A novel extended crossing rate method for time-dependent hybrid reliability analysis under random and interval inputs

With the aim of efficiently estimating the upper bound of time-dependent failure probability for the time-dependent reliability problem involving random and interval inputs (RI-TDFP), an extended crossing rate method is proposed. The proposed method first converts the time-dependent hybrid reliability analysis into a temporal and spatial multi-parameter problem. Then, it uses the extended crossing rate strategy to estimate the RI-TDFP. The proposed strategy is a single-loop strategy, which is more efficient than the nested double-loop strategies. The proposed method avoids using discretization or optimization strategies to estimate the global minimum of the time-dependent performance function with respect to the time parameter and interval inputs, and thus the computational cost is further reduced. Finally, the proposed method avoids using the first order reliability method (FORM) for reliability analysis with respect to the random inputs, and thus the proposed method is more accurate than the FORM.