A Condition-Based Maintenance Policy for Multi-Unit Systems Subject to Deterioration
In this paper, we propose a condition-based
maintenance policy for multi-unit systems considering the
existence of economic dependency among units. We consider a
system composed of N identical units, where each unit deteriorates
independently. Deterioration process of each unit is modeled as a
three-state continuous time homogeneous Markov chain with two
working states and a failure state. The average production rate of
units varies in different working states and demand rate of the
system is constant. Units are inspected at equidistant time epochs,
and decision regarding performing maintenance is determined by the
number of units in the failure state. If the total number of units in the
failure state exceeds a critical level, maintenance is initiated, where
units in failed state are replaced correctively and deteriorated state
units are maintained preventively. Our objective is to determine the
optimal number of failed units to initiate maintenance minimizing
the long run expected average cost per unit time. The problem is
formulated and solved in the semi-Markov decision process (SMDP)
framework. A numerical example is developed to demonstrate the
proposed policy and the comparison with the corrective maintenance
policy is presented.
 HZ. Wang and H. Pham, Reliability and Optimal Maintenance,.
 V. Legat, AH. Zaludova, V. Cervenka, and V. Jurca, Contribution to
optimization of preventive maintenance. Reliability Engineering System,
 AK. Jardine, D. Lin, D. Banjevic, A review on machinery diagnostics
and prognostics implementing condition-based maintenance. Mechanical
systems and signal processing, 20(7):1483-510.
 M. J. Kim, V. Makis, Optimal maintenance policy for a multi-state
deteriorating system with two types of failures under general repair.
Computers & Industrial Engineering 57, 298-303, 2009.
 IT. Castro, NC. Caball, CJ. Prez, A condition-based maintenance for
a system subject to multiple degradation processes and external shocks.
International Journal of Systems Science, 46(9):1692-704, 2015.
 X. Zhang, J. Zeng, Deterioration state space partitioning method
for opportunistic maintenance modeling of identical multi-unit systems.
International Journal of Production Research, 53(7):2100-18, 2015.
 Z. Tian, H. Liao, Condition based maintenance optimization for
multi-component systems using proportional hazards model. Reliability
Engineering and System Safety, 96:581-9, 2011.
 Z. Tian, T. Jin, B. Wu, F. Ding, Condition based maintenance optimization
for wind power generation systems under continuous monitoring.
Renewable Energy,36:1502-1509, 2011.
 B. Liu, Z. Xu, M. Xie, W. Kuo, A value-based preventive
maintenance policy for multi-component system with continuously
degrading components , Reliability Engineering & System Safety, vol.
132, 83-89, 2014.
 Q. Zhu, H. Peng and GJ. Houtum,A condition-based maintenance policy
for multi-component systems with a high maintenance setup cost. OR
Spectrum, 37, 1007-1035, 2015.
 M. Shafiee, M. Finkelstein, An optimal age-based group maintenance
policy for multi-unit degrading systems. Reliability Engineering &
System Safety, 134:230-8, 2015.
 J. Ashayeri, A. Teelen, W. Selenj, A production and maintenance
planning model for the process industry. International Journal of
Production Research. 34(12), pp. 3311-3326, 1996.
 N. Salari, V. Makis, Comparison of two maintenance policies for a
multi-unit system considering production and demand rates. International
Journal of Production Economics, 193:381-91, 2017.
 H. C. Tijms, Stochastic Modeling and Analysis: A computational
Approach. John Wiley & Sons, New York.