Reliability analysis method for multiple failure modes with overlapping failure domains

In reliability analysis, the problem of multiple failure modes with overlapping failure domains has long attracted significant attention. Traditional methods, such as direct integral methods and approximate analytical methods, cannot deal with this issue effectively. Typically, simulation techniques, such as Monte Carlo simulation and kriging, are employed. However, these methods require extensive sampling and computation, resulting in lower efficiency. Therefore, this paper proposes a new reliability analysis method for multiple failure modes with overlapping failure domains and multiple design points. The method combines a simplified formula for the hyperspherical cap area, applicable to both odd and even integer values, with the curved surface integral method, significantly simplifying the failure probability calculation process. Furthermore, by incorporating the hypersphere cap intersection region area, structures or systems with multiple failure modes can be efficiently handled. Five examples demonstrate that the proposed method outperforms traditional methods in both computational efficiency and accuracy.