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History and Value of Uncertainty and Sensitivity Analyses at the Nuclear Regulatory Commission and Center for Nuclear Waste Regulatory Analyses

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History and Value of Uncertainty and Sensitivity Analyses at the Nuclear Regulatory Commission and Center for Nuclear Waste Regulatory Analyses HISTORY AND VALUE OF UNCERTAINTY AND SENSITIVITY ANALYSES AT THE NUCLEAR REGULATORY COMMISSION AND CENTER FOR NUCLEAR WASTE REGULATORY ANALYSES Prepared for U.S. Nuclear Regulatory Commission Contract NRC–02–07–006 Prepared by Sitakanta Mohanty1 Richard Codell2 Y.-T. (Justin) Wu2 Osvaldo Pensado1 Olufemi Osidele1 David Esh3 Tina Ghosh3 1Center for Nuclear Waste Regulatory Analyses 2Consultant 3U.S. Nuclear Regulatory Commission September 2011 ABSTRACT This report documents the uncertainty and sensitivity analysis knowledge acquired over the past 20 years by the U.S. Nuclear Regulatory Commission (NRC) and the Center for Nuclear Waste Regulatory Analyses (CNWRA®) staffs during preparations to develop site-specific regulations for disposal of high-level radioactive waste (HLW) at the proposed Yucca Mountain repository, and to review a license application for that repository. This report is intended to serve the needs of future performance assessors or risk analysts at NRC and CNWRA who may be engaged in future HLW-related regulatory activities. It is intended to serve as a starting point for understanding various uncertainty and sensitivity analysis methods used by the two staffs, several of which were developed in house. Through references, this report points to various other documents for details of the uncertainty and sensitivity analyses staffs produced. For completeness, a chapter in this report also summarizes early uncertainty and sensitivity analyses work for waste package performance assessment (PA) that was carried out during the late 1980s. Uncertainty and sensitivity analysis methods the two staffs developed evolved and matured over time. In some cases, more advanced techniques were developed, and in others, existing advanced methods were used to glean risk insights from PAs. The generality of methods presented in this report also make them applicable to other NRC nuclear fuel cycle programs. ii CONTENTS Section Page ABSTRACT ................................................................................................................................... ii FIGURES ..................................................................................................................................... vi TABLES ...................................................................................................................................... viii EXECUTIVE SUMMARY ............................................................................................................. ix ACKNOWLEDGMENTS ............................................................................................................. xiii 1 INTRODUCTION ............................................................................................................ 1-1 1.1 Objectives of the Report .................................................................................. 1-3 1.2 A Brief Description of the Performance Assessment Models .......................... 1-3 1.2.1 System Conceptualization and Model Description ........................... 1-4 1.2.2 System Performance Estimation ...................................................... 1-4 1.2.3 Performance Metrics ......................................................................... 1-7 1.3 Report Structure .............................................................................................. 1-7 2 UNCERTAINTY ANALYSIS ........................................................................................... 2-1 2.1 Introduction ...................................................................................................... 2-1 2.2 Risk, and Risk Assessment ............................................................................. 2-1 2.2.1 Repository Risk Assessment ............................................................ 2-2 2.2.2 Uncertainty in the Context of Performance Assessment .................. 2-3 2.2.3 Parameter Sampling ......................................................................... 2-4 2.2.3.1 Distribution Functions for Parameters ............................. 2-4 2.2.3.2 Developing Empirical Probability Density Functions ....... 2-4 2.2.3.3 The Maximum Entropy Formalism .................................. 2-6 2.2.3.4 Sampling From a Distribution Function ........................... 2-7 2.2.4 Parameter Correlations ..................................................................... 2-7 2.2.5 Convergence of Model Results ......................................................... 2-9 2.2.6 Calculation of the Peak-of-the-Mean Dose ....................................... 2-9 2.2.7 Calculation of Mean Dose for Disruptive Events ............................ 2-10 2.2.8 Risk Dilution .................................................................................... 2-13 2.3 Granularity and Upscaling of Performance Assessment Models .................. 2-13 2.3.1 Example .......................................................................................... 2-14 2.3.2 Conclusions on Uncertainty Analysis .............................................. 2-16 3 SENSITIVITY ANALYSIS ............................................................................................... 3-1 3.1 General Considerations in Sensitivity Analysis ............................................... 3-1 3.1.1 Sensitivity to Alternative Models ....................................................... 3-1 3.1.2 Use of Intermediate Results To Determine Model Importance ......... 3-1 3.1.3 Use of Barrier or Component Failure Analysis ................................. 3-1 3.1.4 Parameter Sensitivity Analysis ......................................................... 3-2 3.2 Traditional Techniques for Parameter Sensitivity ............................................ 3-2 3.2.1 Statistical Sensitivity Analysis Based on Monte Carlo Sampling ...... 3-2 3.2.1.1 Developing and Manipulating Model Results for Sensitivity Analysis .......................................................... 3-3 3.2.1.2 Variable Transformations and Their Attributes ................ 3-3 3.2.2 Regression Methods ......................................................................... 3-6 3.2.2.1 Single Linear Regression on One Variable ..................... 3-6 3.2.2.2 Stepwise Multiple Linear Regression .............................. 3-7 3.2.2.3 Sensitivity for Non-Monotonic Relationships ................... 3-8 iii CONTENTS (continued) Section Page 3.2.3 Nonparametric Methods ................................................................... 3-9 3.2.3.1 The Kolmogorov-Smirnov Test ....................................... 3-9 3.2.3.2 The Sign Test ................................................................ 3-10 3.2.3.3 The Wilcoxon Rank Sum Test ....................................... 3-11 3.3 Conclusions ................................................................................................... 3-12 4 ADVANCED AND SPECIAL-CASE SENSITIVITY TECHNIQUES ................................ 4-1 4.1 Introduction ...................................................................................................... 4-1 4.2 Cumulative Distribution Function Sensitivity Analysis Method ........................ 4-1 4.2.1 Sampling-Based Cumulative Distribution Function Sensitivities ....... 4-2 4.2.2 Confidence Limits for Accepting Insignificant Parameters ................ 4-4 4.2.3 TPA Examples .................................................................................. 4-4 4.2.4 Correlation Issues ............................................................................. 4-6 4.2.5 Sample Size Requirements .............................................................. 4-7 4.2.6 Summary .......................................................................................... 4-7 4.3 Genetic Algorithms With Cascaded Variable Selection ................................... 4-8 4.3.1 Example—Shallow Land Disposal of Saltstone ................................ 4-8 4.3.2 Conclusions ...................................................................................... 4-9 4.4 Regionalized Sensitivity Analysis .................................................................. 4-10 4.4.1 The Regionalized Sensitivity Analysis Procedure ........................... 4-10 4.4.2 Example .......................................................................................... 4-12 4.4.3 Discussion ...................................................................................... 4-13 4.4.4 Summary ........................................................................................ 4-14 4.5 Fractional Factorial Method ........................................................................... 4-16 4.6 Iterated Fractional Factorial Design ............................................................... 4-18 4.7 Parameter Tree and Distribution Partitioning Intercept Methods ................... 4-18 4.7.1 Parameter Tree Method .................................................................. 4-18 4.7.1.1 Parameter Tree Example .............................................. 4-21 4.7.2 Distribution Partitioning Intercept Method ....................................... 4-22 4.7.2.1 Distribution Partitioning Intercept Example ................... 4-23 4.7.3 Discussion ...................................................................................... 4-23 4.8 Barrier Performance Evaluation by Signal Processing Techniques .............. 4-26 4.8.1 Convolution and Deconvolution Using the Fourier Transform ........ 4-27
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