Optimal preventive maintenance for repairable weighted k-out-of-n systems

Highlights: • A new optimal maintenance strategy for a weighted system is proposed. • The proposed policy involves corrective maintenance and preventive maintenance on each component. • The criteria that will be optimized are the cost and the availability functions. • The derivations of the results rely on the concept of signature. Weighted k-out-of-n systems form an important class of redundant systems with a wide range of applications in reliability engineering. In this paper, we introduce novel optimal preventive maintenance models for the class of weighted k-out-of-n systems based on average cost and availability criteria. Depending on the average number of failed components, we set up a cost (availability) function corresponding to the time that the total weights of the working components become less than a predetermined threshold m, or the age of the system reaches T_PM. The form of the cost (and availability) function relies on the mixture representation of the system reliability based on the notion of the signature of the system. Some examples of weighted k-out-of-n systems are presented to demonstrate the proposed models numerically and graphically.