Abstract
In the present paper, a sequential decision problem on a Markov process
is set up which takes into account a partial maintenance, and observe some monotonic
properties of an optimal policy. We develop an optimal maintenance policy for
products. During their life cycle, a condition of this item deteriorates, and a state of
an item goes from state to state according to a Markovian transition rule based on
the stochastic convexity. The decision-maker decides a level of repair with cost which
varies with this level. This problem is how much to expend to maintain this item
to minimize the total expected cost. A dynamic programming formulation implies a
recursive equation about expected cost obtainable under optimal policy.
