Optimization of extended warranty cost for multi-component systems with economic dependence based on group maintenance

doi:10.23919/JSEE.2023.000009

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (2): 396-407.doi: 10.23919/JSEE.2023.000009

• • 上一篇

收稿日期:2021-02-15 出版日期:2023-04-18 发布日期:2023-04-18

Optimization of extended warranty cost for multi-component systems with economic dependence based on group maintenance

Rongcai WANG¹(), Enzhi DONG¹(), Zhonghua CHENG¹^,*(), Qian WANG²()

¹ Shijiazhuang Campus of Army Engineering University, Shijiazhuang 050003, China
² Training Base, Officers College of PAP, Guangzhou 510080, China

Received:2021-02-15 Online:2023-04-18 Published:2023-04-18
Contact: Zhonghua CHENG E-mail:asd528866@126.com;woailiuxi666@163.com;13143648622@163.com;18003131595@163.com
About author:
WANG Rongcai was born in 1996. He is studying for his M.S. degree in management science and engineering with Shijiazhuang Campus of Army Engineering University. His research interests include reliability engineering and maintenance engineering. E-mail: asd528866@126.com

DONG Enzhi was born in 1997. He is studying for his M.S. degree in management science and engineering with Shijiazhuang Campus of Army Engineering University. His research interests include reliability engineering and maintenance engineering. E-mail: woailiuxi666@163.com

CHENG Zhonghua was born in 1972. He is a professor and Ph.D. tutor in Shijiazhuang Campus of Army Engineering University. His research interests include management science and engineering, equipment support, and reliability engineering. E-mail: 13143648622@163.com

WANG Qian was born in 1989. He received his M.S. degree from Shijiazhuang Campus of Army Engineering University in 2019. He is currently a lecturer in the Training Base, Officers College of PAP. His research interests include maintenance engineering and equipment support. E-mail: 18003131595@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (71871219)

摘要/Abstract

Abstract:

During extended warranty (EW) period, maintenance events play a key role in controlling the product systems within normal operations. However, the modelling of failure process and maintenance optimization is complicated owing to the complex features of the product system, namely, components of the multi-component system are interdependent with each other in some form. For the purpose of optimizing the EW pricing decision of the multi-component system scientifically and rationally, taking the series multi-component system with economic dependence sold with EW policy as a research object, this paper optimizes the imperfect preventive maintenance (PM) strategy from the standpoint of EW cost. Taking into consideration adjusting the PM moments of the components in the system, a group maintenance model is developed, in which the system is repaired preventively in accordance with a specified PM base interval. In order to compare with the system EW cost before group maintenance, the system EW cost model before group maintenance is developed. Numerical example demonstrates that offering group maintenance programs can reduce EW cost of the system to a great extent, thereby reducing the EW price, which proves to be a win-win strategy to manufacturers and users.

Key words: extended warranty (EW) cost, multi-component system, economic dependence, preventive maintenance (PM), group maintenance

. [J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 396-407.

Rongcai WANG, Enzhi DONG, Zhonghua CHENG, Qian WANG. Optimization of extended warranty cost for multi-component systems with economic dependence based on group maintenance[J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 396-407.

图/表 12

参考文献 34

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Component	$\delta_{i}$	$c_{f_i}$ /CNY	$c_{p_i}$ /CNY	$c_{D_i}$ /CNY	$ \alpha_{i} $	$ \beta_{i} $
1	0.9	750	300	300	2.20	710
2	0.8	1200	700	300	2.60	640
3	0.4	950	500	300	2.50	530
4	0.6	1050	550	300	2.80	750
5	0.8	800	400	300	2.65	720
6	0.5	900	450	300	2.90	800

Plan	$ {W_e} $ /d	$C(T_1^ * ) /{\rm{CNY}}$	$C(T_2^ * )/{\rm{CNY}}$	$C(T_3^ * )/{\rm{CNY}}$	$C(T_4^ * )/{\rm{CNY}}$	$C(T_5^ * )/{\rm{CNY}}$	$C(T_6^ * )/{\rm{CNY}}$	${\rm{EC} }(T,W,{W_e})/{\rm{CNY}}$
1	1080	1262.88	2761.64	3538.88	2089.13	1583.05	1729.71	12965.29
2	1260	1598.80	3710.21	5330.73	2850.68	2059.05	2374.30	17923.77
3	1440	2098.20	4755.04	7582.08	3994.79	2771.83	3327.96	24529.89
4	1620	2568.40	5920.16	10080.35	5047.97	3357.46	4392.29	31366.62
5	1800	3036.37	7054.22	12976.19	6302.24	4048.50	5567.00	38984.52
6	1980	3418.42	8111.05	16039.34	7578.48	4643.20	6799.04	46589.54
7	2160	3959.25	9678.70	19772.41	9145.25	5435.03	8396.65	56387.28
8	2340	4423.04	10975.13	23741.97	10725.52	6128.16	9993.73	65987.55
9	2520	4867.08	12307.81	28117.69	12549.36	6919.01	11822.89	76583.84
10	2700	5355.42	13719.87	32913.02	14530.84	7769.58	13927.23	88215.96
11	2880	5957.22	15216.65	38107.82	16704.57	8646.83	16221.34	100854.44
12	3060	6443.48	16692.19	43615.05	18772.56	9341.08	18620.28	113484.64
13	3240	6933.19	18476.24	49877.10	21323.74	10303.77	21332.47	128246.51
14	3420	7458.70	20192.70	56404.36	24010.23	11299.22	24350.95	143716.16
15	3600	8020.46	22109.14	63616.96	27008.07	12379.89	27615.41	160749.94

