Abstract In general, common cause failures (CCFs) have been modeled with the assumption that components within the same group are symmetric. This assumption reduces the number of parameters required for the CCF probability estimation and allows us to use a parametric model, such as the alpha factor model. Although there are various asymmetric conditions in nuclear power plants (NPPs) to be addressed, the traditional CCF models are limited to symmetric conditions. Therefore, this paper proposes the copula-based CCF model to deal with asymmetric as well as symmetric CCFs. Once a joint distribution between the components is constructed using copulas, the proposed model is able to provide the probability of common cause basic events (CCBEs) by formulating a system of equations without symmetry assumptions. In addition, Bayesian inferences for the parameters of the marginal and copula distributions are introduced and Markov Chain Monte Carlo (MCMC) algorithms are employed to sample from the posterior distribution. Three example cases using simulated data, including asymmetry conditions in total failure probabilities and/or dependencies, are illustrated. Consequently, the copula-based CCF model provides appropriate estimates of CCFs for asymmetric conditions. This paper also discusses the limitations and notes on the proposed method.

中文翻译：

---

具有贝叶斯推理的基于 Copula 的共因故障模型

摘要 一般而言，共因故障 (CCF) 已在假设同一组内的组件是对称的情况下建模。这个假设减少了 CCF 概率估计所需的参数数量，并允许我们使用参数模型，例如 alpha 因子模型。尽管核电厂 (NPP) 中存在各种不对称条件需要解决，但传统的 CCF 模型仅限于对称条件。因此，本文提出了基于 copula 的 CCF 模型来处理非对称和对称 CCF。一旦使用 copula 构建了组件之间的联合分布，所提出的模型就能够通过在没有对称假设的情况下制定方程系统来提供共因基本事件 (CCBE) 的概率。此外，引入了对边缘分布和 copula 分布参数的贝叶斯推断，并采用马尔可夫链蒙特卡罗 (MCMC) 算法从后验分布中进行采样。说明了使用模拟数据的三个示例案例，包括总故障概率和/或相关性中的不对称条件。因此，基于 copula 的 CCF 模型为不对称条件提供了对 CCF 的适当估计。本文还讨论了该方法的局限性和注意事项。基于 copula 的 CCF 模型为不对称条件提供了对 CCF 的适当估计。本文还讨论了该方法的局限性和注意事项。基于 copula 的 CCF 模型为不对称条件提供了对 CCF 的适当估计。本文还讨论了该方法的局限性和注意事项。