A numerical study of Markov decision process algorithms for multi-component replacement problems

•A unified model for time-based and condition-based maintenance for multi-component systems.•Markov decision processes can approximate the continuous dynamics of the system.•A coarse discretization of the component condition leads to near-optimal policies.•We solve time-based maintenance models with 200 million states to optimality.•Equivalent condition-based maintenance models are limited to half a million states.