The subsea production system is very important for having deep water oil and gas production. The leakage of the oil and gas in the subsea production system may result in enormous adverse consequences on marine lives, high production loss, and serious deadly disasters to humans. For the safety analysis of subsea production system, importance measures play an important role to rank the components of the system according to their contribution to the leakage of oil and gas for preventive and corrective purposes. In conventional fault tree analysis and fuzzy fault tree analysis, various importance measures are developed for criticality analysis of the system. The objective of the present study is to develop a novel IF-importance measure by employing the concept of α-cut interval under intuitionistic fuzzy environment. The failure possibilities of basic events in fault tree analysis are quantified by triangular and trapezoidal intuitionistic fuzzy numbers. The presented research study applies α-cut intervals of intuitionistic fuzzy numbers, intuitionistic fuzzy fault tree analysis and interval arithmetic operations. The validation is carried out by comparing the developed importance measure with some pre-existing importance measures.