The book has been developed in conjunction with NERS 462, a course offered every year to seniors and graduate students in the University of Michigan NERS program.

The first half of the book covers the principles of risk analysis, the techniques used to develop and update a reliability data base, the reliability of multi-component systems, Markov methods used to analyze the unavailability of systems with repairs, fault trees and event trees used in probabilistic risk assessments (PRAs), and failure modes of systems. All of this material is general enough that it could be used in non-nuclear applications, although there is an emphasis placed on the analysis of nuclear systems.

The second half of the book covers the safety analysis of nuclear energy systems, an analysis of major accidents and incidents that occurred in commercial nuclear plants, applications of PRA techniques to the safety analysis of nuclear power plants (focusing on a major PRA study for five nuclear power plants), practical PRA examples, and emerging techniques in the structure of dynamic event trees and fault trees that can provide a more realistic representation of complex sequences of events. The book concludes with a discussion on passive safety features of advanced nuclear energy systems under development and approaches taken for risk-informed regulations for nuclear plants.

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.

An authoritative guide to enhancing the safety, reliability, and availability of nuclear energy systems

The catastrophic events of March 2011 in Japan serve to remind the next generation of nuclear professionals that a nuclear accident anywhere is a nuclear accident everywhere. This timely resource provides a necessary introduction to risk and reliability assessment as well as an overview of nuclear power plant safety analysis, augmented by real-world examples drawn from design and operating experience. Developed in conjunction with Nuclear Engineering and Radiological Sciences (NERS) 462, a course offered every year to seniors and graduate students in the University of Michigan NERS program, this book is needed more than ever, as nuclear power is once again becoming a viable option for new electrical generation facilities.

The first half of the book covers the principles of risk and reliability analysis, the techniques used to develop and update a reliability database, the reliability of multi-component systems, and Markov methods used to analyze the unavailability of a system with repairs. The second half covers applications of the methods for probabilistic risk assessment of complex engineered systems, together with deterministic safety analysis of nuclear power plants. Also featured are:

• Fault trees and event trees used in probabilistic risk assessments
• Failure modes of systems
• A review of major accidents and incidents in commercial nuclear plants over the past three decades
• Passive safety features of advanced nuclear systems that are under development
• Advanced topics such as dynamic event tree analysis and binary decision diagrams for fault tree evaluation
• Approaches taken for risk-informed regulations for nuclear plants
• More than sixty solved examples and more than 140 exercises

Presenting synergistic coverage of both probabilistic and deterministic risk assessment techniques for nuclear systems, this text is invaluable for advanced undergraduate students in nuclear engineering, first-year graduate students, and practicing engineers in the area of risk and reliability assessment, particularly those in the nuclear industry.

Preface xii

Permissions and Copyrights xiv

List of Tables xvi

List of Figures xviii

1 Risk and Safety of Engineered Systems 1

1.1 Risk and Its Perception and Acceptance 1

1.2 Overview of Risk and Safety Analysis 6

1.3 Two Historical Reactor Accidents 8

1.4 Definition of Risk 9

1.5 Reliability, Availability, Maintainability, and Safety 10

1.6 Organization of the Book 12

References 13

2 Probabilities of Events 15

2.1 Events 15

2.2 Event Tree Analysis and Minimal Cut Sets 17

2.3 Probabilities 19

2.3.1 Interpretations of Probability 19

2.3.2 Axiomatic Approach to Probabilities 20

2.3.3 Intersection of Events 21

2.3.4 Union of Events 22

2.3.5 Decomposition Rule for Probabilities 25

2.4 TimeIndependent Versus TimeDependent Probabilities 25

2.5 TimeIndependent Probabilities 26

2.5.1 Introduction 26

2.5.2 TimeIndependent Probability Distributions 27

2.6 Normal Distribution 31

2.7 Reliability Functions 35

2.8 TimeDependent Probability Distributions 41

2.8.1 Erlangian and Exponential Distributions 42

2.8.2 Gamma Distribution 43

2.8.3 Lognormal Distribution 44

2.8.4 Weibull Distribution 46

2.8.5 Generalized Bathtub Distribution 47

2.8.6 Selection of a TimeDependent Probability Distribution 48

2.9 ExtremeValue Probability Distributions 50

2.10 Probability Models for Failure Analyses 52

References 53

Exercises 53

3 Reliability Data 59

3.1 Estimation Theory 59

3.1.1 Moment Estimators 60

3.1.2 Maximum Likelihood Estimators 61

3.1.3 Maximum Entropy Estimators 64

3.1.4 Comparison of Estimators 65

3.2 Bayesian Updating of Data 65

3.2.1 Bayes Equation 65

3.2.2 Applications of the Bayes Equation 67

3.3 Central Limit Theorem and Hypothesis Testing 70

3.3.1 Interpretation of the Central Limit Theorem 71

3.3.2 Hypothesis Testing with the Central Limit Theorem 72

3.4 Reliability Quantification 74

3.4.1 Central Limit Theorem for Reliability Quantification 74

3.4.2 Engineering Approach for Reliability Quantification 76

3.4.3 ­2Distribution for Reliability Quantification 77

3.4.4 ThreeWay Comparison and Concluding Remarks 78

References 80

Exercises 80

4 Reliability of MultipleComponent Systems 85

4.1 Series and ActiveParallel Systems 86

4.1.1 Systems with Independent Components 86

4.1.2 Systems with Redundant Components 88

4.1.3 FailtoSafety and FailtoDanger Systems 90

4.2 Systems with Standby Components 93

4.3 Decomposition Analysis 96

4.4 Signal Flow Graph Analysis 100

4.5 Cut Set Analysis 101

References 104

Exercises 104

5 Availability and Reliability of Systems with Repair 109

5.1 Introduction 109

5.2 Markov Method 111

5.2.1 Markov Governing Equations 111

5.2.2 Solution of Markov Governing Equations 113

5.2.3 An Elementary Example 116

5.3 Availability Analyses 118

5.3.1 Rules for Constructing Transition Rate Matrices 118

5.3.2 Availabili…