Abstract
The maintenance optimisation of a system with multistate components is a research topic with practical significance. When the dependence among the components is considered, the state of the system becomes the combinations of the states of components. The commonly used Markovian analysis is then not practical for the large system state space. This paper developed an approximate approach to perform the steady-state analysis of the system. The developed method is combined with the simulation-based method to optimise the maintenance strategy of a system with multistate components. The numerical study shows that the steady-state analysis results of the developed approximate method are close to that of the simulation-based method, though the approximate method is much more efficient than the simulation-based method. More importantly, the errors introduced by the approximate approach decrease with the number of components in the system. The numerical study also shows that the hybrid method of maintenance optimisation can find a balance between the efficiency and accuracy.
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Abbreviations
- N :
-
The number of different types of components
- N n :
-
The number of components of type n
- K n :
-
The number of states of components of type n
- λn :
-
The transition intensity matrix of components of type n
- γ n (i):
-
The production rate of a component of type n in state i
- r p :
-
The reward of unit production rate of the system
- L PR,n :
-
The threshold of preventive maintenance of a component of type n
- c R,n (i):
-
The replacement cost of components of type n in state i
- c ST :
-
The setup cost before a group of maintenance activities
- L OP,n :
-
The threshold of opportunistic maintenance of a component of type n
- \( \bar{R}_{P,n} \) :
-
The average production rate of a component of type n
- \( \bar{C}_{M,n} \) :
-
The average maintenance cost per unit time of the component
- \( \bar{R} \) :
-
The average revenue per unit time
- \( \left( {{\varvec{\uppi}}_{{\mathbf{n}}} } \right)_{i} \) :
-
The steady-state probability that a component of type n is under state i
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Acknowledgements
The research work is supported by the National Natural Science Foundation of China (Grant No. 71201025), the Natural Science Foundation of Jiangsu Province for colleges and universities (Grant No. 15KJB460016) and the Science Foundation for the Excellent Youth Scholars of Xuzhou Institute of Technology (Grant No. XKY2014213).
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Zhang, L., Zhou, Y. & Huang, C. An approximate hybrid approach to maintenance optimisation for a system with multistate components. Int J Syst Assur Eng Manag 8, 189–196 (2017). https://doi.org/10.1007/s13198-016-0560-x
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DOI: https://doi.org/10.1007/s13198-016-0560-x