Abstract
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.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
The results depict that for greater sample sizes, less influence of the prior choice and less uncertainty is presented by the posterior distributions
The posterior distributions and the predictions regarding the future number of failures are still affected to a certain degree by informative priors
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Reliability analysis is of significant importance due to its essential role in dealing with the risk arising from failure events. Possible failures or accidents may lead to dangerous outcomes [1], resulting in injuries, death, or damage to the environment [2,3,4]. Safety aspects have received a great deal of attention from the public, leading to enterprises’ more stringent reliability requirements [5]
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