A Note 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 a discretestate Markov chain and which suffers randomly occurring shocks. The system is more likely to deteriorate with occurrence of shocks. At each time epoch, we can select from one of three possible actions: operate, repair, or replace. When a replacement is selected, the number of shocks becomes zero and the system is returned to an initial new state. On the other hand, a repair can reduce the influence which the system suffered through random shocks to an optimal level. For the system, we derive an expected discounted cost for unbounded horizon and show that a generalized control-limit policy holds under certain assumptions on the costs and the transition probabilities. Also several structural properties of the optimal maintenance policy are also investigated from the viewpoint of the occurrence of shocks.
Keywords Markov decision process, random shock, repair, stochastic order relation, monotone property
    Article #:  23-219
Proceedings of the 23rd ISSAT International Conference on Reliability and Quality in Design
August 3-5, 2017 - Chicago, Illinois, U.S.A.