Chemical process systems involve complex dynamic processes, and the state of the system often fluctuates during the production process. To ensure the continuation of production, these fluctuations are often ignored or processed online instead of shutting down the unit. However, the interdependence between components in the system is strong, and small fluctuations or faults will be propagated to downstream nodes in turn if the fluctuation is omitted or processed online. A large number of accident investigations prove that the system risk increments as the failure propagates. This may eventually cause the entire system to collapse, causing severe casualties, property losses, and environmental damage. However, little attention has been paid to this type of risk. To measure the dynamic risk profile considering the fluctuation of the production process, this paper proposes a new risk assessment model that integrates the system-theoretic accident model and process (STAMP) and the failure propagation model. Firstly, the STAMP is used to model and analyze the system safety of a process system. An approach is then developed to quantify the risk accumulation of the model based on the failure propagation model. The process of the Chevron Richmond refinery crude unit and its associated upstream process is used to demonstrate the application of the proposed approach.