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。
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.
[1] Esary J D, Marshall A W, Proschan F. Shock models and wear process [J]. The Annals of Probability, 1973, 1(4): 627-649.
[2] Shanthikumar J G, Sumita U. General shock models associated with correlated renewal sequences [J]. Journal of Applied Probability, 1983, 20(3): 600-614.
[3] Chen J Y, Li Z H. An extended extreme shock maintenance model for a deteriorating system [J]. Reliability Engineering & System Safety, 2008, 93(8): 1123-1129.
[4] Wu Q T, Wu S M. Optimisation of replacement policy for a one-component system subject to Poisson shocks [J]. International Journal of Systems Science: Operations & Logistics, 2016, 3(2): 114-127.
[5] 李泽慧, 黄宝胜, 王冠军. 一种冲击源下冲击模型的寿命分布及其性质[J]. 兰州大学学报, 1999, 4: 1-7.
[6] 王冠军, 张元林.$\delta$-冲击模型及其最优更换策略 [J]. 东南大学学报(自然科学版), 2001, 5: 121-124.
[7] 王小林, 程志君, 郭波, 等. 基于冲击模型劣化系统的不完全维修决策 [J]. 系统工程理论与实践, 2011, 31(12): 2380-2386.
[8] 岳德权, 高俏俏. 具有两种失效状态的$\delta$-冲击模型的最优维修策略 [J]. 系统工程理论与实践, 2015, 35(8): 2113-2119.
[9] 成国庆, 李玲. 串联系统的$\delta$-冲击模型及其维修策略优化 [J]. 计算机集成制造系统, 2020, 26(9): 2422-2428.
[10] Zhao B, Yue D Q, Liao H, et al. Performance analysis and optimization of a cold standby system subject to δ-shocks and imperfect repairs [J]. Reliability Engineering & System Safety, 2021, 208: 107330.
[11] Wang G J, Zhang Y L. A shock model with two-type failures and optimal replacement policy [J]. International Journal of Systems Science, 2005, 36(4): 209-214.
[12] Cha J H, Finkelstein M. On new classes of extreme shock models and some generalizations [J]. Journal of Applied Probability, 2011, 48(1): 258-270.
[13] Eryilmaz S, Tekin M. Reliability evaluation of a system under a mixed shock model [J]. Journal of Computational and Applied Mathematics, 2019, 352: 255-261.
[14] Bohlooli-Zefreh M, Asadi M, Parvardeh A. On the reliability and optimal maintenance of systems under a generalized mixed δ-shock model [J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2021, 235(5): 909-922.
[15] 贾积身. 延迟修理退化冷贮备可修系统的维修更换策略研究[J]. 河南机电高等专科学校学报, 2014, 22(2): 43-47.
[16] 马淑莲, 汪云芬. 延迟修理且定期检修的$\alpha$-幂过程可修系统更换模型 [J]. 郑州大学学报(理学版), 2014, 46(2): 6-10.
[17] Babu D, Govindaraju P, Rizwan U. A δ-shock maintenance model for a deteriorating system with imperfect delayed repair under partial product process [J]. Journal of Mathematical and Computational Science, 2019, 9(5): 571-581.
[18] 李玲, 成国庆, 唐应辉. 带预防性维修的冲击模型最优检测更换策略 [J]. 山东大学学报(理学版), 2011, 46(9): 122-126.
[19] 李海霞, 陈雁东, 孟宪云. 带有多重休假及预防维修的冲击模型二维更换策略 [J]. 经济数学, 2014, 31(2): 55-58.
[20] 张斌, 张岚. 基于退化和随机冲击的非周期不完全预防维修模型 [J]. 统计与决策, 2016, 14: 77-80.
[21] 高俏俏,岳德权.有两种故障状态的$\delta$-冲击模型的检测及预防维修策略研究 [J]. 运筹学学报(中英文), 2025, 29(1): 55-62.
北大中文核心期刊