An analytical comparison of the multivariate normal model and the Reed–McCann procedure

Earthquakes are a significant risk contributor of nuclear power plants, potentially causing simultaneous damage to multiple structures, systems, and components. Various approaches have been proposed to estimate the probability of such simultaneous failures, among which the Reed–McCann procedure is widely recognized and recommended. However, its limitations and differences compared to alternative approaches remain insufficiently explored. In this study, we conduct an analytical comparison between the Reed–McCann procedure and the multivariate normal model, another well-established method in seismic probabilistic risk assessment, to identify a more practical method. To facilitate this comparison, we extend the Reed-McCann procedure by introducing negative common variables, which enables the procedure to represent the parameter space of the multivariate normal model. Then, under the assumptions of linear response and the separation of variables, we prove that the extended Reed-McCann procedure can be expressed as the multivariate normal model. Furthermore, we derive a transformation formula to convert the parameters of the Reed-McCann and extended Reed-McCann procedures into those of the multivariate normal model. This equivalence establishes a common foundation for an analytical comparison to identify a practical method. Our analysis demonstrates that the multivariate normal model offers superior computational efficiency, owing to its lower number of integration variables and an available fast evaluation algorithm. Moreover, the parameter estimation in the multivariate normal model is more straightforward than the Reed-McCann and extended Reed-McCann procedures. These advantages support our recommendation of the multivariate normal model as a preferable choice for practical estimation of seismically induced joint failure probability.