Selective maintenance decision optimization for systems executing multi-mission under stochastic mission duration

doi:10.23919/JSEE.2024.000028

Abstract

Abstract:

This paper investigates the selective maintenance of systems that perform multi-mission in succession. Selective maintenance is performed on systems with limited break time to improve the success of the next mission. In general, the duration of the mission is stochastic. However, existing studies rarely take into account system availability and the repairpersons with different skill levels. To solve this problem, a new multi-mission selective maintenance and repairpersons assignment model with stochastic duration of the mission are developed. To maximize the minimum phase-mission reliability while meeting the minimum system availability, the model is transformed into an optimization problem subject to limited maintenance resources. The optimization is then realized using an analytical method based on a self-programming function and a Monte Carlo simulation method, respectively. Finally, the validity of the model and solution method approaches are verified by numerical arithmetic examples. Comparative and sensitivity analyses are made to provide proven recommendations for decision-makers.

Key words: multi-mission system, selective maintenance problem, stochastic duration, Monte Carlo simulation, availability

Weining MA, Enzhi DONG, Hua LI, Mei ZHAO. Selective maintenance decision optimization for systems executing multi-mission under stochastic mission duration[J]. Journal of Systems Engineering and Electronics, 2025, 36(1): 209-223.

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Notation	Description
$ y $	Preventive maintenance level, $ y \in \{ 0,1,\cdots,Y\} $
$ {\alpha _y} $	Age reduction coefficient
$ \beta $	Failure rate increased factor
k	Break and mission serial numbers
$ {t_0} $	Initial age of the system
$ {T_B} $	Length of each break
$ {Z_k} $	Duration of mission k
$ {z_k} $	Value of the random variable $ {Z_k} $
$ {F_{{Z_k}}}({z_k}) $	Cumulative distribution function of $ {Z_k} $
$ \lambda _{ij}^k(t) $	Failure rate function of the component S_ij during the kth mission
$ {f_{{Z_k}}}(t) $	Probability density function of the duration of the mission
$ A_{ij}^{Ek} $	Expected virtual age of component S_ij at the beginning of the kth break
$ B_{ij}^{Ek} $	Expected virtual age of component S_ij at the beginning and the end of the kth break
$ R_{ij}^k({Z_k}) $	Reliability of component S_ij performing the kth mission
$ {R_k} $	Reliability of the system during the kth mission execution
q	Number of repairpersons
$ {T_{qk}} $	Total working time of the repairperson q during the kth break
$ {T_k} $	System downtime due to preventive maintenance in the kth break
$ {\mathrm{E}}(A) $	Expected availability of the system

Error	VAR	MEA	SD	MAE	RMSE
ER₁	6.0114e−05	−0.0011	0.0078	0.0063	0.0078
ER₂	0.0011	0.0095	0.0327	0.0237	0.0340
ER₃	0.0025	0.0012	0.0499	0.0340	0.0498

S_ij	$ \chi _{ij}^{} $	$ \eta _{ij}^{} $
S₁₁	1.36	152
S₁₂	1.42	157
S₂₁	1.31	141
S₂₂	1.42	152
S₂₃	1.35	147

Y	0	1	2	3	4
$ \alpha $	1	1.1	1.07	1.05	1
$ \beta $	1	0.6	0.4	0.2	0

Break m	Maintenance plan	Reliability of mission m	E(A)
1	Rep.4: S₂₃(3)	0.8477	0.8802
2	Rep.2: S₁₁(2)	0.8840	0.8802
	Rep.3: S₁₂(4)
	Rep.3: S₂₁(3)
	Rep.1: S₂₂(3)
	Rep.4: S₂₃(2)
3	Rep.4: S₁₁(3)	0.8601	0.8802
	Rep.2: S₁₂(3)
	Rep.2: S₂₂(3)
	Rep.3: S₂₃(3)