the multi echelon technique for recoverable item control model, verifying the validity of the proposed model and algorithm.