Perspectives on the application of order-statistics in best-estimate plus uncertainty nuclear safety analysis

The application of order-statistics in best-estimate plus uncertainty nuclear safety analysis has received a considerable amount of attention from methodology practitioners, regulators, and academia. At the root of the debate are two questions: (1) what is an appropriate quantitative interpretation of “high level of probability” in regulatory language appearing in the LOCA rule, 10 CFR 50.46 and (2) how best to mathematically characterize the multi-variate case. An original derivation is offered to provide a quantitative basis for “high level of probability.” At root of the second question is whether one should recognize a probability statement based on the tolerance region method of Wald and Guba, et al., for multi-variate problems, one explicitly based on the regulatory limits, best articulated in the Wallis–Nutt “Testing Method”, or something else entirely. aper reviews the origins of the different positions, key assumptions, limitations, and relationship to addressing acceptance criteria. It presents a mathematical interpretation of the regulatory language, including a complete derivation of uni-variate order-statistics (as credited in AREVAʹs Realistic Large Break LOCA methodology) and extension to multi-variate situations. Lastly, it provides recommendations for LOCA applications, endorsing the “Testing Method” and addressing acceptance methods allowing for limited sample failures.