Department of Industrial Engineering (DIEF), University of Florence, 50123 Florence, Italy.
Department of Civil Engineering, University of Parsian, Qazvin 3176795591, Iran.
Int J Environ Res Public Health. 2021 Mar 24;18(7):3349. doi: 10.3390/ijerph18073349.
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.
在过去的几十年中，由于在风险和资产完整性管理中的重要性，可靠性分析引起了人们的极大兴趣。同时，贝叶斯推断已被证明优于其他统计工具，如最大似然估计（MLE）和最小二乘估计（LSE），在估计描述失效建模的参数方面。实际上，贝叶斯推断可以将先验信念和信息纳入分析中，这可以部分克服数据不足的问题。因此，本文旨在为工业部件的可靠性评估提供贝叶斯分析的封闭数学表示，同时研究先验选择对未来故障预测的影响。为此，针对三个具有不同大小的样本测试了层次贝叶斯建模（HBM），同时考虑了五个不同的先验分布。此外，采用贝塔二项式分布来表示所考虑设备的失效行为。结果表明，即使考虑更大的样本量，选择强信息先验也会导致截然不同的预测。这项研究的结果可以帮助维护工程师和资产经理将他们的先验信念纳入可靠性估计过程。
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