Abstract

The power law process (PLP) is widely used to analyze the failures of repairable systems, and the PLP parameter estimation is the primary concern for reliability assessment or maintenance decision making. Although the Bayesian estimation of the PLP has been studied in existing research, little attention has been paid to how to obtain its prior distribution, especially when the prior information is coming from multiple sources. To address this problem, a framework for Bayesian prior information fusion using evidence theory is proposed in this paper. This framework first uses evidence theory to represent the prior information from multiple sources or experts and then combines them into fused information. Based on the belief and plausibility functions of the fused information, the prior distribution is bounded by an upper and lower probability density functions which are derived by moment equivalence. A case study is also carried out to verify and illustrate the proposed method. The results show that this proposed approach is beneficial for the Bayesian estimation of the power law process.

摘要

幂律过程（PLP）广泛用于分析可修复系统的故障，PLP参数估计是可靠性评估或维护决策的主要关注点。尽管在现有研究中已经研究了 PLP 的贝叶斯估计，但很少关注如何获得其先验分布，尤其是当先验信息来自多个来源时。针对这一问题，本文提出了一种基于证据理论的贝叶斯先验信息融合框架。该框架首先使用证据理论来表示来自多个来源或专家的先验信息，然后将它们组合成融合信息。基于融合信息的可信度和合理性函数，先验分布由由矩等价推导出的上下概率密度函数界定。还进行了案例研究以验证和说明所提出的方法。结果表明，该方法有利于幂律过程的贝叶斯估计。