Plan	$ {W_e} $	$ T_1^ * $	$ T_2^ * $	$ T_3^ * $	$ T_4^ * $	$ T_5^ * $	$ T_6^ * $	$ {T_m} $
1	1080	216	216	216	216	216	216	216
2	1260	288	288	288	288	288	288	288
3	1440	396	252	252	396	252	396	252
4	1620	468	324	324	324	324	468	324
5	1800	396	288	288	396	396	396	288
6	1980	432	324	324	324	324	432	324
7	2160	504	396	396	396	396	504	396
8	2340	432	360	432	432	432	432	360
9	2520	468	324	396	468	468	468	324
10	2700	504	288	360	432	432	504	288
11	2880	468	324	324	468	468	468	324
12	3060	396	396	396	396	396	396	396
13	3240	432	324	432	432	432	432	324
14	3420	468	396	396	396	396	468	396
15	3600	504	324	324	432	432	432	324

Plan	${W_e}/{\rm{d}}$	${C^o}({T_1})/{\rm{CNY}}$	${C^o}({T_2})/{\rm{CNY}}$	${C^o}({T_3})/{\rm{CNY}}$	${C^o}({T_4})/{\rm{CNY}}$	${C^o}({T_5})/{\rm{CNY}}$	${C^o}({T_6})/{\rm{CNY}}$
1	1080	1262.88	2761.64	3538.88	2089.13	1583.04	1729.71
2	1260	1598.80	3710.21	5330.73	2850.68	2059.05	2374.30
3	1440	2443.28	4755.04	7582.08	4618.52	2771.83	3756.71
4	1620	2250.04	5920.16	10080.35	5047.97	3357.46	4028.07
5	1800	2868.64	7054.22	12976.19	6030.83	3774.27	5394.41
6	1980	3272.01	8111.05	16039.34	7578.48	4643.20	6651.06
7	2160	3940.75	9678.70	19772.41	9145.25	5435.03	8447.69
8	2340	4487.26	10975.13	24015.53	10972.47	6246.93	10211.76
9	2520	4616.49	12307.81	28163.05	12157.72	6516.96	11578.10
10	2700	5643.60	13719.87	32715.04	15504.14	8625.78	14319.45
11	2880	5823.54	15216.65	38107.82	16605.35	8449.27	16205.65
12	3060	6443.48	16692.19	43615.05	18772.56	9341.08	18620.28
13	3240	6924.47	18476.24	50030.32	21469.23	10314.58	21490.94
14	3420	7508.06	20192.70	56404.36	24010.23	11299.22	24523.46
15	3600	8673.67	22109.14	63616.96	27076.50	12341.18	27711.10

Plan	$ {W_e} $ /d	${\rm{EC}}(T,W,{W_e})$ /CNY	${{\rm{EC}}^o}(T,W,{W_e})$ /CNY	RC/%	$ P({T^ * },{W_e}) $ /CNY	$ {P_0} $ /CNY	RP/%
1	1080	12965.29	11465.29	11.57	14965.29	13465.29	10.02
2	1260	17923.77	16423.77	8.37	20923.77	19423.77	7.17
3	1440	24529.89	23827.47	2.86	28529.89	27827.47	2.46
4	1620	31366.62	28284.04	9.83	36366.62	33284.04	8.48
5	1800	38984.52	34798.55	10.74	44984.52	40798.55	9.31
6	1980	46589.54	42395.14	9.00	53589.54	49395.14	7.83
7	2160	56387.28	52519.82	6.86	64387.28	60519.82	6.01
8	2340	65987.55	62409.08	5.42	74987.55	71409.08	4.77
9	2520	76583.84	70540.13	7.89	86583.84	80540.13	6.98
10	2700	88215.96	84827.87	3.84	99215.96	95827.87	3.41
11	2880	100854.44	93808.28	6.99	112854.44	105808.28	6.24
12	3060	113484.64	105984.64	6.61	126484.64	118984.64	5.93
13	3240	128246.51	121205.78	5.49	142246.51	135205.78	4.95
14	3420	143716.16	135538.03	5.69	158716.16	150538.03	5.15
15	3600	160749.94	152228.55	5.30	176749.94	168228.55	4.82

Optimization of extended warranty cost for multi-component systems with economic dependence based on group maintenance

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