This paper deals with an infinite-horizon discrete-event dynamic programming model with discounting, and with Borel state and action spaces. Instead of the usual n-stage contraction assumption [4], uniform over all admissible state-action pairs, we propose milder conditions, sufficient for regularity, and allowing any number of simulteneous events. This model permits one to treat properly a number of problems typically associated with continuous-time maintenance models [5,6,11,12].

The main results concern the uniform convergence of the dynamic programming (DP) procedure to the optimal cost-to-go function, the existence of an ϵ-optimal policy for any ϵ > 0, and a set of sufficient conditions for the convergence of the DP procedure to an optimal policy.