Reliability estimation and its variance analysis of structure with truncated normal distribution by directional sampling and directional importance sampling

For 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 normal distribution. Then directional sampling and directional importance sampling are employed to estimate the system reliability with multiple parallel failure modes transformed from the original reliability with the truncated normal distribution. The presented method is applicable not only to a single failure mode but also to multiple failure modes in series or in parallel. The variances of the reliability estimations by two sampling methods are derived approximately. After the concept and the detailed implementation are described, several examples are used to compare the efficiency and the precision of the directional sampling, the directional importance sampling and the direct Monte Carlo numerical simulation. The results of the examples show that the efficiency of the directional sampling is higher than that of the direct Monte Carlo numerical simulation in case of the acceptable precision, and the efficiency of the directional importance sampling is higher than that of the directional sampling. The reliability for the model of wing structure with the truncated normal distribution is compared with that without the truncated normal distribution, the results show that relatively big error will be brought without considering the existing truncation of the distribution.