考虑竞争失效的二维预防性维修策略优化

doi:10.12305/j.issn.1001-506X.2026.06.14

摘要/Abstract

摘要：

以连续监测条件下存在竞争失效现象的机电产品为对象，研究有限时间区间内不完美维修策略对维修成本的影响规律。针对因突发失效和性能退化失效引起的竞争失效，提出一种二维预防性维修策略。其中，二维预防性维修策略的一个维度是基于不完美维修时间间隔的维修，另一个维度是基于产品性能退化阈值的视情维修，以先发生为准。考虑事后维修为最小维修和不完美维修两种情形，采用改进的离散网格方法优化有限时间区间内实施二维预防性维修和事后维修的总维修成本。以电梯制动器为案例，验证所提维修策略和方法的有效性。结果表明：实施事后最小维修和二维预防性不完美维修能实现维修成本的最小化。此外，在特定改善因子下，最优参数的二维预防性维修等价于基于性能退化阈值的维修。

关键词: 竞争失效, 二维预防性维修, 有限时间区间, 改进的离散网格法, 电梯制动器

Abstract:

Taking the electromechanical products with competing failure phenomenon under continuous monitoring as the research object, the influence of imperfect maintenance on maintenance cost is investigated within finite time horizon. To address competing failures caused by sudden failure and performance-degradation failure, a two-dimensional preventive maintenance （2D PM） strategy is proposed. In this strategy, one dimension of the 2D PM refers to the time interval of imperfect maintenance, and the other dimension refers to the performance-degradation threshold of product degradation failures, whichever occurs first. Considering two corrective maintenance （CM） scenarios, i.e., corrective minimal maintenance and corrective imperfect maintenance, an improved discrete grid method is proposed to optimize the total cost of 2D PM and CM within a finite time horizon. Using the elevator brake as a case study, the effectiveness of the proposed maintenance policy and method is validated. The results indicate that implementing 2D preventive imperfect maintenance combined with minimal corrective maintenance can minimize the overall maintenance cost. In addition, for certain values of the improvement factor, 2D PM with optimal parameters is equivalent to maintenance based on the performance-degradation threshold.

Key words: competing failure, two-dimensional preventive maintenance, finite time horizon, improved discrete grid method, elevator brake

中图分类号:

TH 17

王开颜, 苏春. 考虑竞争失效的二维预防性维修策略优化[J]. 系统工程与电子技术, 2026, 48(6): 1925-1932.

Kaiyan WANG, Chun SU. Optimization of two-dimensional preventive maintenance strategy considering competing failure[J]. Systems Engineering and Electronics, 2026, 48(6): 1925-1932.

