Reliability-based selective maintenance for redundant systems with dependent performance characteristics of components

doi:10.23919/JSEE.2023.000086

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (3): 804-814.doi: 10.23919/JSEE.2023.000086

• RELIABILITY • Previous Articles

Reliability-based selective maintenance for redundant systems with dependent performance characteristics of components

Hui CAO(), Fuhai DUAN(), Yu’nan DUAN()

¹ School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China

Received:2021-02-18 Online:2023-06-15 Published:2023-06-30
Contact: Fuhai DUAN E-mail:caoh1128@163.com;duanfh@dlut.edu.cn;18842610108@163.com
About author:
CAO Hui was born in 1985. She received her B.S. and M.S. degrees from Shenyang University of Technology, Shenyang, China. She is currently pursuing her Ph.D. degree in measurement techniques and instruments with the School of Mechanical Engineering, Dalian University of Technology, Dalian, China. Her research interests are reliability modeling and evaluation of complex redundancy systems, reliability-based selective maintenance planning, and integrated design of mechanical product reliability and performance. E-mail: caoh1128@163.com

DUAN Fuhai was born in 1965. He received his B.S., M.S., and Ph.D. degrees respectively from Northwestern Polytechnical University, Xi’an, China. He has over ten years of research and teaching experience in areas of reliability and maintainability engineering. He is currently a professor, a doctoral supervisor, and a reliability specialist of the School of Mechanical Engineering, Dalian University of Technology, Dalian, China. He has published and presented more than 50 papers in domestic and international professional journals and international conferences. His recent research interests include reliability testability, and maintainability of aeronautical system engineering, prognostics and health management, and machinery products life-cycle management. E-mail: duanfh@dlut.edu.cn

DUAN Yu’nan was born in 1994. He received his B.S. degree from Dalian Jiaotong University. He is currently pursuing his M.S. degree in mechanical engineering with the School of Mechanical Engineering, Dalian University of Technology, Dalian, China. His research interests include system reliability analysis, the modeling method of system reliability, and performance degradation research. E-mail: 18842610108@163.com
Supported by:
This work was supported by the Aeronautical Science Foundation of China (20150863003)

Abstract

Abstract:

The reliability-based selective maintenance (RSM) decision problem of systems with components that have multiple dependent performance characteristics (PCs) reflecting degradation states is addressed in this paper. A vine-Copula-based reliability evaluation method is proposed to estimate the reliability of system components with multiple PCs. Specifically, the marginal degradation reliability of each PC is built by using the Wiener stochastic process based on the PC’s degradation mechanism. The joint degradation reliability of the component with multiple PCs is established by connecting the marginal reliability of PCs using D-vine. In addition, two RSM decision models are developed to ensure the system accomplishes the next mission. The genetic algorithm (GA) is used to solve the constraint optimization problem of the models. A numerical example illustrates the application of the proposed RSM method.

Key words: D-vine, genetic algorithm (GA), reliability-based selective maintenance (RSM), redundant system, Wiener stochastic process

Hui CAO, Fuhai DUAN, Yu’nan DUAN. Reliability-based selective maintenance for redundant systems with dependent performance characteristics of components[J]. Journal of Systems Engineering and Electronics, 2023, 34(3): 804-814.

