Risk and Safety Analysis of Nuclear Systems

JOHN C. LEE, PhD, has been Professor of Nuclear Engineering at the University of Michigan since 1974, following five years of employment at Westinghouse Electric Corporation and General Electric Company. He has written for approximately 180 publications on broad areas of nuclear reactor physics and engineering, including nuclear systems analysis and diagnostics. Dr. Lee is a Fellow of the American Nuclear Society.NORMAN J. McCORMICK, PhD, is an emeritus professor of mechanical engineering at the University of Washington who retired in 2003. From 1966 until the early 1990s, he was a professor of nuclear engineering. Dr. McCormick is the author of the book Reliability and Risk Analysis Methods and Nuclear Power Applications (upon which part of NERS 462 is based) and has authored approximately 150 journal articles. He is a Fellow of the American Nuclear Society.

• Preface xiiPermissions and Copyrights xivList of Tables xviList of Figures xviii1 Risk and Safety of Engineered Systems 11.1 Risk and Its Perception and Acceptance 11.2 Overview of Risk and Safety Analysis 61.3 Two Historical Reactor Accidents 81.4 Definition of Risk 91.5 Reliability, Availability, Maintainability, and Safety 101.6 Organization of the Book 12References 132 Probabilities of Events 152.1 Events 152.2 Event Tree Analysis and Minimal Cut Sets 172.3 Probabilities 192.3.1 Interpretations of Probability 192.3.2 Axiomatic Approach to Probabilities 202.3.3 Intersection of Events 212.3.4 Union of Events 222.3.5 Decomposition Rule for Probabilities 252.4 TimeIndependent Versus TimeDependent Probabilities 252.5 TimeIndependent Probabilities 262.5.1 Introduction 262.5.2 TimeIndependent Probability Distributions 272.6 Normal Distribution 312.7 Reliability Functions 352.8 TimeDependent Probability Distributions 412.8.1 Erlangian and Exponential Distributions 422.8.2 Gamma Distribution 432.8.3 Lognormal Distribution 442.8.4 Weibull Distribution 462.8.5 Generalized “Bathtub” Distribution 472.8.6 Selection of a TimeDependent Probability Distribution 482.9 ExtremeValue Probability Distributions 502.10 Probability Models for Failure Analyses 52References 53Exercises 533 Reliability Data 593.1 Estimation Theory 593.1.1 Moment Estimators 603.1.2 Maximum Likelihood Estimators 613.1.3 Maximum Entropy Estimators 643.1.4 Comparison of Estimators 653.2 Bayesian Updating of Data 653.2.1 Bayes Equation 653.2.2 Applications of the Bayes Equation 673.3 Central Limit Theorem and Hypothesis Testing 703.3.1 Interpretation of the Central Limit Theorem 713.3.2 Hypothesis Testing with the Central Limit Theorem 723.4 Reliability Quantification 743.4.1 Central Limit Theorem for Reliability Quantification 743.4.2 Engineering Approach for Reliability Quantification 763.4.3 ­2Distribution for Reliability Quantification 773.4.4 ThreeWay Comparison and Concluding Remarks 78References 80Exercises 804 Reliability of MultipleComponent Systems 854.1 Series and ActiveParallel Systems 864.1.1 Systems with Independent Components 864.1.2 Systems with Redundant Components 884.1.3 FailtoSafety and FailtoDanger Systems 904.2 Systems with Standby Components 934.3 Decomposition Analysis 964.4 Signal Flow Graph Analysis 1004.5 Cut Set Analysis 101References 104Exercises 1045 Availability and Reliability of Systems with Repair 1095.1 Introduction 1095.2 Markov Method 1115.2.1 Markov Governing Equations 1115.2.2 Solution of Markov Governing Equations 1135.2.3 An Elementary Example 1165.3 Availability Analyses 1185.3.1 Rules for Constructing Transition Rate Matrices 1185.3.2 Availability Transition Rate Matrices 1195.3.3 TimeDependent Availability Examples 1235.3.4 