Optimal maintenance policies for coherent systems with multi-type components

We propose two new optimal maintenance strategies for preservation of a complex n-component coherent system. The criteria that will be optimized are some given imposed cost functions formulated based on the costs of the repairs of components (system) to get the optimal time of preventive maintenance of the system. The first strategy involves minimal repair on the failed components in an early life period of the system and then corrective maintenance on the entire system upon its failure or preventive/corrective maintenance on each component when the age of the system reaches t. In the second strategy, we assume that the system is inspected at times t, 2t, ...,mt, m = 1, 2.... At each inspection time, depending on the system conditions, a maintenance action is performed on the components of the system and then the imposed cost function is minimized to get the optimal preventive maintenance time. To interpret the theoretical results, a system constructed from 12 components of three types is examined for which the optimal preventive maintenance times are explored for both strategies under given cost functions.