考虑自身退化的混合冲击模型的预防维修策略研究

doi:10.15960/j.cnki.issn.1007-6093.2026.02.010

摘要/Abstract

摘要： 本文研究了一个单部件可修系统的预防维修策略,系统在运行过程中会受到随机冲击的影响,冲击有两种类型:极端冲击和$\delta$-冲击。运行过程中每隔$T$时间进行一次预防维修,预防维修使系统恢复到上一次故障维修后的状态。系统故障后以一定概率延迟修理,第$N$次故障后用一个全新的系统更换。根据更新报酬定理,利用二维策略$(T,N)$,求出了系统长期运行单位时间期望成本的表达式。最后通过数值算例验证了该模型的可行性,并对一些参数做了敏感度分析,可以指导企业对不同的系统进行预防维修。

关键词: 极端冲击, $\delta$-冲击, 几何过程, 预防维修, 维修策略

Abstract: The preventive maintenance strategy of a single component repairable system is studied in this paper. The system is subject to random external shocks during operation. The shock has two types: extreme shock and $\delta$-shock. When the working time reaches to a certain value $T$, the preventive maintenance will be carried out, preventive maintenance restores the state of the system to the state it was in after the last repair. There is a certain probability of delayed repair after the system failure, and the system will be replaced by a completely new one after the $N$th failure.According to the renewal reward theory, an expression for the expected cost per unit time of long-term operation is derived by using the replacement strategy $(T,N)$. Finally the feasibility of the model is verified by numerical examples, and the sensitivity analysis of some parameters is made, which can guide enterprises to carry out preventive maintenance of different systems.

Key words: extreme shock, $\delta$-shock, geometric process, preventive maintenance, maintenance strategy

中图分类号:

O225

高俏俏, 张俊楠. 考虑自身退化的混合冲击模型的预防维修策略研究[J]. 运筹学学报（中英文）, 2026, 30(2): 137-148.

GAO Qiaoqiao, ZHANG Junnan. The inspection and preventive maintenance policy for a δ-shock model which has two types of failures[J]. Operations Research Transactions, 2026, 30(2): 137-148.

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