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参考文献 30

1	PASCUAL F G, NAVELSKI J P. Monitoring reliability under competing risks using field data[J]. Journal of Quality Technology, 2022, 55 (2): 123- 139. doi: 10.1080/00224065.2022.2080617
2	PAN G Z, GUO G K, LI D, et al. A reliability analysis method based on the mixed correlated competition model considering multi-performance degradation and sudden failures[J]. Engineering Failure Analysis, 2023, 146, 107126. doi: 10.1016/j.engfailanal.2023.107126
3	GAO R, LI X Y. Reliability modeling and analysis of uncertain competing failure systems [J]. Computers & Industrial Engineering, 2024: 110583.
4	姜宇迪, 胡晖, 殷跃红. 基于无监督迁移学习的电梯制动器剩余寿命预测[J]. 上海交通大学学报, 2021, 55 (11): 1408- 1416. doi: 10.16183/j.cnki.jsjtu.2020.175
	JIANG Y D, HU H, YIN Y H. Unsupervised transfer learning for remaining useful life prediction of elevator brake[J]. Journal of Shanghai Jiao Tong University, 2021, 55 (11): 1408- 1416. doi: 10.16183/j.cnki.jsjtu.2020.175
5	ELSAYED A E. Reliability engineering [M]. 3rd ed. Hoboken: John Wiley & Sons, 2021.
6	MAI Y X, XUE J W, WU B. Optimal maintenance policy for systems with environment-modulated degradation and random shocks considering imperfect maintenance[J]. Reliability Engineering & System Safety, 2023, 240, 109597. doi: 10.1016/j.ress.2023.109597
7	ANDERSEN J F, NIELSEN B F. A comparative study of time-based maintenance and condition-based maintenance for multi-component systems [J]. Reliability Engineering & System Safety, 2025: 110759.
8	ALASWAD S, XIANG Y S. A review on condition-based maintenance optimization models for stochastically deteriorating system[J]. Reliability Engineering & System Safety, 2017, 157, 54- 63. doi: 10.1016/j.ress.2016.08.009
9	赵斐, 李鑫, 张建. 考虑竞争失效的视情维修和备件订购联合策略优化[J]. 系统工程与电子技术, 2023, 45 (1): 291- 301. doi: 10.12305/j.issn.1001-506X.2023.01.34
	ZHAO F, LI X, ZHANG J. Joint policy optimization of condition-based maintenance and spare ordering considering competing failure[J]. Systems Engineering and Electronics, 2023, 45 (1): 291- 301. doi: 10.12305/j.issn.1001-506X.2023.01.34
10	ZHAO X J, HE S G, HE Z, et al. Optimal condition-based maintenance policy with delay for systems subject to competing failures under continuous monitoring[J]. Computers & Industrial Engineering, 2018, 124, 535- 544. doi: 10.1016/j.cie.2018.08.006
11	HU J W, SUN Q Z, YE Z S. Condition-based maintenance planning for systems subject to dependent soft and hard failures[J]. IEEE Trans. on Reliability, 2021, 70 (4): 1468- 1480. doi: 10.1109/TR.2020.2981136
12	XIAO H, YAN Y M, GANG K, et al. Optimal inspection policy for a single-unit system considering two failure modes and production wait time[J]. IEEE Trans. on Reliability, 2023, 72 (1): 395- 407. doi: 10.1109/TR.2021.3125963
13	DE JONGE B, SCARF P A. A review on maintenance optimization[J]. European Journal of Operational Research, 2019, 285 (3): 805- 824.
14	MERCIER S, CASTRO I T. Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system[J]. European Journal of Operational Research, 2019, 273 (1): 237- 248. doi: 10.1016/j.ejor.2018.06.020
15	NIU D P, GUO L, BI X L, et al. Preventive maintenance period decision for elevator parts based on multi-objective optimization method[J]. Journal of Building Engineering, 2021, 44, 102984. doi: 10.1016/j.jobe.2021.102984
16	GAN S Y, SONG Z F, ZHANG L. A maintenance strategy based on system reliability considering imperfect corrective maintenance and shocks[J]. Computers & Industrial Engineering, 2022, 164, 107886. doi: 10.1016/j.cie.2021.107886
17	CHENG W Q, ZHAO X J. Maintenance optimization for dependent two-component degrading systems subject to imperfect repair[J]. Reliability Engineering & System Safety, 2023, 240, 109581. doi: 10.1016/j.ress.2023.109581
18	COUSINO T, BRISSAUD F, DOYEN L, et al. Imperfect maintenance modelling and estimation for interval-censored data[J]. Reliability Engineering & System Safety, 2024, 252, 110424. doi: 10.1016/j.ress.2024.110424
19	ARTS J, BOUTE R N, LOEYS S, et al. Fifty years of maintenance optimization: reflections and perspectives[J]. European Journal of Operational Research, 2025, 322 (3): 725- 739. doi: 10.1016/j.ejor.2024.07.002
20	ZHAO X, GUO B, CHEN Y. A condition-based inspection-maintenance policy for critical systems with an unreliable monitor system[J]. Reliability Engineering & System Safety, 2023, 242, 109710. doi: 10.1016/j.ress.2023.109710
21	ZHANG Y J, OUYANG L H, MENG X H, et al. Condition-based maintenance considering imperfect inspection for a multi-state system subject to competing and hidden failures[J]. Computers & Industrial Engineering, 2024, 188, 109856. doi: 10.1016/j.cie.2023.109856
22	ZHENG R, FANG H J, HU C M. Joint optimization of inspection and condition-based maintenance for a deteriorating product under extended warranty[J]. Reliability Engineering & Systems Safety, 2024, 245, 110043. doi: 10.1016/j.ress.2024.110043
23	ZHANG W Y, ZHANG X H, HE S G, et al. Optimal condition-based maintenance policy for multi-component repairable systems with economic dependence in a finite-horizon[J]. Reliability Engineering & System Safety, 2024, 241, 109612. doi: 10.1016/j.ress.2023.109612
24	PENG S Z, JIANG W, HUANG W P, et al. The impact of gamma usage processes on preventive maintenance policies under two-dimensional warranty[J]. Reliability Engineering & Systems Safety, 2024, 242, 10974. doi: 10.1016/j.ress.2023.109743
25	WANG W K, CHEN X. Piecewise deterministic Markov process for condition-based imperfect maintenance models[J]. Reliability Engineering & System Safety, 2023, 236, 109271. doi: 10.1016/j.ress.2023.109271
26	WEI Y, CHENG Y. An optimal two-dimensional maintenance policy for self-service systems with multi-task demands and subject to competing sudden and deterioration-induced failures[J]. Reliability Engineering & System Safety, 2025, 255, 110628. doi: 10.1016/j.ress.2024.110628
27	YE Z S, XIE M. Stochastic modeling and analysis of degradation for highly reliable products[J]. Applied Stochastic Models in Business and Industry, 2015, 31 (1): 16- 32. doi: 10.1002/asmb.2063
28	VAN NOORTWIJK J M. A survey of the application of gamma processes in maintenance[J]. Reliability Engineering & System Safety, 2009, 94 (1): 2- 21. doi: 10.1016/j.ress.2007.03.019
29	SU C, HUANG K. Design and pricing of maintenance service contract based on NASH non-cooperative game approach[J]. Journal of Systems Engineering and Electronics, 2024, 35 (1): 118- 129. doi: 10.23919/JSEE.2024.000010
30	陈严嘉. 乘客电梯块式制动器剩余寿命预测方法研究 [D]. 杭州: 浙江理工大学, 2023.
	CHEN Y J. Research on remaining useful life prediction method of elevator block brake [D]. Hangzhou: Zhejiang Sci-Tech University, 2023.

