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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 some well-known criteria such as cost criterion and availability criterion.
Using the concept of signature of the system and 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 $T_{PM}$.
Some examples of weighted $k$-out-of-$n$ are presented to demonstrate the proposed models numerically and graphically. A related sensitivity analysis is performed to illustrate the effects of the parameters on the proposed cost and availability functions.
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