Abstract
This paper investigates an optimal replacement problem for a discrete-time Markovian deterioration system. We consider partially observable Markov decision processes with finite core state and observation spaces and finite action set. The problem is to obtain an optimal replacement control-limit policy. Sufficient conditions, are then derived for a bounded solution to the average cost optimality equation to exist. Furthermore, under some reasonable conditions reflecting the practical meaning of the deterioration, structural properties for average costs policies are obtained for a two state replacement problem, and we develop a solution procedure utilizing these structural properties. We have that control permits working directly making it suitable for dealing with real-world processes and applications.
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