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

Abstract

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

CLC Number:

O225

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.

References

[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.

The inspection and preventive maintenance policy for a δ-shock model which has two types of failures

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 6

Recommended Articles

Metrics

Comments

[1]	Fengrui LI, Yinghui TANG. Analysis of M/G/1 queue with maintenance strategy and different arrival rates under service startup N-policy control [J]. Operations Research Transactions, 2025, 29(2): 113-127.
[2]	Qiaoqiao GAO, Dequan YUE. The inspection and preventive maintenance policy for a δ-shock model which has two types of failures [J]. Operations Research Transactions, 2025, 29(1): 55-62.
[3]	Dayong ZHANG, Honglei WANG. Optimization strategy for preventive maintenance of wind turbines in low wind speed areas based on Markov models [J]. Operations Research Transactions, 2024, 28(3): 108-120.
[4]	GAO Qiaoqiao, YUE Dequan, ZHAO Bing. The preventive maintenance policy for a two-component series system with delay repair [J]. Operations Research Transactions, 2018, 22(4): 69-78.
[5]	CHENG Xiaoxuan, YUE Dequan, ZHAO Bing. Maintenance strategy of restricted working time for single-unit repairable system [J]. Operations Research Transactions, 2017, 21(1): 78-86.
[6]	LI Ling, CHENG Guoqing. Optimization of shock model being maintained under imperfect inspection [J]. Operations Research Transactions, 2013, 17(4): 33-42.