• An analytical method solving SIFs of asymmetric circular and elliptical hole-edge cracks is proposed. • The impact of multiple interactive cracks on SIFs is studied. • Safe cracks tip distance is advised based on the reliability analysis of an engineering case. In this paper, a successive conformal mapping technique is used to propose an analytical method for solving the stress intensity factor (SIF) of asymmetrical hole-edge cracks on the basis of Muskhelishvili's complex variable function analysis method. Based on this analytical solution, the superposition method is used to get the SIF under the interaction of multiple cracks. Subsequently, according to the plastic collapse criterion, the residual strength under the interaction of two collinear asymmetric elliptical hole-edge cracks with different sizes on the side rail of a dumper's frame is analyzed through the method established. The failure probability of the plate part is obtained by the Kriging meta-model. This study provides a theoretical guide for the operation and maintenance plan of plate parts with multiple cracks. [ABSTRACT FROM AUTHOR]