Determining the adjusting bias in reactor pressure vessel embrittlement trend curve using Bayesian multilevel modelling

A sophisticated Bayesian multilevel model for estimating group bias was developed to improve the utility of the ASTM E900-15 embrittlement trend curve (ETC) to assess the conditions of nuclear power plants (NPPs). For multilevel model development, the Baseline 22 surveillance dataset was basically classified into groups based on the NPP name, product form, and notch orientation. By including the notch direction in the grouping criteria, the developed model could account for TTS differences among NPP groups with different notch orientations, which have not been considered in previous ETCs. The parameters of the multilevel model and biases of the NPP groups were calculated using the Markov Chain Monte Carlo method. As the number of data points within a group increased, the group bias approached the mean residual, resulting in reduced credible intervals of the mean, and vice versa. Even when the number of surveillance test data points was less than three, the multilevel model could estimate appropriate biases without overfitting. The model also allowed for a quantitative estimate of the changes in the bias and prediction interval that occurred as a result of adding more surveillance test data. The biases estimated through the multilevel model significantly improved the performance of E900-15.