I consider a system whose deterioration follows a discrete-time and
discrete-state Markov chain with an
absorbing state. When the system is put into practice, I may select operation
(wait), imperfect repair, or replacement at each discrete-time
point. The true state of the system is not known when it is operated. Instead,
the system is monitored after operation and some incomplete information
concerned with the deterioration is obtained for decision making. Since there
are multiple imperfect repairs, I can select one option from them when the imperfect repair is preferable to operation and replacement. To express
this situation, I propose a POMDP model and theoretically investigate the structure of an optimal maintenance policy minimizing a total expected
discounted cost for an unbounded horizon. Then two stochastic orders are used for the analysis
of our problem.
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