Structural Properties of an Optimal Maintenance Policy for a Makovian Deteriorating System Subject to Random Shocks  
Author Nobuyuki Tamura




Abstract This paper considers a discrete-time and discrete-state Markovian deteriorating system. We propose the system whose transition probabilities vary with the occurrence of random shocks and it is more likely to deteriorate with repetition of the shocks. At each decision epoch, we can select one of the three actions; operation, repair, or replacement. The difference between repair and replacement is whether the influence of the shocks is removed or not. This indicates that the number of shocks do not change after completion of repair. For the system, we derive an expected discounted cost for unbounded horizon and discuss the structure of the optimal maintenance policy. We show that a generalized control limit policy holds under the reasonable assumptions. Also, we investigate the properties of the optimal maintenance policy from the view points of the number of shocks


Keywords Markov decision process, random shock, repair, stochastic order relation, monotone property
    Article #:  19151
Proceedings of the 19th ISSAT International Conference on Reliability and Quality in Design
August 5-7, 2013 - Honolulu, Hawaii, U.S.A.