‎Large engineering infrastructures such as power grids‎, ‎communication systems‎, ‎and cyber-physical systems are exposed to shocks of varying intensity and scope‎, ‎which due to the dependence between components‎, ‎can cause successive failures throughout the entire network‎. ‎The classical reliability models are generally based on the assumption of independence between components and shocks and therefore face limitations in describing the real behavior of the systems‎. ‎In this paper‎, ‎a comprehensive framework for analyzing the reliability of networks in the presence of signed shocks time-dependent is presented‎. ‎In this framework‎, ‎each network node is modeled by a signed process that simultaneously captures the magnitude and timing of shocks‎, ‎and the dependence structure between components is described through a copula function‎. ‎In addition to statistical dependence‎, ‎the proposed model also includes cumulative failure mechanisms‎, ‎incomplete repair‎, ‎and reinforcement resource allocation policies.