During the last decades, the optimization of the maintenance plan in process plants has lured the attention of many researchers due to its vital role in assuring the safety of operations. Within the process of scheduling maintenance activities, one of the most significant challenges is estimating the reliability of the involved systems, especially in case of data scarcity. Overestimating the average time between two consecutive failures of an individual component could compromise safety, while an underestimate leads to an increase of operational costs. Thus, a reliable tool able to determine the parameters of failure modelling with high accuracy when few data are available would be welcome. For this purpose, this paper aims at comparing the implementation of three practical estimation frameworks in case of sparse data to point out the most efficient approach. Hierarchical Bayesian modelling (HBM), maximum likelihood estimation (MLE), and least square estimation (LSE) are applied on data generated by a simulated stochastic process of a natural gas regulating and metering station (NGRMS), which was adopted as a case of study. The results identify the Bayesian methodology as the most accurate for predicting the failure rate of the considered devices, especially for the equipment characterized by less data available. The outcomes of this research will assist maintenance engineers and asset managers in choosing the optimal approach to conduct reliability analysis either when sufficient data or limited data are observed.

Over the last few decades, reliability analysis has attracted significant interest due to its importance in risk and asset integrity management. Meanwhile, Bayesian inference has proven its advantages over other statistical tools, such as maximum likelihood estimation (MLE) and least square estimation (LSE), in estimating the parameters characterizing failure modelling. Indeed, Bayesian inference can incorporate prior beliefs and information into the analysis, which could partially overcome the lack of data. Accordingly, this paper aims to provide a closed-mathematical representation of Bayesian analysis for reliability assessment of industrial components while investigating the effect of the prior choice on future failures predictions. To this end, hierarchical Bayesian modelling (HBM) was tested on three samples with distinct sizes, while five different prior distributions were considered. Moreover, a beta-binomial distribution was adopted to represent the failure behavior of the considered device. The results show that choosing strong informative priors leads to distinct predictions, even if a larger sample size is considered. The outcome of this research could help maintenance engineers and asset managers in integrating their prior beliefs into the reliability estimation process.