Article ID: 2021EAP1042
In this paper, we study the number of failed components in a consecutive-k-out-of-n:G system. The distributions and expected values of the number of failed components when system is failed or working at a particular time t are evaluated. We also apply them to the optimization problems concerned with the optimal number of components and the optimal replacement time. Finally, we present the illustrative examples for the expected number of failed components and give the numerical results for the optimization problems.