Abstract: To improve the computational efficiency and accuracy in the reliability analysis of gear heat transfer error， an efficient reliability analysis method combining PC-Kriging and active learning function LIF is proposed. Polynomial-chaos-expansion (PCE) is adopted to replace the regression basis function of the traditional Kriging model to enhance its global approximation accuracy and its ability to capture local features. The least-angle regression (LAR) is used to construct the optimal polynomial quantity set of the regression basis function， and the Akaike information criterion (AIC) is utilized to determine the optimal truncated set. Furthermore， the active learning function LIF is employed to select the optimal sample during each iteration to improve the convergence efficiency of the PC-Kriging model. The application to gear heat transfer error shows that compared with the traditional Kriging model， the proposed method can significantly reduce the number of performance function evaluations while ensuring accuracy in the reliability analysis.

Key words: reliability analysis, PC-Kriging model, active learning function, Monte Carlo, gear heat transfer error