Abstract: Aiming at the multi-unit systems,the opportunistic maintenance policy based on time was presented.The joint life-space partition with maintenance demand for any M part were described and modeled uniformly,and the relationships between them were established.According to the partition result,all possible maintenance combinations and their corresponding probabilities were deduced.A two-unit system was taken as an example to develop the expected maintenance cost rate based on the stationary probabilistic density function and its numerical solution.The correctness and validity of the partition method were verified with numerical experiments.

Key words: deterioration state space, multi-unit systems, opportunistic maintenance policy, joint life-space, stationary probabilistic density function, numerical solution

摘要： 将退化状态空间划分方法应用到多部件系统联合寿命空间的建模研究中。针对多部件系统提出了基于时间的机会维修策略,对任意M部件系统的联合寿命空间划分及维修需求进行了统一描述和建模,并建立了二者间的对应关系。依据联合寿命空间划分结果,推导出了各维修需求的概率统一的计算模型。以两部件系统为例,推导了系统的稳态联合概率密度函数及其数值解法,以此为基础建立了系统长期费用率模型。通过数值实验,验证了联合寿命空间划分方法、联合概率密度的推导模型、系统的维修决策模型及数值解法的正确性和有效性。

关键词: 退化状态空间, 多部件系统, 基于时间的机会维修, 联合寿命空间, 联合概率密度, 数值解法