In general, a system deteriorates due to internal physical degradation and external random shocks. Previous studies mainly focused on establishing dependent competing risk models to evaluate mutual effects of degradation processes and random shocks affecting system health. However, there is a lack of consideration about the magnitude of impacts caused by random shocks on degradation processes. Thus, a shock-loading-based degradation model is proposed to classify the magnitude of impacts from random shocks on degradation processes based on the threshold of the cumulative shock loading. Copula methods are utilized to derive joint reliability function from multiple marginal distributions of degradation processes. Two numerical examples are utilized to demonstrate the reliability prediction performance of the proposed model. First, a simulated example is used. The second example employs the turbofan engine degradation data from the NASA Prognostic Data Repository to show the performance of the proposed shock-loading-based degradation process and its corresponding system reliability model.