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
References
Dao CD, Zuo MJ, Pandey M (2014) Selective maintenance for multi-state series–parallel systems under economic dependence. Reliab Eng Syst Saf 121(1):240–249
Ding F, Tian Z (2012) Opportunistic maintenance for wind farms considering multi-level imperfect maintenance thresholds. Renew Energy 45(3):175–182
Gürler Ü, Kaya A (2002) A maintenance policy for a system with multi-state components: an approximate solution. Reliab Eng Syst Saf 76(2):117–127
Hou WR, Jiang ZH (2012) An optimization opportunistic maintenance policy of multi-unit series production system. Adv Mater Res 421:617–624
Kumar G, Jain V, Gandhi OP (2014) Steady-state availability analysis of repairable mechanical systems with opportunistic maintenance by using Semi-Markov process. Int J Syst Assur Eng Manag 5(4):664–678
Liu Y, Huang HZ (2010a) Optimal replacement policy for multistate system under imperfect maintenance. IEEE Trans Reliab 59(3):483–495
Liu Y, Huang HZ (2010) Optimization of multi-state elements replacement policy for multi-state systems. In: Proceedings of IEEE international conference on reliability and maintainability (RAM2010)
Marseguerra M, Zio E, Podofillini L (2002) Condition-based maintenance optimization by means of genetic algorithms and Monte Carlo simulation. Reliab Eng Syst Saf 77(2):151–165
Nicolai RP, Dekker R (2006). Optimal maintenance of multi-component systems: a review. In: Econometric institute research papers (EI 2006-29). pp 263–286
Nourelfath M, Châtelet E, Nahas N (2012) Joint redundancy and imperfect preventive maintenance optimization for series–parallel multi-state degraded systems. Reliab Eng Syst Saf 103(4):51–60
Pandey M, Zuo MJ, Moghaddass R, Tiwari MK (2013) Selective maintenance for binary systems under imperfect repair. Reliab Eng Syst Saf 113(1):42–51
Taghipour S, Banjevic D, Jardine AKS (2010) Periodic inspection optimization model for a complex repairable system. Reliab Eng Syst Saf 95(9):944–952
Tambe PP, Kulkarni MS (2014) A novel approach for production scheduling of a high pressure die casting machine subjected to selective maintenance and a sampling procedure for quality control. Int J Adv Manuf Technol 5(3):407–426
Tambe PP, Mohite S, Kulkarni MS (2013) Optimisation of opportunistic maintenance of a multi-component system considering the effect of failures on quality and production schedule: a case study. Int J Adv Manuf Technol 69(5):1743–1756
Wang W, Banjevic D, Pecht M (2010) A multi-component and multi-failure mode inspection model based on the delay time concept. Reliab Eng Syst Saf 95(8):912–920
Xu M, Chen T, Yang X (2012) Optimal replacement policy for safety-related multi-component multi-state systems. Reliab Eng Syst Saf 99(3):87–95
You MY, Li H, Meng G (2011) Control-limit preventive maintenance policies for components subject to imperfect preventive maintenance and variable operational conditions. Reliab Eng Syst Saf 96(5):590–598
Zhang Z, Zhou Y, Sun Y, Ma L (2012) Condition-based maintenance optimisation without a predetermined strategy structure for a two-component series system. Maint Reliab 14(2):120–129
Zhou X (2010) A dynamic opportunistic preventive maintenance policy for multi-unit series systems with intermediate buffers. Int J Ind Syst Eng 6(3):276–288
Zhou X, Xi L, Lee J (2009) Opportunistic preventive maintenance scheduling for a multi-unit series system based on dynamic programming. Int J Prod Econ 118(2):361–366
Zhou X, Lu Z, Xi L, Lee J (2010) Opportunistic preventive maintenance optimization for multi-unit series systems with combing multi-preventive maintenance techniques. J Shanghai Jiaotong Univ (Sci) 15(5):513–518
Zhou X, Lu Z, Xi L (2012) Preventive maintenance optimization for a multi-component system under changing job shop schedule. Reliab Eng Syst Saf 101(101):14–20
Zhou Y, Zhang Z, Lin TR, Ma L (2013) Maintenance optimisation of a multi-state series–parallel system considering economic dependence and state-dependent inspection intervals. Reliab Eng Syst Saf 111(111):248–259
Zhou Y, Lin TR, Sun Y, Ma L (2016) Maintenance optimisation of a parallel-series system with stochastic and economic dependence under limited maintenance capacity. Reliab Eng Syst Saf 155:137–146
Zhu Y, Elsayed EA, Liao H, Chan LY (2010) Availability optimization of systems subject to competing risk. Eur J Oper Res 202(3):781–788
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