考虑经济相关性的复杂二维保修装备组合维修策略

doi:10.12305/j.issn.1001-506X.2022.07.18

摘要/Abstract

摘要：

针对保修期内孤立地对各单部件进行维修增加装备保修费用的问题, 结合复杂装备的二维保修现状, 以保修期内的保修费用为主要定量化分析指标, 以单部件二维预防性维修费用模型为基础, 将研究对象由单部件系统拓展到包含串联多部件系统的复杂装备。引入预防性维修基准间隔期, 采用组合维修的方法, 将各单部件预防性维修工作组合优化, 建立了多部件系统二维预防性组合维修费用模型。最后, 实例分析验证了该方法的可行性，可为二维预防性维修服务下多部件系统组合维修策略的制订提供科学依据与定量化分析方法。

Abstract:

In order to solve the problem of increasing the maintenance cost of the contractor by maintaining each single component in isolation during the warranty period, combined with the maintenance status of complex equipment, based on the two-dimensional preventive maintenance cost model of single component, the research object is expanded from single component system to complex equipment including series multi component system with the main quantitative analysis index of warranty cost during the warranty period. Based on the introduction of preventive maintenance benchmark interval and the method of combined maintenance, a two-dimensional preventive combined maintenance cost model of multi-component system is established. Finally, an example is given to verify the feasibility of the method. This strategy can provide a scientific basis and quantitative analysis method for the formulation of multi component system combined maintenance strategy under two-dimensional preventive maintenance service.

Key words: economic dependence, complex equipment, two-dimensional warranty, two-dimensional preventive maintenance, combined maintenance

中图分类号:

E92
F403.8

董恩志, 程中华, 王荣财. 考虑经济相关性的复杂二维保修装备组合维修策略[J]. 系统工程与电子技术, 2022, 44(7): 2219-2228.

Enzhi DONG, Zhonghua CHENG, Rongcai WANG. Combined maintenance strategy of complex two-dimensional warranty equipment considering economic dependence[J]. Systems Engineering and Electronics, 2022, 44(7): 2219-2228.

