Some Results on an Optimal Maintenance Policy for a Markovian Deteriorating System Subject to Random Shocks  
Author Nobuyuki Tamura




Abstract This paper considers a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state and which suffers randomly occurring shocks. The system is more likely to deteriorate with occurrence of shocks. At each time epoch, we can select one of three actions as operating, repair, and replacement. The difference between repair and replacement is whether the influence of shocks is removed or not. While repair cannot change the number of shocks that the system has suffered, replacement can return it to zero. For the system, we derive an expected discounted cost for unbounded horizon and show that a generalized control limit policy holds under the similar assumptions on the costs and the transition probability. Several structural properties of the optimal maintenance policy are also investigated from the viewpoint of the occurrence of shocks. Furthermore, we provide some results for special cases.


Keywords Markov decision process, random shock, repair, stochastic order relation, monotone property
    Article #:  22050
Proceedings of the 22nd ISSAT International Conference on Reliability and Quality in Design
August 4-6, 2016 - Los Angeles, California, U.S.A.