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Uncertainty Guide ICSBEP Guide to the Expression of Uncertainties Editor V. F. Dean Subcontractor to Idaho National Laboratory Independent Reviewer Larry G. Blackwood (retired) Idaho National Laboratory Guide to the Expression of Uncertainties for the Evaluation of Critical Experiments ACKNOWLEDGMENT We are most grateful to Fritz H. Fröhner, Kernforschungszentrum Karlsruhe, Institut für Neutronenphysik und Reaktortechnik, for his preliminary review of this document and for his helpful comments and answers to questions. Revision: 4 i Date: November 30, 2007 Guide to the Expression of Uncertainties for the Evaluation of Critical Experiments This guide was prepared by an ICSBEP subgroup led by G. Poullot, D. Doutriaux, and J. Anno of IRSN, France. The subgroup membership includes the following individuals: J. Anno IRSN (retired), France J. B. Briggs INL, USA R. Bartholomay Westinghouse Safety Management Solutions, USA V. F. Dean, editor Subcontractor to INL, USA D. Doutriaux IRSN (retired), France K. Elam ORNL, USA C. Hopper ORNL, USA R. Jeraj J. Stefan Institute, Slovenia Y. Kravchenko RRC Kurchatov Institute, Russian Federation V. Lyutov VNIITF, Russian Federation R. D. McKnight ANL, USA Y. Miyoshi JAERI, Japan R. D. Mosteller LANL, USA A. Nouri OECD Nuclear Energy Agency, France G. Poullot IRSN (retired), France R. W. Schaefer ANL (retired), USA N. Smith AEAT, United Kingdom Z. Szatmary Technical University of Budapest, Hungary F. Trumble Westinghouse Safety Management Solutions, USA A. Tsiboulia IPPE, Russian Federation O. Zurron ENUSA, Spain The contribution of French participants had strong technical support from Benoit Queffelec, Director of the Société Industrielle d’Etudes et Réalisations, Enghien (France). He is a consultant on statistics applied to industrial and fabrication processes. Revision: 4 ii Date: November 30, 2007 Guide to the Expression of Uncertainties for the Evaluation of Critical Experiments FOREWORD The methods used by the International Criticality Safety Benchmark Evaluation Project (ICSBEP) to treat uncertainties encountered in experimental data and in the derivation of benchmark models have evolved significantly since the project was initiated in 1992. At an ICSBEP Meeting in Portland, Maine (1999), the Working Group expressed the need for a guide to the treatment of uncertainties in order to assist the work of both evaluator and reader. Because of this historic background, when using an evaluation reported in the “International Handbook of Evaluated Criticality Safety Benchmark Experiments,” the reader will often encounter, especially in evaluations written before 2001, • mixing of uncertainties in physical parameters that are standard deviations coming from a large number of measurements with those given as tolerances, or bounds, • lack of information about the sources of given uncertainty values, including level of confidence and degrees of freedom corresponding to reported uncertainties, • inconsistencies in the coverage factor (corresponding to 1, 2 or 3 σ) between the different uncertainties, • after the uncertainties in physical parameters are propagated to obtain an equivalent reactivity uncertainty of keff, this total experimental uncertainty is given without mentioning the level of confidence. The mean and standard deviation are now recommended as optimal estimates for a parameter and its uncertainty. If these are used for the benchmark model and to calculate the uncertainty in keff, then, when the probability distribution of keff is Gaussian (a reasonable assumption in many cases), the level of confidence of the keff uncertainty range will be approximately 68%. This guide, written to develop a consistency among evaluators in the uncertainty treatment (Sections 2, 3.1, and 3.5 of the ICSBEP evaluation), is based on two main references, which are the respective U.S. and European standards. The standards are very similar and have the same origin, namely, the International Standard Organization (ISO) Guide to the Expression of Uncertainty in Measurement, published in 1995. These two main references are o Reference 1 – “American National Standard for Expressing Uncertainty - U.S. Guide to the Expression of Uncertainty in Measurement,” ANSI/NCSL Z540-2-1997 (Copyright © 1997 by National Conference of Standards Laboratories, All rights reserved.). and o Reference 2 – “Guide pour l'expression de l’incertitude de mesure.” European Pre-standard NF ENV 13005 Août 1999. Revision: 4 iii Date: November 30, 2007 Guide to the Expression of Uncertainties for the Evaluation of Critical Experiments TABLE OF CONTENTS 1.0 GENERAL CONSIDERATIONS IN THE DETERMINATION OF UNCERTAINTIES......................................................................................................1 1.1 Benefits of determining best estimates of uncertainties ........................................1 1.2 The uncertainty analysis .......................................................................................2 1.2.1 Evaluation of experimental data ................................................................2 1.2.2 Additional uncertainty from creating the benchmark model .......................2 1.2.3 An objective, rigorous, graded approach ...................................................3 1.3 Level of confidence...............................................................................................4 1.4 The guide .............................................................................................................4 2.0 METROLOGY AND ASSOCIATED STATISTICS............................................. 6 2.1 Type A evaluation of standard uncertainty ............................................................8 2.2 Type B evaluation of standard uncertainty ............................................................9 2.3 “Uncertainty of the uncertainty”.............................................................................11 2.4 Determining combined standard uncertainty.........................................................11 3.0 INVENTORY OF UNCERTAINTIES .................................................................. 14 3.1 Uncertainties from physics, chemistry, and isotopics of materials ...............17 3.2 Uncertainties on geometry................................................................................19 3.3 Uncertainties of dates ................................................................................ 20 3.4 Uncertainties from modeling.............................................................................21 3.5 General remarks on calculations of uncertainties ..........................................21 Revision: 4 iv Date: November 30, 2007 Guide to the Expression of Uncertainties for the Evaluation of Critical Experiments TABLE OF CONTENTS (cont’d) 4.0 CALCULATION OF EFFECTS OF UNCERTAINTIES ON keff.......................... 23 4.1 One-variable-at-a-time strategy ............................................................................23 4.1.1 Analytical method......................................................................................24 4.1.2 Deterministic method ................................................................................24 4.1.3 Monte Carlo method..................................................................................25 4.1.4 Monte Carlo perturbation method..............................................................25 4.1.5 Uncertainties of the calculated uncertainties .............................................26 4.2 Experimental-design methodology........................................................................27 5.0 ESTIMATIONS OF SYSTEMATIC EFFECTS AND THEIR UNCERTAINTIES .............................................................................................29 5.1 Systematic error ...................................................................................................29 5.2 Uncertainty of the estimate of systematic error .....................................................29 5.3 Systematic effect of modeling simplifications ........................................................30 5.4 Uncertainty from modeling simplifications .............................................................30 5.5 Systematic effect of modeling similar components as equal .................................30 6.0 ESTIMATION OF THE FINAL COMBINED STANDARD UNCERTAINTY ....... 32 6.1 General formula....................................................................................................32 6.2 Application cases..................................................................................................32 6.3 Value, small or dominant, of individual uncertainty ...............................................33 6.4 Effective degrees of freedom and level of confidence...........................................33 7.0 REFERENCES................................................................................................... 36 Revision: 4 v Date: November 30, 2007 Guide to the Expression of Uncertainties for the Evaluation of Critical Experiments TABLE OF CONTENTS (cont’d) APPENDICES APPENDIX A: GLOSSARY OF METROLOGY AND ASSOCIATED STATISTICS ................................................................................. 37 A.1 Metrology ..............................................................................................................37 A.2 Basic statistical terms............................................................................................38 APPENDIX B: SUMMARY OF SOME PRINCIPLES FOR
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