<p>The adaptive reliability analysis method has been widely applied in research. However, when addressing rare failure probability problems, the Kriging model, while serving as a surrogate for the structural performance function, still heavily relies on extensive Monte Carlo simulation to estimate probabilities and evaluate convergence. Therefore, this study introduces subset simulation into the previously established adaptive analysis framework, Confidence Interval Squeeze (CIS), presenting a sequential and parallel adaptive structural reliability analysis method. The core innovation of the proposed method lies in replacing Monte Carlo simulation samples with subset simulation samples. By integrating SS samples into the convergence condition framework, the method leverages importance sampling to achieve both efficiency and accuracy in convergence assessment, thereby preserving the precision of failure probability estimation. The proposed method retains the full benefits of CIS, offering unique advantages as it requires only a small sample size to accurately estimate rare failure probabilities that meet accuracy requirements. Finally, several numerical and engineering examples verify the accuracy and efficiency of the proposed method.</p>