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• Applying Bayesian regression to predict the risk condition in an autonomous process. • Addressing the involved and, most of the time, unconsidered risks. • Simulating the likelihood function using Monte Carlo Markov Chain approach. • quantifying the uncertainties associated with operational data using Bayesian model. • The model was examined on Natural Gas Regulating and Metering Stations. 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. [ABSTRACT FROM AUTHOR]

• Applying Non-Homogenous Poisson Process (NHPP) and Homogenous Poisson Process (HPP) to predict the condition of a system. • Presenting the possible differentiation within failure assessment of random processes. • Investigating the effect of utilizing observed data in inter-arrival failure time modelling. • The model was examined on degradation process of the Natural Gas Regulating and Metering Stations (NGRMS). Failure modelling and reliability assessment of repairable systems has been receiving a great deal of attention due to its pivotal role in risk and safety management of process industries. Meanwhile, the level of uncertainty that comes with characterizing the parameters of reliability models require a sound parameter estimator tool. For the purpose of comparison and cross-verification, this paper aims at identifying the most efficient and minimal variance parameter estimator. Hierarchical Bayesian modelling (HBM) and Maximum Likelihood Estimation (MLE) approaches are applied to investigate the effect of utilizing observed data on inter-arrival failure time modelling. A case study of Natural Gas Regulating and Metering Stations in Italy has been considered to illustrate the application of proposed framework. The results highlight that relaxing the renewal process assumption and taking the time dependency of the observed data into account will result in more precise failure models. The outcomes of this study can help asset managers to find the optimum approach to reliability assessment of repairable systems. [ABSTRACT FROM AUTHOR]