Abstract
Maintenance and replacement schedule is one of the most important issues in industrial-production systems to ensure that the system is sufficient. This chapter presents a multi-objective model to schedule preventive maintenance activities for a series system of several standby subsystems where each component has an increasing rate of occurrence of failure (ROCOF). The planning horizon divided into the same length and discrete intervals that in each period three different maintenance actions such as maintenance, replacement, and do nothing can be performed. The objectives of this model are maximizing the system reliability and minimizing the total system cost. Because of nonlinear and complex structure of the mathematical model, non-dominated sorting genetic algorithm (NSGA-II) is used to solve this model. Finally, a numerical example is illustrated to show the model’s effectiveness.
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Abbreviations
- N :
-
Number of subsystems
- T :
-
Length of planning horizon
- J :
-
Number of intervals
- K :
-
Number of maintenance levels
- C :
-
Number of components in each subsystem
- λ:
-
Characteristic life (scale) parameter of component c of subsystem i
- β c i :
-
Shape parameter of component c of subsystem i
- α k i :
-
Improvement factor of subsystem i in maintenance level k
- ϑ c i (t):
-
ROCOF of component c of subsystem i
- F i :
-
Unexpected failure of subsystem i
- M c,k i :
-
Level kth maintenance cost of component c of subsystem i
- R c i :
-
Replacement cost of component c of subsystem i
- S i :
-
Switching cost in subsystem i
- Z :
-
System outage cost
- Cost:
-
Total system cost
- E(N i,j ):
-
Number of expected failures in subsystem i in period j
- Reliability c i,j :
-
Reliability of component c of subsystem i in period j
- Reliability SS i,j :
-
Reliability of subsystem i in period j
- Reliability:
-
Total system reliability
- Re SS,c i,j :
-
Reliability of subsystem i if component c be loaded at the start of period j
- Re c i,j (t):
-
Operation probability of component c of subsystem i in interval [0,t] of period j
- Q c i,j (t):
-
Failure probability of component c of subsystem i in interval [0,t] of period j
References
Usher JS, Kamal AH, Hashmi SW (1998) Cost optimal preventive maintenance and replacement scheduling. IIE Transactions 30(12):1121–1128
Moghaddam KS, Usher JS (2011) Preventive maintenance and replacement scheduling for repairable and maintainable systems using dynamic programming. Computers & Industrial Engineering 60:654–665
Srinivas N, Deb K (1995) Multiobjective function optimization using nondominated sorting genetic algorithms. Evol Comput 2(3):221–248
Deb K, Agrawal S, Pratap A, Meyarivan T (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, vol 5. In: Proceedings of the parallel problem solving from nature VI conference, 16–20 September, Paris, pp 849–858
Smith CO (1976) Introduction to reliability in design. Illustrated, McGraw-Hill
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Ayatollahi, S.A., Seyyed-Esfahani, M., Hejazi, TH. (2015). Preventive Maintenance and Replacement Scheduling in Multi-component Systems. In: Kadry, S., El Hami, A. (eds) Numerical Methods for Reliability and Safety Assessment. Springer, Cham. https://doi.org/10.1007/978-3-319-07167-1_29
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DOI: https://doi.org/10.1007/978-3-319-07167-1_29
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