图/表 14

图1

图2

表1

图3

图4

图5

表2

图6

图7

图8

表3

表4

表5

表6

参考文献 34

1	WANG D F , HE Z , HE S G , et al. Dynamic pricing of two-dimensional extended warranty considering the impacts of product price fluctuations and repair learning[J]. Reliability Engineering and System Safety, 2021, 210 (5): 36- 50.
2	TALEIZDEH A A , MOKHTARZADEH M . Pricing and two-dimensional warranty policy of multi-products with online and offline channels using a value-at-risk approach[J]. Computers & Industrial Engineering, 2020, 148 (2): 56- 64.
3	李欣玥, 高勇民, 王维强, 等. 基于二维工龄更换的保修服务优化研究[J]. 航空科学技术, 2017, 28 (10): 66- 72.
	LI X Y , GAO Y M , WANG W Q , et al. Research on warranty service optimization based on two-dimensional age replacement[J]. Aeronautical Science & Technology, 2017, 28 (10): 66- 72.
4	WANG X L , LI L S , XIE M . An unpunctual preventive maintenance policy under two-dimensional warranty[J]. European Journal of Operational Research, 2020, 282 (1): 304- 318. doi: 10.1016/j.ejor.2019.09.025
5	FAN D M , ZHANG A B , FENG Q , et al. Group maintenance optimization of subsea Xmas trees with stochastic dependency[J]. Reliability Engineering and System Safety, 2021, 209 (7): 107450.
6	WANG X L , WEI X . Two-dimensional warranty: a literature review[J]. Journal of Risk and Reliability, 2018, 232 (3): 284- 307.
7	ISKANDAR B P , MURTHY D N P , JACK N . A new repair-replace strategy for items sold with a two-dimensional warranty[J]. Computers & Operations Research, 2005, 16 (3): 669- 682.
8	程中华, 王谦, 白永生, 等. 二维保修装备可用度优化模型[J]. 装甲兵工程学院学报, 2019, 33 (3): 34- 39. doi: 10.3969/j.issn.1672-1497.2019.03.007
	CHENG Z H , WANG Q , BAI Y S , et al. Optimization model of two-dimensional warranty equipment availability[J]. Journal of Academy of Armored Force Engineering, 2019, 33 (3): 34- 39. doi: 10.3969/j.issn.1672-1497.2019.03.007
9	程中华, 杨志远, 杨红兵. 预防性维修下装备二维保修策略优化模型[J]. 工业工程, 2017, 20 (4): 79- 86. doi: 10.3969/j.issn.1007-7375.e15-0555
	CHENG Z H , YANG Z Y , YANG H B . Optimization model of equipment two-dimensional warranty strategy under preventive maintenance[J]. Industrial Engineering Journal, 2017, 20 (4): 79- 86. doi: 10.3969/j.issn.1007-7375.e15-0555
10	CHEN T , POPOVA E . Maintenance policies with two-dimensional warranty[J]. Reliability Engineering & System Safety, 2002, 7 (1): 61- 69.
11	JACK N , MURTHY D N P , ISKANDAR B P . Comments on "maintenance policies with two-dimensional warranty"[J]. Reliability Engineering and System Safety, 2003, 82 (1): 105- 109. doi: 10.1016/S0951-8320(03)00119-4
12	JIAN Y , XIANG Z C . Research on a two-dimensional warranty strategy based on minimal and imperfect repairs[J]. Industrial Engineering and Management, 2009, 14 (3): 65- 69.
13	VARNOSAFADERANI S , CHUKONA S . A two-dimensional warranty servicing strategy based on reduction in product failure intensity[J]. Computers & Mathematics with Applications, 2012, 63 (1): 201- 205.
14	PENG S Z , JIANG W , ZHAO W H . A preventive maintenance policy with usage-dependent failure rate thresholds under two-dimensional warranties[J]. ⅡSE Transactions, 2020, 13 (1): 136- 145.
15	BAIK J , MURTHY D N P , JACK N . Two-dimensional failure modeling with minimal repair[J]. Naval Research Logistics, 2010, 51 (3): 345- 362.
16	WANG X , YE Z S . Design of customized two-dimensional extended warranties considering use rate and heterogeneity[J]. ⅡSE Transactions, 2020, 11 (2): 170- 190.
17	ZHENG R , SU C . A flexible two-dimensional basic warranty policy with two continuous warranty regions[J]. Quality and Reliability Engineering International, 2020, 6 (6): 2003- 2018.
18	WANG X L , LI L S , XIE M . An unpunctual preventive maintenance policy under two-dimensional warranty[J]. European Journal of Operational Research, 2020, 282 (1): 304- 318. doi: 10.1016/j.ejor.2019.09.025
19	HE Z , WANG D F , HE S G , et al. Two-dimensional extended warranty strategy including maintenance level and purchase time: a win-win perspective[J]. Computers & Industrial Engineering, 2020, 41 (2): 15- 30.
20	WANG Q , CHENG Z H , GAN Q T , et al. Cost optimization of two-dimensional warranty products under preventive maintenance[J]. Mathematical Problems in Engineering, 2021, 16 (2): 30- 50.
21	WANG R C , CHENG Z H , WANG Q . Research on availability model of two-dimensional warranty products based on incomplete maintenance[J]. IOP Conference Series: Materials Science and Engineering, 2021, 1043 (3): 741- 766.
22	朱会会. 基于预防性维修的二维保修建模与优化[D]. 石家庄: 石家庄铁道大学, 2020.
	ZHU H H. Two dimensional warranty modeling and optimization based on preventive maintenance[D]. Shijiazhuang: Shijiazhuang Railway University, 2020.
23	DAI A S , ZHANG Z M , HOU P W , et al. Warranty claims forecasting for new products sold with a two-dimensional warranty[J]. Journal of Systems Science and Systems Engineering, 2019, 28 (6): 715- 730. doi: 10.1007/s11518-019-5434-8
24	TONG P , LIU C L . Designing differential service strategy for two-dimensional warranty based on warranty claim data under consumer-side modularization[J]. Proceedings of the Institution of Mechanical Engineers Part O-Journal of Risk and Reliability, 2019, 234 (3): 550- 561.
25	LIN K S , CHEN Y X . Analysis of two-dimensional warranty data considering global and local dependence of heterogeneous marginals[J]. Reliability Engineering and System Safety, 2021, 207 (2): 53- 70.
26	ZHOU Y F , ZHANG Z S , LIN T R , et al. Maintenance optimisation of a multi-state series-parallel system considering economic dependence and state-dependent inspection intervals[J]. Reliability Engineering and System Safety, 2013, 111 (2): 42- 60.
27	PHUC D , ROY A , PHIL S , et al. Modelling and application of condition-based maintenance for a two-component system with stochastic and economic dependencies[J]. Reliability Engineering and System Safety, 2019, 182 (3): 42- 60.
28	DAO C D , ZUO M J , PANDEY M . Selective maintenance for multi-state series-parallel systems under economic dependence[J]. Reliability Engineering and System Safety, 2014, 121 (1): 240- 249.
29	苏春, 陈武. 考虑部件经济相关性的风力机系统状态维修优化[J]. 东南大学学报(自然科学版), 2016, 46 (5): 1007- 1012.
	SU C , CHEN W . Condition based maintenance optimization of wind turbine system considering economic correlation of components[J]. Journal of Southeast University (Natural science edition), 2016, 46 (5): 1007- 1012.
30	PHUC D , HAI C V , BARROS A , et al. Maintenance grouping for multi-component systems with availability constraints and limited maintenance teams[J]. Reliability Engineering and System Safety, 2015, 142 (11): 56- 67.
31	ZHANG X H , ZENG G C . Deterioration state space partitioning method for opportunistic maintenance modelling of identical multi-unit systems[J]. International Journal of Production Research, 2015, 53 (7): 2100- 2118. doi: 10.1080/00207543.2014.965354
32	王谦, 程中华, 白永生, 等. 复杂部件二维保修费用优化模型研究[J]. 火炮发射与控制学报, 2020, 41 (2): 98- 103.
	WANG Q , CHENG Z H , BAI Y S , et al. Optimization model of two-dimensional warranty cost for complex components[J]. Journal of Gun Launch and Control, 2020, 41 (2): 98- 103.
33	LAELESS J , HU J , CAO J . Methods for estimation of failure distributions and rates from automobile warranty data[J]. Lifetime Data Analysis, 1995, 1 (3): 227- 240. doi: 10.1007/BF00985758
34	KIJIMA M , MORIMURA H , SUZUKI Y . Periodical replacement-problem without assuming minimal repair[J]. European Journal of Operational Research, 1988, 37 (2): 194- 203. doi: 10.1016/0377-2217(88)90329-3

