Regional importance effect analysis of the input variables on failure probability

•A new regional importance measure (RIM) of the input variable is proposed.•The new RIM can identify regional importance of the inputs on failure probability.•The properties of the proposed RIM are analyzed and proved.•The high-efficient ARBIS solution for the proposed RIM is established.

To analyze the effects of the different regions within input variables on failure probability, a regional importance measure (RIM) is proposed, and its properties are analyzed and verified. The proposed RIM can not only detect the important variables, but also identify regions of the input variable that contribute substantially to the failure probability. To calculate the RIM efficiently, its calculation model is transformed, and the highly efficient adaptive radial-based importance sampling (ARBIS) method is introduced. Numerical and engineering examples have demonstrated the effectiveness of the proposed RIM, and the efficiency and accuracy of the established ARBIS method.