有两种故障状态的δ-冲击模型的检测及预防维修策略研究

doi:10.15960/j.cnki.issn.1007-6093.2025.01.005

Abstract

Abstract:

In this paper, the preventive maintenance policy for a δ-shock model is studied. The system is a geometric process degradation system. The failure of the system on the one hand is because of the lifetime of the system, on the other hand is because of the interval of two consecutive shocks less than a fixed value. The fault of the system can only be found by inspection. When the working time of the system reaches a certain value, the inspect will be carried out, and preventive maintenance will be carried out if there is no fault. Preventive maintenance will restore the system to the state after the last fault maintenance, and if the system fault, a fault repair will be carried out. Based on the two-dimensional policy composed of the interval of system detection and the failure times before replacement, the expression of the expected cost per unit time of system is obtained by using the renewal process and geometric process theory. Finally, numerical examples are given.

Key words: shock, inspection, preventive maintenance, geometric process, expected cost

CLC Number:

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.

Figures/Tables 4

References 16

1	Esary J D , Marshall A W , Proschan F . Shock models and wear process[J]. Journal of Applied Probablity, 1973, 1, 627- 649.
2	Barlow R E , Proschan F . Statistical Theory of Reliability and Life Testing[M]. New York: Holt, Rinehart and Winston, Inc, 1975.
3	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.
4	李玲, 成国庆. 考虑不完全检测的冲击模型最优维修策略[J]. 运筹学学报, 2013, 17 (4): 33- 42.
5	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.
6	张权, 李艳君, 王希彬. 连续有效冲击模型的可靠性[J]. 数学的实践与认识, 2018, 48 (19): 194- 198.
7	Zhao X , Sun L P , Wang M Y , et al. A shock model for multi-component system considering the cumulative effect of severely damaged components[J]. Computers & Industrial Engineering, 2019, 137, 1- 12.
8	Wang G J , Zhang Y L . δ-shock model and its optimal replacement policy[J]. Journal of Southeast University, 2001, 31, 121- 124.
9	Lam Y , Zhang Y L . A shock model for the maintenance of a repairable system[J]. Computer and Operations Research, 2004, 31, 1807- 1820. doi: 10.1016/S0305-0548(03)00121-7
10	Lam Y , Zhang Y L . A geometric-process maintenance model for a deteriorating system under a random environment[J]. IEEE Transactions on Reliability, 2003, 52 (1): 83- 90. doi: 10.1109/TR.2002.807243
11	成国庆, 李玲. 串联系统的δ-冲击模型及其维修策略优化[J]. 计算机集成制造系统, 2019, 25, 1- 12.
12	岳德权, 高俏俏. 具有两种失效状态的δ-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.
13	Wang G J , Zhang Y L . Geometric process model for a system with inspections and preventive repair[J]. Computers & Industrial Engineering, 2014, 75, 13- 19. doi: 10.3969/j.issn.1001-3695.2014.01.003
14	Yang L , Ma X B , Peng R , et al. A preventive maintenance policy based on dependent twostage deterioration and external shocks[J]. Reliability Engineering & System Safety, 2017, 160, 201- 211.
15	Zheng Z B , Zhou W H , Zheng Y F , et al. Optimal maintenance policy for a system with preventive repair and two types of failures[J]. Computers & Industrial Engineering, 2016, 98, 102- 112.
16	Li Y , Sheng Z , Lee C G , et al. A two-phase preventive maintenance policy considering imperfect repair and postponed replacement[J]. European Journal of Operational Research, 2019, 274 (3): 966- 977. doi: 10.1016/j.ejor.2018.10.049

	3	4	5	6	7	8	9
6	$ - $50.994 2	$ - $51.668 7	$ - $51.975 0	$ - $52.088 0	$ - $52.086 1	$ - $52.009 4	$ - $51.880 6
7	$ - $52.687 5	$ - $53.419 4	$ - $53.670 2	$ - $53.749 1	$ - $53.722 8	$ - $53.626 6	$ - $53.480 6
8	$ - $53.679 5	$ - $54.450 9	$ - $54.804 9	$ - $54.941 4	$ - $54.889 4	$ - $54.772 0	$ - $54.607 2
9	$ - $54.422 2	$ - $55.208 3	$ - $55.569 4	$ - $55.707 6	$ - $55.712 9	$ - $55.631 3	$ - $55.488 9
10	$ - $54.888 9	$ - $55.726 0	$ - $56.110 9	$ - $56.244 2	$ - $56.242 6	$ - $56.152 4	$ - $55.999 8
11	$ - $55.183 6	$ - $56.042 3	$ - $56.435 8	$ - $56.585 8	$ - $56.590 5	$ - $56.488 6	$ - $56.323 3
12	$ - $55.344 6	$ - $56.224 2	$ - $56.621 0	$ - $56.768 7	$ - $56.767 5	$ - $56.668 8	$ - $56.501 5
13	$ - $55.388 1	$ - $56.282 0	$ - $56.686 1	${\bf - 56.833 3}$	$ - $56.824 1	$ - $56.715 1	$ - $56.535 9
14	$ - $55.341 3	$ - $56.246 5	$ - $56.651 2	$ - $56.793 6	$ - $56.779 2	$ - $56.658 8	$ - $56.466 6
15	$ - $55.217 4	$ - $56.130 4	$ - $56.534 7	$ - $56.670 8	$ - $56.647 1	$ - $56.518 2	$ - $56.315 1
16	$ - $55.029 8	$ - $55.947 8	$ - $56.349 1	$ - $56.478 5	$ - $56.444 2	$ - $56.302 9	$ - $56.085 9
17	$ - $54.787 7	$ - $55.708 4	$ - $56.105 1	$ - $56.225 8	$ - $56.181 0	$ - $56.027 1	$ - $55.795 6

$ \theta $	$ (T^{}, N^{}) $	$ C(T^{}, N^{}) $	$ \delta $	$ (T^{}, N^{}) $	$ C(T^{}, N^{}) $
0.01	(17, 5)	$ - $65.921 5	1	(15, 6)	$ - $61.034 8
0.02	(17, 5)	$ - $64.537 8	2	(13, 6)	$ - $56.833 3
0.03	(15, 6)	$ - $62.427 9	3	(12, 6)	$ - $53.231 2
0.04	(14, 6)	$ - $59.813 6	4	(11, 7)	$ - $49.548 9
0.05	(13, 6)	$ - $56.833 3	5	(13, 6)	$ - $46.239 1
0.06	(12, 7)	$ - $53.665 2	6	(15, 5)	$ - $42.343 1
0.07	(11, 7)	$ - $50.415 3	7	(10, 8)	$ - $40.299 0
0.08	(10, 7)	$ - $47.103 8	8	(11, 7)	$ - $38.217 2
0.09	(9, 8)	$ - $43.865 0	9	(11, 5)	$ - $36.010 1
0.10	(9, 8)	$ - $40.688 8	10	(13, 6)	$ - $33.995 0

[1]	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.
[2]	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.
[3]	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.
[4]	LI Ling, CHENG Guoqing. Optimization of shock model being maintained under imperfect inspection [J]. Operations Research Transactions, 2013, 17(4): 33-42.

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

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 4

References 16

Related Articles 4

Recommended Articles

Metrics

Comments