In the present paper, a sequential decision problem on a Markov process is set up which takes into account a partial maintenance. We develop an optimal maintenance policy for the products. During their life cycle, a condition of this item changes, and a state of an item changes 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 an optimal policy, and the purpose of this paper is to observe some monotonic properties for an optimal policy and optimal expected cost.