Truncated importance sampling method for failure probability estimation with truncated normal distribution

Based on the traditional importance sampling (IS), truncated importance sampling(TIS) has been proposed to calculate the failure probability by adopting the truncated importance sampling function, this paper utilizes TIS to solve truncated normal distribution commonly existing in the engineering structures. The original reliability with the truncated normal distribution is transformed to the system reliability with multiple parallel failure modes and non-truncated distribution, then TIS is employed to estimate the system reliability, and the variances of the reliability estimations by TIS are derived approximately. The results of the examples show that TIS is applicable to reliability analysis with truncated normal distribution, and compared to traditional IS, in the case of the same precision, the efficiency of TIS is higher than that of traditional IS.