Adjustment of reactor pressure vessel embrittlement trend curves using a mixed-effects model

Abstract

This study presents a novel approach for adjusting the generic reactor pressure vessel embrittlement trend curve (ETC), ASTM E900-15, using a mixed-effects model based on Baseline22, a compiled dataset of surveillance test data from nuclear power plants worldwide. Using this statistical framework, systematic deviations owing to initial material properties, notch orientations, and other plant-specific factors were separated from measurement errors, providing a more accurate assessment of embrittlement trends. Two types of adjustment models were explored: an intercept-only model (AM3) and a combined intercept-slope model (AM6). The AM3 model, which estimates only group-specific intercepts, effectively reduces prediction errors compared to ASTM E900-15 model while maintaining interpretability and simplicity, making it particularly suitable for regulatory applications. AM6, which incorporates group-specific slopes and covariance terms, further improves predictive accuracy, but introduces estimation complexities, so its suitability for conservate regulatory applications requires further discussion. To facilitate the practical implementation of AM3, closed-form expressions for group-specific intercept adjustments were derived, enabling the estimation of adjustment factors without the need for Bayesian Markov chain Monte Carlo models or complex statistical tools. Additionally, the standard deviations of the intercept means and prediction intervals were formulated as functions of the group size, providing a straightforward method for assessing embrittlement trends as new surveillance test results became available. This study demonstrates that existing generic ETC models can be dynamically refined and updated using plant-specific surveillance test data, while maintaining robustness and regulatory applicability. These findings lay the groundwork for the future refinement of standard ETC models, potential integration with regulatory frameworks, and improved long-term integrity assessments of reactor pressure vessels in aging nuclear power plants.