Offshore oil and gas processing equipment operating in harsh environments poses high risk. This risk is further increased by the susceptibility of the equipment to natural disasters such as hurricanes and snowstorms due to harsh environments. When equipment functionality is compromised, it can become a hazard to personnel as well as to other equipment. The key safety practice on the offshore facility is to isolate the equipment and minimize consequences associated with processing equipment failures. When and how to isolate vulnerable equipment is a challenge due to limited understanding of the equipment's susceptibility and dependency to failure causes and consequences. This paper presents a methodology to analyze potential failure scenarios considering causation dependency and also determine which parameter(s) have the most impact on the failure. The results of the analysis are used to identify most sensitive equipment and their potential failure causes. This analysis will help to develop effective risk management strategies focusing on critical equipment.