SteadyState Availability 1275.4 Reliability Analyses 1285.4.1 Reliability Transition Rate Matrices 1295.4.2 TimeDependent Reliability Examples 1305.4.3 Mean Time to Failure 1305.5 Additional Capabilities of Markov Models 1335.5.1 Imperfect Switching Between System States 1345.5.2 Systems with Nonconstant Hazard Rates 136References 137Exercises 1376 Probabilistic Risk Assessment 1416.1 Failure Modes 1426.2 Classification of Failure Events 1436.2.1 Primary, Secondary, and Command Failures 1436.2.2 Common Cause Failures 1446.2.3 Human Errors 1486.3 Failure Data 1506.3.1 Hardware Failures 1506.3.2 Human Errors 1506.4 Combination of Failures and Consequences 1526.4.1 Inductive Methods 1526.4.2 Event Tree Analysis 1546.5 Fault Tree Analysis 1566.5.1 Introduction 1566.5.2 Fault Tree Construction 1576.5.3 Qualitative Fault Tree Analysis 1576.5.4 Quantitative Fault Tree Analysis 1606.5.5 Common Cause Failures and Fault Tree Analysis 1656.6 Master Logic Diagram 1656.7 Uncertainty and Importance Analysis 1686.7.1 Types of Uncertainty in PRAs 1686.7.2 Stochastic Uncertainty Analysis 1696.7.3 Sensitivity and Importance Analysis 170References 172Exercises 1727 Computer Programs for Probabilistic Risk Assessment 1797.1 Fault Tree Methodology of the SAPHIRE Code 1797.1.1 Gate Conversion and Tree Restructuring 1807.1.2 Simplification of the Tree 1807.1.3 Fault Tree Expansion and Reduction 1827.2 Fault and Event Tree Evaluation with the SAPHIRE Code 1837.3 Other Features of the SAPHIRE Code 1857.4 Other PRA Codes 1857.5 Binary Decision Diagram Algorithm 1877.5.1 Basic Formulation of the BDD Algorithm 1877.5.2 Generalization of the BDD Formulation 1897.5.3 Zero Suppressed BDD Algorithm and the FTREX Code 193References 194Exercises 1958 Nuclear Power Plant Safety Analysis 1978.1 Engineered Safety Features of Nuclear Power Plants 1978.1.1 Pressurized Water Reactor 1988.1.2 Boiling Water Reactor 2108.2 Accident Classification and General Design Goals 2158.2.1 Plant Operating States 2178.2.2 Accident Classification in 10 CFR 50 2178.2.3 General Design Criteria and Safety Goals 2198.3 Design Basis Accident: LargeBreak LOCA 2208.3.1 Typical Sequence of a ColdLeg LBLOCA in PWR 2218.3.2 ECCS Specifications 2258.3.3 Code Scaling, Applicability, and Uncertainty Evaluation 2278.4 Severe (Class 9) Accidents 2318.5 Anticipated Transients Without Scram 2338.5.1 History and Background of the ATWS Issue 2338.5.2 Resolution of the ATWS Issues 2358.5.3 Power Coefficients of Reactivity in LWRs 2378.6 Radiological Source and Atmospheric Dispersion 2418.6.1 Radiological Source Term 2428.6.2 Atmospheric Dispersion of Radioactive Plume 2438.6.3 Simple Models for Dose Rate Calculation 2478.7 Biological Effects of Radiation Exposure 250References 252Exercises 2549 Major Nuclear Power Plant Accidents and Incidents 2599.1 Three Mile Island Unit 2 Accident 2609.1.1 Sequence of the Accident—March 1979 2609.1.2 Implications and FollowUp of the Accident 2609.2 PWR InVessel Accident Progression 2639.2.1 Core Uncovery and Heatup 2659.2.2 Cladding Oxidation 2669.2.3 Clad Melting and Fuel Liquefaction 2689.2.4 Molten Core Slumping and Relocation 2709.2.5 Vessel Breach 2719.3 Chernobyl Accident 2729.3.1 Cause and Nature of the Accident—April 1986 2729.3.2 Sequence of the Accident 2749.3.3 Estimate of Energy Release in the Accident 2759.3.4 Accident Consequences 2759.3.5 Comparison of the TMI and Chernobyl Accidents 2769.4 Fukushima Station Accident 2779.4.1 Overview of the Accident–March 2011 2779.4.2 Radiological Consequences of the Accident 2789.4.3 Implications and FollowUp of the Fukushima Accident 2799.5 Salem Anticipated Transient Without Scram 2819.5.1 Chronology and Cause of the