In this paper, we present a framework for the condition-based maintenance optimization. A technical system which can be in one of N operational states or in a failure state is considered. The system state is not observable, except the failure state. The information that is stochastically related to the system state is obtained through condition monitoring at equidistant inspection times. The system can be replaced at any time; a preventive replacement is less costly than failure replacement. The objective is to find a replacement policy minimizing the long run expected average cost per unit time. The replacement problem is formulated as an optimal stopping problem with partial information and transformed to a problem with complete information by applying the projection theorem to a smooth semimartingale process in the objective function. The dynamic equation is derived and analyzed in the piecewise deterministic Markov process stopping framework. The contraction property is shown and an algorithm for the calculation of the value function is presented, illustrated by an example.
