The Arctic is known for its abundant reserve of natural resources. Last decade has seen some exploration and production activities in this region. The assurance of safe operations in this region is a critical and challenging task because of the harsh environment, the remoteness of operation sites, the limited infrastructure, and resources available in response to emergent situations, the application of costly equipment and facilities, and the sensitive marine environment. For complex process systems operating in a harsh environment, the scope of conventional risk assessment is not enough because of the highly uncertain environment, and its impacts on equipment performance. Risk assessment needs to be extended to include both the pre-failure and the post-failure phases. Additionally, risk assessment approaches under normal operating, and environmental conditions may not be applicable in the Arctic regions with unique and uncertain characteristics of the harsh environment. Therefore, this study aims to develop a quantitative resilience assessment method for process units operating under Arctic extreme conditions. Dynamic Bayesian network (DBN) is applied to model the probabilistic relationships between causes and effects in a dynamic manner. The proposed method is applied to the resilience assessment of a separator (as part of an oil production system). The proposed approach will help reveal the critical operating parameters under extreme conditions for process units. It also helps identify potential design improvement to enhance process safety.