The probabilistic analysis on condition monitoring data has been widely established through the energy supply process to specify the optimum risk remediation program. In such studies, the fluctuations and uncertainties of the operational data including the variability between source of data and the correlation of observations, have to be incorporated if the efficiency is of importance. This study presents a novel probabilistic methodology based on observation data for signifying the impact of risk factors on safety indicators when consideration is given to uncertainty quantification. It provides designers, risk managers and operators a framework for risk mitigation planning within the energy supply processes, whilst also assessing the online reliability. These calculations address the involved and, most of the time, unconsidered risk to make a prediction of safety conditions of the operation in future. To this end, the generalized linear model (GLM) is applied to offer the explanatory model as a regression function for risk factors and safety indicators. Hierarchical Bayesian approach (HBA) is then inferred for the calculations of regression function including interpretation of the intercept and coefficient factors. With Markov Chain Monte Carlo simulation from likelihood function and prior distribution, the HBA is capable of capturing the aforementioned fluctuations and uncertainties in the process of obtaining the posterior values of the intercept and coefficient factors. To illustrate the capabilities of the developed framework, an autonomous operation of Natural Gas Regulating and Metering Station in Italy has been considered as case study.@en