Surface discharge or surface tracking is one of the destructive types of discharge that travels along the insulation surface. In cables, surface partial discharge (SPD) can be caused due to contamination and moisture. Poor installation and maintenance are also major causes of SPD. Partial discharge (PD) measurement is an efficient technique, used for the assessment of insulation conditions in medium and high voltage assets. PD pulses contain information that describes the nature of PD and the severity of a defect in the insulation. Several characteristics such as accumulated charge, average discharging current, and discharge power are used that indirectly describe behaviour of a PD activity within the insulation. This study investigates the behaviour of quantities related to partial discharge pulse such as the number of pulses (observed during full AC cycle of the applied voltage) and pulse amplitude (peak and average) at progressive electrical stress. An algorithm has been developed that efficiently identifies the first occurring PD pulse of individual PD event, its polarity, and peak amplitude. The probabilistic analysis is also performed to investigate the behavior of pulse characteristics at progressive degradation.