Abstract: To solve the maintenance optimization problem of serial system's shock model,a repair-replacement model for serial systems was proposed which suffered δ-shocks.Under the assumption that the repair was imperfect,the long-run average cost rate of the system was derived by using the renewal reward theorem and the joint replacement policy based on the components' failure numbers.The existence of the optimal joint replacement policy was proved analytically and the corresponding algorithm was provided to obtain the optimal policy.A numerical experiment was given to illustrate the model.The sensitivity analysis revealed the relationship between the optimal joint policy of the system and the individual optimal policy of each component.

Key words: serial system, δ-shock model, geometric process, maintenance strategy, optimization

摘要： 为解决串联系统冲击模型的维修优化问题,以δ-冲击模式下的串联系统为研究对象,在故障修复非新的条件下,建立了系统的维修更换模型。以各部件接受更换前的故障次数为更换策略,利用更新过程理论求得系统长期运行下的平均费用率。从理论上证明了最优更换策略的存在性,并给出最优策略的求解算法。通过数值实验对该方法进行了验证。敏感性分析结果揭示了系统的整体最优策略与各部件独立最优策略之间的关系。

关键词: 串联系统, &delta, -冲击模型, 几何过程, 维修策略, 优化