Abstract: The phenomenon of electric field distortion under DC electric field significantly affects the long-term voltage endurance characteristics of cross-linked polyethylene (XLPE). Existing methods for obtaining the n value of the voltage endurance coefficient of XLPE do not take into account the effect of the distortion field on insulation damage, resulting in large differences in the n value obtained for similar samples under different test conditions in AC and DC. Therefore, the effect of aberrant field strength on the cumulative damage is characterized by modeling, which takes into account factors such as temperature, space charge density, and externally applied field strength, etc. The cumulative damage D_sc produced by different types of aberrant field strengths is obtained by applying the model to the accelerated life test of stepping stress. A method is proposed to analyze the data from the stepping stress test, which obtains the n value by solving the eigenvalue of the m-order cumulative damage square matrix. Four sets of cumulative damage data from the step stress tests are analyzed, and the n values are obtained with and without considering D_sc, the former is in the range of 14.42~15.36 and the latter is in the range of 13.69~13.88, which indicates that the aberrant field strengths show a tendency to reducing the n value. In addition, increasing the step-up ∆U decreases D_sc to a minimum of D_sc =8.3×10²¹, corresponding to an n value that deviates only by 3.7% from the one without taking D_sc into account, indicating that the selection of a larger ∆U in the step-stress test helps to weaken the effect of the field-strength distortion.