Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance

This paper concerns with the performance analysis for controlled semi-Markov systems in Borel state and action spaces. The performability of the system is defined as the probability that the system reaches a prescribed reward level during a first passage time to some target set. Under mild conditions, we develop a value iteration algorithm for computing the optimal value, and establish the existence of optimal policies with the maximal performability. Our main results are applied to a maintenance problem.