Abstract
In this paper, we consider a coherent system consisting of different types of components. It is of interest to study the number of failed components of each type when the system fails. The obtained results are next used in the classical age replacement policy when the corrective replacement of the system is applied if a system has failed, while the preventive replacement is done before failure. We formulate the optimization problem. We wish to find the optimal replacement time. We provide a numerical example to illustrate the theoretical results.
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