Component reallocation and system replacement maintenance based on availability and cost in series systems

doi:10.23919/JSEE.2022.000153

Abstract

Abstract:

Component reallocation (CR) is receiving increasing attention in many engineering systems with functionally interchangeable and unbalanced degradation components. This paper studies a CR and system replacement maintenance policy of series repairable systems, which undergoes minimal repairs for each emergency failure of components, and considers constant downtime and cost of minimal repair, CR and system replacement. Two binary mixed integer nonlinear programming models are respectively established to determine the assignment of CR, and the uptime right before CR and system replacement with the objective of minimizing the system average maintenance cost and maximizing the system availability. Further, we derive the optimal uptime right before system replacement with maximization of the system availability, and then give the relationship between the system availability and the component failure rate. Finally, numerical examples show that the CR and system replacement maintenance policy can effectively reduce the system average maintenance cost and improve the system availability, and further give the sensitivity analysis and insights of the CR and system replacement maintenance policy.

Key words: component reallocation (CR), system replacement, maintenance cost, availability, binary mixed integer nonlinear programming, minimal repair

Yuqiang FU, Xiaoyang MA. Component reallocation and system replacement maintenance based on availability and cost in series systems[J]. Journal of Systems Engineering and Electronics, 2022, 33(6): 1342-1353.

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References 33

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Case	Assignment of CR $\boldsymbol{X}$	$ \tau $	$ T $	$ N $	$\displaystyle\sum\limits _{j=1}^{n}{\lambda }_{j}\left(T+{B}_{j}\left(\tau \right)-\tau \right)$	$C\left(\tau ,\boldsymbol{X},T\right)$	Red.C/%
1	(0,0,1;0,1,0;1,0,0)	5.29	6.74	111.14	40.10	40.02	0.16
2	(0,1,0;0,0,1;1,0,0)	4.13	7.89	83.07	25.07	35.74	10.83
3	(0,0,1;1,0,0;0,1,0)	4.19	7.82	92.31	27.31	36.60	8.69
4	(0,1,0;1,0,0;0,0, 1)	3.88	7.60	87.01	27.46	36.65	8.56
5	(1,0,0;0,0,1;0,1,0)	4.39	8.12	87.82	24.86	35.66	11.04

Case	Assignment of CR $\boldsymbol{X}$	$ \tau $	$ T $	$ N $	$\displaystyle\sum\limits _{j=1}^{n}{\lambda }_{j}\left(T+{B}_{j}\left(\tau \right)-\tau \right)$	$A\left(\tau ,\boldsymbol{X},T\right)$	Imp.A/%
1	(0,0,1;0,1,0;1,0,0)	2.22	2.22	7.56	8.21	0.55	−1.26
2	(0,1,0;0,0,1;1,0,0)	1.54	2.92	8.05	6.36	0.61	9.54
3	(0,0,1;1,0,0;0,1,0)	1.58	2.75	8.58	6.94	0.59	5.79
4	(0,1,0;1,0,0;0,0,1)	1.41	2.76	7.83	6.64	0.60	7.65
5	(1,0,0;0,0,1;0,1,0)	1.67	2.92	8.77	6.60	0.60	7.92

$ {d}_{R} $	$ {c}_{R} $	Assignment of CR ${\boldsymbol{X} }^{\mathit{*} }$	$ {\tau }^{*} $	$ {T}^{*} $	$C\left({\tau }^{},{\boldsymbol{X} }^{\mathit{} },{T}^{*}\right)$	Red.C/%
0.05	1	(1,0,0;0,0,1;0,1,0)	4.39	8.12	35.66	11.04
	50	(1,0,0;0,0,1;0,1,0)	5.23	9.74	38.01	5.16
	150	(1,0,0;0,0,1;0,1,0)	6.93	13.03	41.23	−2.85
0.5	1	(1,0,0;0,0,1;0,1,0)	4.12	7.60	34.74	13.33
	50	(1,0,0;0,0,1;0,1,0)	4.94	9.18	37.28	6.98
	150	(1,0,0;0,0,1;0,1,0)	6.62	12.42	40.75	−1.67
1	1	(1,0,0;0,0,1;0,1,0)	3.84	7.05	33.67	15.99
	50	(1,0,0;0,0,1;0,1,0)	4.64	8.60	36.42	9.13
	150	(1,0,0;0,0,1;0,1,0)	6.28	11.77	40.19	−0.26

$ {d}_{P} $	$ {c}_{P} $	Assignment of CR ${\boldsymbol{X} }^{\mathit{*} }$	$ {\tau }^{*} $	$ {T}^{*} $	$C\left({\tau }^{},{\boldsymbol{X} }^{\mathit{} },{T}^{*}\right)$	Red.C/%
0.1	100	(0,1,0;0,0,1;1,0,0)	2.91	5.54	30.24	13.96
	500	(0,1,0;0,0,1;1,0,0)	9.82	18.86	44.79	4.96
	1000	(1,0,0;0,0,1;0,1,0)	18.70	36.06	47.52	2.75
1	100	(0,1,0;0,0,1;1,0,0)	2.44	4.63	27.23	13.50
	500	(1,0,0;0,0,1;0,1,0)	9.48	18.00	43.98	6.00
	1000	(1,0,0;0,0,1;0,1,0)	17.97	34.63	47.38	2.88
3	100	(0,1,0;0,0,1;1,0,0)	1.68	3.18	20.81	9.75
	500	(1,0,0;0,0,1;0,1,0)	8.04	15.19	42.64	6.88
	1000	(1,0,0;0,0,1;0,1,0)	16.37	31.48	47.03	3.22

$ {d}_{M} $	$ {c}_{M} $	Assignment of CR ${\boldsymbol{X} }^{\mathit{*} }$	$ {\tau }^{*} $	$ {T}^{*} $	$C\left({\tau }^{},{\boldsymbol{X} }^{\mathit{} },{T}^{*}\right)$	Red.C/%
0.05	1	(1,0,0;0,0,1;0,1,0)	10.42	19.83	16.13	9.14
	10	(0,1,0;0,0,1;1,0,0)	2.00	3.79	62.50	16.05
	20	(0,1,0;0,0,1;1,0,0)	1.32	2.50	81.92	14.97
0.1	1	(1,0,0;0,0,1;0,1,0)	18.04	34.76	9.48	2.85
	10	(0,1,0;0,0,1;1,0,0)	2.43	4.62	54.34	13.70
	20	(0,1,0;0,0,1;1,0,0)	1.50	2.83	75.82	14.21
1	1	(0,1,0;0,0,1;1,0,0)	12.12	257.13	1.00	0.00
	10	(1,0,0;0,0,1;0,1,0)	17.18	33.07	9.94	0.33
	20	(1,0,0;0,0,1;0,1,0)	8.45	15.98	19.68	0.84