System failures can be induced either by internal degradation mechanisms or by external causes. In this article, we consider the reliability of systems experiencing both degradation and random shock processes. The dependencies between degradation processes and random shocks and those among the degradation processes are explicitly modeled. The degradation processes of system components are modeled using Multi-State Models (MSMs) and Physics-Based Models (PBMs). The piecewise-deterministic Markov process modeling framework is employed to combine MSMs and PBMs and to incorporate degradation and random shocks dependencies. The Monte Carlo simulation and finite-volume methods are used to compute the system reliability. A subsystem of a residual heat removal system in a nuclear power plant is considered as an illustrative case.