## 1 Introduction  
Uncertainties existing in engineering structure problems are often associated with the material property, load and manufacturing error. Reliability and its sensitivity analysis play an important role in the design of engineering structures, with reliability analysis providing the probabilities of failure and sensitivity analysis identifying the contributions of random analysis inputs to those probabilities. Compared with the traditional analysis methods, a structural reliability analysis is helpful in improving the safety of the structure. In particular, the sensitivity analysis of structural reliability is of great value in identifying the factors that have an important influence on structure safety and improving them [1]. Various reliability and sensitivity analysis methods have been proposed for use, including the first-order reliability method [2; 3; 4; 5; 6; 7; 8], the moment method [9; 10; 11; 12], the importance sampling method [13; 14; 15; 16; 17; 18; 19; 20], etc. While in some circumstances, highly nonlinear performance functions, especially those involving non-normal random variables or dealing with a problem of extremely small failure probability, might result in a poor estimation of reliability and its sensitivity. The importance sampling method, as an alternative method for reliability and its sensitivity with less computation cost and good accuracy, has drawn much attention from scholars for a long time. For instance, an algorithm using the modified importance-samplingmethod with the continuously varying standard deviation of sampling density-function is developed to calculate the design point [21], the von Mises-Fisher mixture model is selected as the sampling density to generate direction vectors on the unit hypersphere to improve the computational efficiency compared to original directional sampling and other cross-entropy-based importance sampling methods [22], the relevance vector machine surrogate model is applied in importance sampling methods to decrease the number of expensive model simulations [23,24], the sensitivity of the failure probability estimator to uncertainties is quantified by the Gaussian process and the sampling strategy [25], artificial neural network based second order reliability method and importance sampling are combined to be applied towards failure probability and sensitivity estimates of variable stiffness composite laminate plates [26], the active Kriging-Monte Carlo simulation and the adaptive linked importance sampling are employed to estimate the small failure probability and the corresponding reliability sensitivity indices efficiently [27], etc. The importance sampling function has a significant effect on the accuracy of results. The regions that contribute more to the failure probability and its sensitivity often do not overlap in nonlinear problems [28]; in other words, the samples generated by the same importance sampling function may not be able to simultaneously obtain the high accuracy in reliability and sensitivity analysis. The importance sampling function is often established upon the most probable failure point obtained by the first-order reliability method (FORM). The quasi-Monte Carlo method is beneficial to significantly reduce the sample size, obtain low-discrepancy samples, and improve the accuracy and stability of structural reliability analysis [29]. The axis orthogonal importance sampling method samples on the tangent plane at the most probable failure point of the limit state surface, in which reliability analysis becomes a simple problem of solving the distances from the sample points to a straight line. As a consequence, it lessens one dimension of samples and improves the sampling efficiency, implying more and more applications in the future for structural reliability analysis [17,30].