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In this contribution, a mathematical model is proposed to predict the discharge inception voltage on polluted insulators under a non-uniform field of a high-voltage DC system. The present study is derived from the modified Peek's law used for predicting the threshold voltage of a typical corona discharge. An onset criterion useful for practical electrode geometries was experimentally validated by considering insulators' level of pollution along with the electro-geometrical parameters including inter-electrode distance, HV electrode radius, and width of the ground electrode. It was observed that the proposed mathematical model is much precise for smaller electrode radii and inter-electrode distances with higher conductivity of the pollution layer. Since prediction of the electrical onset on a polluted surface is of general interest for designing HV equipment suitable for heavily polluted regions in the world, it is hoped that the results presented can be viewed as a benchmark and a challenge for further research. [ABSTRACT FROM AUTHOR]