As the weighted average simulation (WAS) method is an efficient approach to approximate the failure probability and the most probable point, using WAS and the adaptive interpolation (AI) method, this study has proposed an adaptive interpolation-based weighted average simulation (AI-WAS) method capable of reducing the number of WAS-required performance function evaluations without reducing the required accuracy. To this end, the grid method or low-discrepancy sequences are used to generate some representative sampling points in the design space, which are used to predict the performance function of other uniformly generated samples (WAS population) by an interpolation technique. To estimate the performance function value for other samples more accurately, a new adaptive method is proposed by introducing a critical region. The AI-WAS method has been applied to different numerical and engineering problems with complex and implicit limit state functions. According to the results, the proposed approach, compared to the original approach and popular reliability methods, can highly reduce the number of actual limit state function evaluations required for an accurate estimation of the failure probability.
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