Managing failure dependence of complex systems with hybrid uncertainty is one of the hot problems in reliability assessment. Epistemic uncertainty is attributed to complex working environment, system structure, human factors, imperfect knowledge, etc. Probability-box has powerful characteristics for uncertainty analysis and can be effectively adopted to represent epistemic uncertainty. However, arithmetic rules on probability-box structures are mostly used among structures representing independent random variables. In most practical engineering applications, failure dependence is always introduced in system reliability analysis. Therefore, this paper proposes a developed Bayesian network combining copula method with probability-box for system reliability assessment. There are four main steps involved in the reliability computation process: marginal distribution identification and estimation, copula function selection and parameter estimation, reliability analysis of components with correlations and Bayesian forward analysis. The benefits derived from the proposed approach are used to overcome the computational limitations of n-dimensional integral operation, and the advantages of useful properties of copula function in reliability analysis of systems with correlations are adopted. To demonstrate the effectiveness of the developed Bayesian network, the proposed method is applied to a real large piston compressor.

中文翻译：

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故障相关和不确定系统的可靠性评估：基于 copula 方法和概率盒的贝叶斯网络

管理具有混合不确定性的复杂系统的故障依赖性是可靠性评估中的热点问题之一。认知不确定性归因于复杂的工作环境、系统结构、人为因素、不完善的知识等。概率盒具有强大的不确定性分析特性，可以有效地用于表示认知不确定性。然而，概率盒结构的算术规则主要用于表示独立随机变量的结构中。在大多数实际工程应用中，系统可靠性分析中总是引入故障相关性。因此，本文提出了一种开发的贝叶斯网络，将 copula 方法与概率盒相结合用于系统可靠性评估。可靠性计算过程涉及四个主要步骤：边缘分布识别和估计、Copula 函数选择和参数估计、具有相关性的组件的可靠性分析和贝叶斯前向分析。从所提出的方法中获得的好处用于克服计算限制采用n维积分运算，利用copula函数在具有相关性的系统可靠性分析中的有用性质的优点。为了证明所开发的贝叶斯网络的有效性，将所提出的方法应用于真实的大型活塞式压缩机。