Data from: Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

This paper presents a quantitative reliability modelling and analysis method for multi-state elements (MSEs) based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables (CPTs), can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network (BN) model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit.本文提出了一种结合马尔可夫过程（Markov process）与动态贝叶斯网络（dynamic Bayesian network, DBN）的多状态元件（multi-state elements, MSEs）定量可靠性建模与分析方法，同时考量完美修复、非完美修复与状态检修（condition-based maintenance, CBM）三种场景。首先构建了无修复及状态检修场景下的元件马尔可夫模型，并引入吸收集（absorbing set）以确定可修复元件的可靠性；随后依据马尔可夫过程确定的状态间转移关系，搭建动态贝叶斯网络模型。此外，针对串并联系统，其条件概率表（conditional probability tables, CPTs）的参数可通过参考条件退化概率计算得到。最后以故障模型中的控制单元为例：先将动态故障树（dynamic fault tree, DFT）转换为贝叶斯网络（Bayesian network, BN）模型，再进一步扩展为动态贝叶斯网络；研究人员通过微分方程绘制吸收集并完成验证，据此得到无修复、经完美/非完美修复以及实施状态检修的元件与系统的状态概率。通过正向推理，可确定不同工况下控制单元的可靠性数值，并最终标记出控制单元中的薄弱节点。