预防性维修次数	保修期限	数值
n₁	[0, T_W)	int [T_W/T_0j]
n₂	[0, T_W)	int [(T_Wr)/U_0j]
n₃	[0, U_W)	int [U_W/U_0j]
n₄	[0, U_W)	int [U_W/T_0jr]

部件	α_s	φ	r_s	γ	β	C_fj/元	C_pj/元	C_Di/元	δ	η
1	0.3	2.2	1.0	1.15	0.9	600	1 500	500	2	5
2	1	2	1.0	1.4	0.8	800	2 000	500	2	5
3	0.8	1.2	1.0	1.6	0.7	650	1 800	500	2	5

对比指标	保修方式			保修费用变化率/%
对比指标	一维保修	二维保修		保修费用变化率/%
预防性维修基准间隔期	T_m/年0.3/年	T_m/年 0.4/年	U_m/万公里 1.5/万公里	- -
C^*(T_W, U_W)/元	66 758	58 998.5		11.6

部件编号	不采取预防性维修措施	采取预防性维修措施			变化率/%
部件编号	C_j(T_W, U_W)/元	T_0j^*/年	U_0j^*/万公里	C_j^*(T_W, U_W)/元	变化率/%
1	144 714	0.4	2.0	36 134	-75.03
2	22 160	1.5	1.6	17 966	-18.93
3	8 647	1.5	1.5	10 290	19
费用合计	175 521	-	-	64 390	-63.31

部件	r/(万公里/年)	T_m	2T_m	3T_m	4T_m	5T_m	6T_m	7T_m
1	r≤5	+	+	+	+	+	+	+
2	r≤1.07	-	-	-	+	-	-	+
3	r≤1	-	-	-	+	-	-	+