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Rank statistics and bootstrap: a more precise evaluation of the 95th percentile in nuclear safety LB-LOCA calculations



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J. Joucla, P. Probst,
14th International Conference on Nuclear Engineering (ICONE 14), Miami, Floride, USA, 17-20, juillet 2006,
Rapport DSR 136


  In 1988, since the revision of the 10 CFR50.46, the best estimate codes may be used in safety demonstration and licensing, provided that uncertainties are added to the relevant output parameters before comparing them with the acceptance criteria. The uncertainty of output parameters is coming principally from the lack of knowledge of the input parameters (initial and boundary conditions of the calculated transient, empirical models of the code, etc.). In the safety analysis of the large break loss of coolant accident (LB-LOCA), for a best-estimate analysis, it was decided that the acceptance criteria should not be exceeded by the 95th percentile estimated with a high degree of confidence. Best-estimate plus uncertainty (BEPU) analysis of the LB-LOCA allows significant margin gains. Therefore the nuclear industry develops and uses widely this type of analysis for power uprating, longer fuel cycles, fuel design etc. It appeared necessary to IRSN, technical support of the French Safety Authority, to get more insight to these strategies.
The assessment of the 95th percentile can be made in three steps:
1.        The definition and the evaluation of uncertainties of the input parameters.
2.        The modelling and understanding of the output parameters.
3.        The evaluation of the 95th percentile with a high degree of confidence.
This paper presents and shows two new methods of how to deal with the third point.
The standard approach is the use of a non-parametric approach called the Wilks’ formula which requires only 59 calculations to get a majorant of the 95th percentile with a 95% degree of confidence. This method was applied in the 90’s when the calculation resources were not sufficient to perform many calculations in a reasonable time. However, at the present time, the growth of computer power and the fall in prices allow to run many more calculations in the same physical time. We propose to use rank statistics or bootstrap to estimate the 95th percentile with a high confidence level, using some hundreds of calculations.
This paper presents the results of the LOFT (Loss-of-Fluid Test) loss of coolant experiment L2-5 using these new methodologies. LOFT L2-5 was the subject of the former ISP 13 and the ongoing BEMUSE international problem. The output parameter is the second maximum peak cladding temperature of the fuel. The best estimate code used is CATHARE2 V2.5. Rank statistics and bootstrap improve the information on the estimation of the 95th percentile: a higher degree of confidence, a more precise estimation etc.