In an engineering system, multiple components may fail simultaneously due to a shared cause or common cause (CC). This kind of failure is referred to as a common-cause failure (CCF), and it contributes greatly to system risk. However, the propagation of a cause condition to the affected components is not always certain (deterministic). The propagation may be probabilistic due to many reasons, such as system specific defences against cause condition propagation. This kind of CCF is also called the probabilistic CCF (PCCF) which is defined as any condition or event that causes multiple components to fail or malfunction simultaneously with different occurrence probabilities. A system subject to PCCFs is sometimes affected by multiple CCs. This paper proposes explicit and implicit Bayesian Network (BN)-based methods to model systems subject to PCCFs considering different relationships among multiple CCs within a single model. The originality of this work lies in the use of BN to model the probabilistic dependencies among multiple CCs under different relationships and their affected components. Both methods are suitable for systems in which multiple CCs affect different components with different dependencies. Finally, the proposed methods are applied to model the risk of gas explosion in coal mines to evaluate the occurrence probability of accidents.

在工程系统中，由于共同原因或共同原因（CC），多个组件可能同时失效。这种故障称为“常见原因故障（CCF）”，它极大地增加了系统风险。但是，原因条件到受影响组件的传播并不总是确定的（确定的）。由于多种原因，传播可能是概率性的，例如针对原因条件传播的系统特定防御措施。这种CCF也称为概率CCF（PCCF），它定义为导致多个组件同时发生故障或发生故障且出现概率不同的任何条件或事件。受PCCF约束的系统有时会受到多个CC的影响。本文提出了基于显式和隐式贝叶斯网络（BN）的方法来对受PCCF约束的系统进行建模，并考虑了单个模型中多个CC之间的不同关系。这项工作的独创性在于使用BN对不同关系及其受影响组件下的多个CC之间的概率依赖性进行建模。两种方法都适用于多个CC影响具有不同依赖性的不同组件的系统。最后，将所提出的方法应用于煤矿瓦斯爆炸的风险模型，以评估事故发生的可能性。这项工作的独创性在于使用BN对不同关系及其受影响组件下的多个CC之间的概率依赖性进行建模。两种方法都适用于多个CC影响具有不同依赖性的不同组件的系统。最后，将所提出的方法应用于煤矿瓦斯爆炸的风险模型，以评估事故发生的可能性。这项工作的独创性在于使用BN对不同关系及其受影响组件下的多个CC之间的概率依赖性进行建模。两种方法都适用于多个CC影响具有不同依赖性的不同组件的系统。最后，将所提出的方法应用于煤矿瓦斯爆炸的风险模型，以评估事故发生的可能性。