Figures/Tables 13

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References 30

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Copula	c(u, v; θ)	h(u, v; θ)
Gaussian	$\dfrac{1}{ {\sqrt {1 - {\theta ^2} } } }\exp ( - \dfrac{ { {\theta ^2}({\phi ^{ - 2} }(u) + {\phi ^{ - 2} }(v)) - 2\theta {\phi ^{ - 1} }(u){\phi ^{ - 1} }(v)} }{ {2(1 - {\theta ^2})} })$	$\varPhi (\dfrac{ { {\varPhi ^{ - 1} }(u) - \theta {\varPhi ^{ - 1} }(v)} }{ {\sqrt {1 - {\theta ^2} } } })$
Frank	$\dfrac{ { - \theta \exp ( - \theta u)\exp ( - \theta v)(\exp ( - \theta ) - 1)} }{ { { {((\exp ( - \theta ) - 1) + (\exp ( - \theta u) - 1)(\exp ( - \theta v) - 1))}^2} } }$	$\dfrac{ {\exp ( - \theta v)(\exp ( - \theta u) - 1)} }{ {(\exp ( - \theta ) - 1) + (\exp ( - \theta u) - 1)(\exp ( - \theta v) - 1)} }$
Clayton	$ {u^{ - \theta - 1}}{v^{ - \theta - 1}}(1 + \theta ){({u^{ - \theta }} + {v^{ - \theta }} - 1)^{ - 1/\theta - 2}} $	$ {v^{ - \theta - 1}}{({u^{ - \theta }} + {v^{ - \theta }} - 1)^{ - 1 - 1/\theta }} $
Gumbel	$\begin{gathered} C(u,v){(uv)^{ - 1} }{({( - \ln u)^\theta } + {( - \ln v)^\theta })^{ - 2 + 2/\theta } }{(\ln u\ln v)^{\theta - 1} }\cdot \\ \qquad (1 + (\theta - 1){({( - \ln u)^\theta } + {( - \ln v)^\theta })^{ - 1/\theta } }) \\ \end{gathered}$	$ C(u,v){v^{ - 1}}{( - \ln v)^{\theta - 1}}{({( - \ln u)^\theta } + {( - \ln v)^\theta })^{1/\theta - 1}} $

Parameter	C_1jk	C_2j	C_3j	C_4j	C_5jk
μ	(0.3172, 0.1399 0.0965)	0.2401	0.4213	0.1165	(0.2066, 0.1164, 0.1414)
σ	(2.8908, 2.6244, 1.5906)	1.001	2.9238	2.5922	(1.9917, 1.6394, 1.4731)
D_f	(80, 130, 100)	80	102	68	(120, 98, 70)
d	(55, 112, 80)	68	52	44	(98, 82, 48)

h-function	Candidate Copulas	Parameter of the pair-Copulas (θ)		AIC
h-function	Candidate Copulas	C_1j	C_5j	C_1j	C_5j
h₁₂	Gaussian	0.0645	−0.0091	0.3321	1.9669
	Clayton	0.0270	0.0144	1.8199	1.9407
	Frank	0.3992	−0.0070	0.0384	1.9994
	Gumbel	1.0351	1.0000	0.6659	2.0001
h₂₃	Gaussian	0.1251	0.1164	−4.3102	−3.4530
	Clayton	0.1376	0.1510	−2.7710	−3.3602
	Frank	0.8052	0.6710	−5.7434	−3.5202
	Gumbel	1.0758	1.0698	−3.0865	−2.9090
h_13\|2	Gaussian	0.0292	0.0080	1.6586	1.9743
	Clayton	0.0135	0.0567	1.3759	0.9508
	Frank	0.1576	0.0196	1.7052	1.9954
	Gumbel	1.0227	1.0000	1.9449	2.0000

Component	C_1j			C_5j
Component	h₁₂	h₂₃	h_13\|2	h₁₂	h₂₃	h_13\|2
Copula	Frank	Frank	Clayton	Clayton	Frank	Clayton
Estimation	0.1133	0.1155	0.5730	0.1014	0.1029	0.1476

Maintenance action	Efficiency (η)	Maintenance cost/time
Maintenance action	Efficiency (η)	C_1j	C_2j	C_3j	C_4j	C_5j
Replacement	1	49/3	47/3.2	48/3.2	50/3	53/3.4
Preventative maintenance	0.3	35/2.7	36/2.8	39/2.5	41/2.3	43/2.1
Cleaning and adjusted	0.1	32/1.4	24/1.5	27/1.5	33/1.6	35/1.4

Reliability-based selective maintenance for redundant systems with dependent performance characteristics of components

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Policy	Model	Cost	Time	System reliability
Policy	Model	Cost	Time	Dep. PCs	Ind. PCs
RSM	Model 1	118	7.9	0.9888	0.9884
RSM	Model 2	87	5.1	0.9193	0.9138

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Component	C_1j	C_2j	C_3j	C_4j	C_5j	System reliability
Reliability (dependent)	0.3961	0.5463	0.9428	0.7885	0.6450	0.4060
Reliability (independent)	0.3423	0.5463	0.9428	0.7885	0.5626	0.3158