ρ₁	ρ₂	策略1			策略2
ρ₁	ρ₂	Δt*/天	$X_{{\mathrm{PM}}}^* $/mm	C₁/元	Δt*/天	$X_{{\mathrm{PM}}}^* $/mm	C₂/元
0.1	0.1	235	2.00	4 474	280~360	2.00	3 993
0.2	0.2	230	2.00	3 680	280~360	2.00	3 974
0.3	0.3	230	2.00	3 364	280~360	2.00	4 399
0.4	0.4	195	1.85	3 616	280~360	2.00	4 810
0.5	0.5	270~360	2.00	3 490	280~360	2.00	5 109
0.6	0.6	240	2.00	2 966	280~360	2.00	5 365
0.7	0.7	230~360	2.00	3 058	280~360	2.00	5 561
0.8	0.8	240	2.00	3 177	280~360	2.00	5 691
0.9	0.9	255~360	2.00	3 301	280~360	2.00	5 756
1.0	1.0	235	2.00	4 474	280~360	2.00	5 762

M	N	C₁/元	C₂/元
30	360	3 055.3	5 541.9
60	360	3 055.3	5 538.6
60	720	3 057.8	5 553.7
60	1 440	3 058.2	5 561.4
120	1 440	3 058.3	5 559.9
120	2 880	3 058.9	5 563.5
120	5 760	3 059.2	5 565.6
240	11 520	3 059.1	5 565.9

M	N	所提方法		文献[24]方法
M	N	C₁/元	耗时/min	C₁/元	耗时/min
60	360	3 055.3	0.47	3 055.8	1.05
60	720	3 057.8	1.01	3 055.8	1.65
60	1 440	3 058.2	1.81	3 057.6	3.33
120	1 440	3 058.3	5.31	3 058.6	8.27
240	11 520	3 059.1	88.51	3 059.2	117.43

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[5]	蔡忠义, 项华春, 王攀, 王泽洲, 李超. 竞争失效下多元退化建模的导弹贮存寿命评估[J]. 系统工程与电子技术, 2018, 40(5): 1183-1188.
[6]	黄文平, 周经伦, 宁菊红, 金光. 基于变失效阈值的竞争失效可靠性模型[J]. 系统工程与电子技术, 2017, 39(4): 941-946.
[7]	黄文平, 周经伦, 宁菊红, 金光. 基于竞争失效数据的Lindley分布参数估计[J]. 系统工程与电子技术, 2016, 38(2): 464-469.
[8]	黄秀平，汤衍真，孙权，周经伦. 突发和退化竞争失效产品的老练时间优化[J]. Journal of Systems Engineering and Electronics, 2013, 35(8): 1803-1808.