共因失效条件下多状态系统选择性维修优化

共因失效（CCF）广泛存在于多状态系统（MSS）中，研究共因失效条件下多状态系统的维修优化问题，对于提高系统任务成功概率、降低故障损失具有重要意义。考虑多状态系统、任务剖面和随机共因失效的模糊特性，采用模糊马尔可夫模型（FMM）和模糊通用生成函数（FUGF）法，建立了模糊随机共因失效条件下模糊多状态系统（FMSS）任务成功概率评估解析模型（AM），采用Monte Carlo仿真（MCS）方法对模型进行了验证；考虑维修费用约束，建立了模糊随机共因失效条件下模糊多状态系统选择性维修优化模型，为生成最优维修方案提供支持，结合实际案例，分析了随机共因失效对选择性维修优化和系统各状态的模糊概率的影响，验证了模型的有效性。研究结果表明，模糊随机共因失效和各模糊参数的α水平截集可能会影响选择性维修优化的结果，且忽略模糊随机共因失效会高估系统任务成功概率。

Selective maintenance optimization for multi-state systems subject to common cause failures

Common Cause Failure (CCF) exists extensively in the Multi-State System (MSS). It is of great significance to investigate the maintenance optimization for the MSS subject to CCF to improve the probability of mission success and reduce the failure cost of the system. Taking into account the fuzzy properties of the multi-state system, mission profile and Random Common Cause Failure(RCCF), an analytic model (AM) is proposed to evaluate the mission success probability of the fuzzy multi-state system (FMSS) subject to RCCF based on the Fuzzy Markov Model (FMM) and Fuzzy Universal Generating Function (FUGF), and its validity is verified by the well-known Monte Carlo Simulation (MCS) method. Based on the proposed model, a selective maintenance optimization model for the FMSS considering the maintenance cost constraint is developed, and the optimal maintenance option is obtained. An illustrative example is presented to demonstrate the effectiveness of the proposed selective maintenance model, and the effects of the RCCF on the results of selective maintenance optimization and system state probability are analyzed. The results show that the RCCF and the α-cut level of the fuzzy number may affect the result of selective maintenance optimization, and neglecting the RCCF will cause overestimate of the mission success probability of the system.