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

• Published in: Nuclear engineering and design 2011, Vol.241 (1), p.274-284
• Main Authors: Martin, Robert P., Nutt, William T.
• Format: Article
• Language: English
• Subjects: Applied sciences; Controled nuclear fusion plants; Derivation; Energy; Energy. Thermal use of fuels; Exact sciences and technology; Failure; Fission nuclear power plants; Fuels; GENERAL AND MISCELLANEOUS; Installations for energy generation and conversion: thermal and electrical energy; LOCA; Mathematical analysis; Methodology; Nuclear fuels; Nuclear reactor components; Nuclear safety; nuclear safety analysis; PROBABILITY; RADIATION PROTECTION; RECOMMENDATIONS; Roots; TESTING; TOLERANCE; Uncertainty
• ISSN: 0029-5493; 1872-759X
• DOI: 10.1016/j.nucengdes.2010.10.034

▶ Historical recitation on application of order-statistics models to nuclear power plant thermal-hydraulics safety analysis. ▶ Interpretation of regulatory language regarding 10 CFR 50.46 reference to a “high level of probability”. ▶ Derivation and explanation of order-statistics-based evaluation methodologies considering multi-variate acceptance criteria. ▶ Summary of order-statistics models and recommendations to the nuclear power plant thermal-hydraulics safety analysis community. 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. This paper 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 AREVA's 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.