Reliability optimization for series and parallel systems with series subsystem and comprising of dependent components under random shock environment

In this article, we investigate the optimal component allocation policy (CAP) for series [parallel] system with series subsystems under random shock environment, wherein the components in each series subsystem are dependent and the series subsystems are independent of each other. The dependence of the components in each series subsystem under shock are modeled by an Archimedean copula. We consider the extreme and cumulative shock models, in which the shock process for each series subsystem is described by a non-homogeneous Poisson process. We compare systems with different component allocation policies in the sense of hazard rate order and usual stochastic order. We also study the influence of the number of the series subsystems on the system reliability. Finally, we analyze the aging properties of the system under the extreme shock model.