Joint optimization of inspection-based and age-based preventive maintenance and spare ordering policies for single-unit systems

doi:10.23919/JSEE.2022.000120

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (5): 1268-1280.doi: 10.23919/JSEE.2022.000120

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Joint optimization of inspection-based and age-based preventive maintenance and spare ordering policies for single-unit systems

Weining MA¹, Fei ZHAO^1,^2,^3,*(), Xin LI³, Qiwei HU¹, Bingcong SHANG^2,³

¹ Department of Equipment Command and Management Shijiazhuang Campus, Army Engineering University, Shijiazhuang 050003, China
² School of Business Administration, Northeastern University, Shenyang 110057, China
³ Northeastern University at Qinhuangdao, Qinhuangdao 066099, China

Received:2021-04-07 Online:2022-10-27 Published:2022-10-27
Contact: Fei ZHAO E-mail:zhaofeiaeu@163.com
About author:|MA Weining was born in 1982. He received his B.S. and M.S. degrees in management engineering from the Army Engineering University of PLA, Shijiazhuang, in 2006 and 2009, respectively. Now he is a Ph.D. candidate in maintenance engineering. He is currently a lecturer at the Shijiazhuang Campus of Army Engineering University of PLA. His research interests include equipment maintenance engineering, maintenance management of complex system, and optimization algorithm.E-mail: maweiningxq@126.com||ZHAO Fei was born in 1984. She received her B.S. and M.S. degrees in School of Economics and Management from Hebei University of Engineering, Handan, China, in 2008 and 2011, respectively. She received her Ph.D. degree from University of Science and Technology Beijing, China, in 2015. She is currently an associate professor with the School of Business Administration, Northeastern University. Her research interests include system reliability, maintenance, and operations research and optimization.E-mail: zhaofei@neuq.edu.cn||LI Xin was born in 1996. He received his B.S. degree in School of Electronic Information Engineering from Taiyuan University of Science and Technology, in 2018. He is currently a postgraduate from Northeastern University at Qinhuangdao. His research interests include system reliability, and maintenance and spare parts optimization.E-mail: 15735169458@163.com||HU Qiwei was born in 1979. He received his M.S. and Ph. D. degrees in management engineering from the Army Engineering University of PLA, Shijiazhuang, in 2005 and 2016, respectively. Now he is currently an associate professor at the Shijiazhuang Campus of Army Engineering University of PLA. His research interests include maintenance optimization, and spare parts management.E-mail: huqiweiaeu@163.com||SHANG Bingcong was born in 1989. She received her B.S. and M.S. degrees from School of Information Science and Engineering, Northeastern University, Shenyang, China, in 2011 and 2015. She is currently a lecturer with the School of Business Administration, Northeastern University. Her research interests include system reliability, and operations research and optimization.E-mail: shangbingcong@163.com
Supported by:
This work was supported by the Naitonal Natural Science Foundation of China (71701038), China Ministry of Education Humanities and Social Sciences Research Youth Fund Project (16YJC630174), the Natural Science Foundation of Hebei Province (G2019501074), the Fundamental Research Funds for the Central Universities (N2123019), and the Postgraduate Funding Project of PLA (JY2020B085).

Abstract

Abstract:

This paper presents a joint optimization policy of preventive maintenance (PM) and spare ordering for single-unit systems, which deteriorate subject to the delay-time concept with three deterioration stages. PM activities that combine a non-periodic inspection scheme with age-replacement are implemented. When the system is detected to be in the minor defective stage by an inspection for the first time, place an order and shorten the inspection interval. If the system has deteriorated to a severe defective stage, it is either repaired imperfectly or replaced by a new spare. However, an immediate replacement is required once the system fails, the maximal number of imperfect maintenance (IPM) is satisfied or its age reaches to a pre-specified threshold. In consideration of the spare ’s availability as needed, there are three types of decisions, i.e., an immediate or a delayed replacement by a regular ordered spare, an immediate replacement by an expedited ordered spare with a relative higher cost. Then, some mutually independent and exclusive renewal events at the end of a renewal cycle are discussed, and the optimization model of such a joint policy is further developed by minimizing the long-run expected cost rate to find the optimal inspection and age-replacement intervals, and the maximum number of IPM. A Monte-Carlo based integration method is also designed to solve the proposed model. Finally, a numerical example is given to illustrate the proposed joint optimization policy and the performance of the Monte-Carlo based integration method.

Key words: maintenance optimization, imperfect maintenance (IPM), three-stage failure process, spare ordering

Weining MA, Fei ZHAO, Xin LI, Qiwei HU, Bingcong SHANG. Joint optimization of inspection-based and age-based preventive maintenance and spare ordering policies for single-unit systems[J]. Journal of Systems Engineering and Electronics, 2022, 33(5): 1268-1280.

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Renewal scenario		Whether ${S_2}$ has been identified	${T_p} < {T_q}$	Availability of the ordered spare	Decision- making
A failure renewal		No	—	—	ER
		Yes	Yes	No	DR
			Yes	Yes	IR
			No	No	DR
			No	Yes	IR
An age-replacement renewal at ${T}_{{\rm{age}}}$	The system is in the state ${S_1}$	No	—	—	ER
		Yes	No	No	DR
		Yes	No	Yes	IR
	The system is in the state ${S_2}$	No	—	—	ER
		Yes	Yes	No	DR
			Yes	Yes	IR
			No	No	DR
			No	Yes	IR
	The system is in the state ${S_3}$	No	—	—	ER
		Yes	Yes	No	DR
			Yes	Yes	IR
			No	No	DR
			No	Yes	IR
An inspection renewal after the number of IPM reaches the pre-specified threshold		No	—	—	ER
		Yes	Yes	No	DR
			Yes	Yes	IR
			No	No	DR
			No	Yes	IR

Stage	$ {\varphi _0}(y) $	$ {\eta _0}(z) $
$ {\lambda _0}\left( x \right) $	0.008	1.3
${\varphi _0}\left( y \right) $	0.013	1.7
${\eta _0}\left( z \right)$	0.021	2.3

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[3]	Wei Zhou, Dongfeng Wang, Jingyu Sheng, and Bo Guo. Collaborative optimization of maintenance and spare ordering of continuously degrading systems [J]. Journal of Systems Engineering and Electronics, 2012, 23(1): 63-70.
[4]	Changyou Li, Minqiang Xu, Song Guo, and Rixin Wang. Multiobjective maintenance optimization of the continuously monitored deterioration system [J]. Journal of Systems Engineering and Electronics, 2010, 21(5): 791-795.

Joint optimization of inspection-based and age-based preventive maintenance and spare ordering policies for single-unit systems

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