Assessments of aging and insulation degradation in power components are important to observe and track their condition during operation. Partial discharge (PD) diagnostics is an efficient method for health estimation of the components’ insulation. PD is initiated when the dielectric strength of localized insulation part is decreased. The intensity of PD increases with time, which may lead to insulation failure. This paper investigates the influence of the electrical stresses on the behavior of PD activity in medium voltage (MV) cable containing insulation defects. For this purpose, insulation defects such as internal, surface, and corona are developed in the MV cable environment under laboratory conditions. PD behavior is studied in these defects at gradually increased voltage levels by observing different PD characteristic features including PD inception voltage (PDIV), pulse repetition rate, accumulated apparent charge, average discharge current, discharge power, and quadratic rate. The Tobit regression model is developed for these progressing defects to identify the trends and to predict the behavior based on PD characteristic features. The presented work proposes a framework for the evaluation of the progression of insulation degradation due to increased electrical stress. The study is carried out on XLPE cables, however, the developed approach can be equally implemented on other types of dielectrics and components.