Salem Incident 2819.5.2 Implications and FollowUp of the Salem ATWS Event 2829.6 LaSalle Transient Event 2849.6.1 LaSalle NuclearCoupled DensityWave Oscillations 2849.6.2 Simple Model for NuclearCoupled DensityWave Oscillations 2879.6.3 Implications and FollowUp of the LaSalle Incident 2929.7 DavisBesse Potential LOCA Event 2929.7.1 Background and Chronology of the Incident 2929.7.2 NRC Decision to Grant DB Shutdown Delay 2939.7.3 Causes for the DavisBesse Incident and FollowUp 298References 298Exercises 30110 PRA Studies of Nuclear Power Plants 30310.1 WASH1400Reactor Safety Study 30410.2 Assessment of Severe Accident Risks: NUREG1150. 31110.2.1 Background and Scope of the NUREG1150 Study 31110.2.2 Overview of NUREG1150 Methodology 31310.2.3 Accident Frequency Analysis 31510.2.4 Accident Progression Analysis 32010.2.5 Radionuclide Transport Analysis 32410.2.6 Offsite Consequence Analysis 32710.2.7 Uncertainty Analysis 33010.2.8 Risk Integration 33110.2.9 Additional Perspectives and Comments on NUREG1150. 33710.3 Simplified PRA in the Structure of NUREG1150. 34010.3.1 Description of the Simplified PRA Model 34010.3.2 Parametric Studies and Comments on the Simplified PRA Model 344References 345Exercises 34711 Passive Safety and Advanced Nuclear Energy Systems 34911.1 Passive Safety Demonstration Tests at EBRII 34911.1.1 EBRII Primary System and Simplified Model 35011.1.2 Unprotected LossofFlow and LossofHeatSink Tests 35711.1.3 Simplified Fuel Channel Analysis 36111.1.4 Implications of EBRII Passive Safety Demonstration Tests 36211.2 Safety Characteristics of Generation III+ Plants 36411.2.1 AP1000 Design Features 36411.2.2 SmallBreak LOCA Analysis for AP1000 36611.2.3 Economic Simplified Boiling Water Reactor 37111.2.4 Reliability Quantification of SBWR Passive Safety Containment 37511.3 Generation IV Nuclear Power Plants 38211.3.1 SodiumCooled Fast Reactor 38311.3.2 Hypothetical Core Disruptive Accidents for Fast Reactors 38711.3.3 VHTR and Phenomena Identification and Ranking Table 393References 396Exercises 39912 RiskInformed Regulations and ReliabilityCentered Maintenance 40112.1 Risk Measures for Nuclear Plant Regulations 40212.1.1 Principles of RiskInformed Regulations and Licensing 40212.1.2 Uncertainties in RiskInformed Decision Making 40512.1.3 Other Initiatives in RiskInformed Regulations 40612.2 ReliabilityCentered Maintenance 40612.2.1 Optimization Strategy for Preventive Maintenance 40712.2.2 ReliabilityCentered Maintenance Framework 40912.2.3 CostBenefit Considerations 410References 413Exercises 41513 Dynamic Event Tree Analysis 41713.1 Basic Features of Dynamic Event Tree Analysis 41813.2 Continuous Event Tree Formulation 42113.2.1 Derivation of the Stochastic Balance Equation 42113.2.2 Integral Form of the Stochastic Balance Equation 42313.2.3 Numerical Solution of the Stochastic Balance Equation 42513.3 CelltoCell Mapping for Parameter Estimation 42613.3.1 Derivation of the Bayesian Recursive Relationship 42713.3.2 CCM Technique for Dynamic Event Tree Construction 43013.4 Diagnosis of Component Degradations 43413.4.1 Bayesian Framework for Component Diagnostics 43413.4.2 Implementation of the Probabilistic Diagnostic Algorithm 437References 441Exercises 442Appendix A: Reactor Radiological Sources 443A.1 Fission Product Inventory and Decay Heat 443A.2 Health Effects of Radiation Exposure 446References 448Appendix B: Some Special Mathematical Functions 449B.1 Gamma Function 449B.2 Error Function 451References 451Appendix C: Some Failure Rate Data 453Appendix D: Linear Kalman Filter Algorithm 457References 461Answers to Selected Exercises 462Index and Acronyms 467

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