Optimization of Reliability and Cost in Series-Parallel-Repairable Systems with Bathtub-Shaped Failure Rate

When a system is used, it is often of interest to determine with what probability it will work longer than a pre-fixed time. In other words, determining the reliability of this system is of interest. On the other hand, the reliability of each system depends on the structure and reliability of its components. Therefore, in order to improve the reliability of the system, the reliability of its components should be improved. For this purpose, it is necessary to carry out maintenance operations, which will increase costs. Another way to increase the reliability of systems is to change the location of the components. In this paper, the location of system components and optimal maintenance period are determined by minimizing the costs and maximizing the reliability of a series-parallel system. Finally, a numerical example is presented to evaluate the results in the paper.