An Approach to Analysis of Dependency in Risk Assessment using Copula

This thesis is intended to propose a methodology for estimating the probability of dependent failures in nuclear power plants (NPPs) using a copula to address the limitations of traditional dependency analysis via probabilistic safety assessment (PSA). These limitations include the asymmetry and uncertainty due to subjectivity in estimating the probabilities of common-cause failures (CCFs). Incorporating inter-unit dependency into the multi-unit PSA (MUPSA) model is also limited to the modelling of CCFs, making modeling and quantification of the MUPSA model difficult. It is believed that constructing a joint-probability distribution using a copula to model dependency will be able to cope with these problems. This thesis divides the limitations of conventional dependency analysis into two topics. First of all, Chapter 3 develops the copula-based CCF model to estimate the probability of asymmetric CCFs and to reduce the subjectivity-based uncertainty in estimating the CCF probability. Bayesian inference was employed to determine the parameters of the distribution and a Markov chain Monte Carlo (MCMC) was used to sample from the posterior distribution. Selection of the prior distribution of the copula parameter was discussed, and the dependent-failure probabilities were estimated through the prediction distribution using the sampling results. These probabilities were decomposed into the probabilities of common-cause basic events (CCBEs) to apply to a fault-tree analysis. The MCMC and decomposition methods were incorporated to represent the uncertainty of CCBEs; in conclusion, various asymmetric conditions were addressed using the proposed model. It was confirmed that the copula-based CCF model could describe the differences between components without any engineering judgement, even though relatively little data were collected. In Chapter 4, a copula-based estimation scheme for site surrogate metrics such as the site conditional core damage probability (SCCDP) is proposed. A single-unit conditional core damage probability (CCDP) is considered as a random variable in a joint probability distribution and extended to n units via a copula function. The copula parameter representing the level of interunit dependency was estimated by combining two-unit MUPSA models, and a simplified fourunit MUPSA model was constructed to compare the results of the SCCDP with the copula combining two-unit MUPSA models. It was confirmed that the n-unit SCCDP could be estimated using the proposed estimation scheme without developing an n-unit MUPSA model. Additionally, the indices representing the dependency levels of multiple units were developed. The site conditional probability of a multi-unit accident (SCPMA) was proposed by revising the definition of the single-unit CPMA and the site dependence index (SDI) was developed based on the banking stability index (BSI) used in financial engineering. In conclusion, using the quantification results of the MUPSA model, the proposed indices could complement site-surrogate metrics such as the SCCDP