Unplanned downtimes caused by system failures incur high costs for many complex systems such as wind turbines, aircrafts, and advanced medical equipment. It is crucial to prevent failures for such systems by applying maintenance policies. Maintenance models can be classified as corrective or preventive maintenance (PM). PM is performed to prevent severe deterioration or failure of the system. The most advanced PM program is known as condition-based maintenance (CBM) which is a maintenance approach that takes into account collected information concerning the working condition of a system to determine the optimal maintenance actions.

Studies in the area of CBM have focused mainly on single unit systems, however in reality most of the systems consist of more than one unit. Maintenance models for single unit systems cannot be applied to multi-unit systems when there is a dependency between units. This research presents a new framework for maintenance modeling of multi-unit systems.

We proposed CBM policies for multi-unit systems taking into account external demand and production rates which depend on the state of a unit. Units of the system are subject to gradual deterioration and deterioration process of each unit is a threestate continuous time homogeneous Markov chain with two working states and a failure state. We have applied semi-Markov decision process (SMDP) framework to formulate the maintenance decision problem and to determine the optimal control parameters. Two computational approaches were proposed to find the optimal policy by applying 1) the first step of policy iteration algorithm, and 2) the first and second steps of policy iteration algorithm. We showed that a lower average cost rate can be obtained by applying the second approach. We also derived an analytical formula for the average cost considering a corrective maintenance policy for multi-unit systems applying Markov renewal processes.

We also developed a powerful model for joint CBM and just-in-time spare parts provisioning policies for a multi-unit production system. SMDP framework is applied to formulate the maintenance problem to determine the optimal control parameters.