Analysis of a Markovian Deteriorating System with Imperfect Repair under Incomplete Information on Operating Environment  
Author Nobuyuki Tamura




Abstract We consider a system whose deterioration follows a discrete-time and discrete-state Markov chain with an absorbing state as a failure of the system. The true state of the system is surely identified through inspection at each discrete time point. After inspection, one can choose one of three actions: keep, repair or replacement. When operation is selected, an environment could change according to a Markov chain, and one cannot know the environment for operation. While the result of repair is imperfect and uncertain, replacement always returns the system to an initial state immediately after installing the system. We formulate this system as a partially observable Markov decision process and derive a total expected discounted cost for unbounded horizon as an objective function. For this model, we show that several monotone properties hold under a special structure of the transition probability matrix for the deterioration and unusual stochastic order.


Keywords operating environment, partially observable Markov decision process, stochastic order, likelihood ratio order, monotone property
    Article #:  RQD27-64

Proceedings of 27th ISSAT International Conference on Reliability & Quality in Design
Virtual Event

August 4-6, 2022