Partial discharge (PD) measurements have been widely accepted as an efficient online insulation condition assessment method in high voltage equipment. Two sets of experimental PD measuring setups were established with the aim to study the variations in the partial discharge characteristics over the insulation degradation in terms of the physical phenomena taking place in PD sources, up to the point of failure. Probabilistic lifetime modeling techniques based on classification, regression and multivariate time series analysis were performed for a system of PD response variables, i.e. average charge, pulse repetition rate, average charge current, and largest repetitive discharge magnitude over the data acquisition period. Experimental lifelong PD data obtained from samples subjected to accelerated degradation was used to study the dynamic trends and relationships among those aforementioned response variables. Distinguishable data clusters detected by the T-Stochastics Neighborhood Embedding (tSNE) algorithm allows for the examination of the state-of-the-art modeling techniques over PD data. The response behavior of trained models allows for distinguishing the different stages of the insulation degradation. An alternative approach utilizing a multivariate time series analysis was performed in parallel with Classification and Regression models for the purpose of forecasting PD activity (PD response variables corresponding to insulation degradation). True observed data and forecasted data mean values lie within the 95th percentile confidence interval responses for a definite horizon period, which demonstrates the soundness and accuracy of models. A life-predicting model based on the cointegrated relations between the multiple response variables, trained model responses correlated with experimentally evaluated time-to-breakdown values and well-known physical discharge mechanisms, can be used to set an emergent alarming trigger and as a step towards establishing long-term continuous monitoring of partial discharge activity. Furthermore, this dissertation also proposes an effective PD monitoring system based on wavelet and deflation compression techniques required for an optimal data acquisition as well as an algorithm for high-scale, big data reduction to minimize PD data size and account only for the useful PD information. This historically recorded useful information can thus be used for, not only postault diagnostics, but also for the purpose of improving the performance of modelling algorithms as well as for an accurate threshold detection.