A reliability analysis method for fuzzy multi-state system with common cause failure based on improved the weakest T-norm

•A reliability analysis method for fuzzy multi-state system with common cause failure.•A novel fuzzy arithmetic operation based on the weakest n-dimension T-norm is designed to solve fuzzy information accumulation.•A numerical example to verify the effectiveness and feasibility of the proposed method. Recently, the reliability analysis of complex engineering systems has been confronted with a range of challenges, including fuzziness, multiple states, and common cause failures. In particular, factors such as changes in the working environment and human error contribute to the fuzzy probability value for each state in the system, which brings great challenges to its reliability analysis. In this paper, a new reliability analysis method for fuzzy multi-state system with common cause failure is proposed, which developed the fault tree analysis method and fuzzy set theory. First, a model integrating common cause failure with fuzzy T-S fault tree analysis model has been illustrated, and the equivalent model is given. Meanwhile, a novel fuzzy arithmetic method based on the weakest n-dimension T-norm is designed to solve the proposed model. Finally, the aircraft power system is analyzed as an example to verify the effectiveness of the proposed method. The result shows that the proposed method effectively enhances the capacity of failure tree analysis in assessing the reliability of complex systems characterized by multiple states, fuzziness, and common cause failures.