With the uncertainties related to operating conditions,in-service non-destructive testing(NDT) measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram(FAD) approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics(PFM) assessment method is proposed.By integrating 2D kernel density estimation(KDE) technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures. With the uncertainties related to operating conditions, in-service non-destructive testing (NDT) measurements and material properties considered in the structural integrity assessment, probabilistic analysis based on the failure assessment diagram (FAD) approach has recently become become an important concern. However, the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored. To obtain more detailed and direct knowledge from the reliability analysis, an improved probabilistic fracture mechanics (PFM) assessment method is proposed. By integrating 2D kernel density estimation (KDE) technology into the traditional probabilistic assessment, the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram. Moreover, a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis. improved reliability analysis method is applied to the assessment of a high pr essure pipe containing an axial internal semi-elliptical surface crack. These results that both of these methods can give consistent sensitivities of input parameters, but the interval sensitivity analysis is computationally more efficient. Meanwhile, the point density distribution and its contour are plotted in the FAD, so better revealing the characteristics of PFM assessment. This study provides a powerful tool for the reliability analysis of critical structures.