Ajit Reliability and Safety Engineering

1. Auflage 2010
ISBN: 978-1-84996-232-2
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 557 Seiten

Reliability and safety are core issues that must be addressed throughout the life cycle of engineering systems. Reliability and Safety Engineering presents an overview of the basic concepts, together with simple and practical illustrations. The authors present reliability terminology in various engineering fields, viz., • electronics engineering, • software engineering, • mechanical engineering, • structural engineering, and • power systems engineering. They describe the latest applications in the area of probabilistic safety assessment, such as technical specification optimization, risk monitoring and risk informed in-service inspection. Reliability and safety studies must, inevitably, deal with uncertainty, so the book includes uncertainty propagation methods: Monte Carlo simulation, fuzzy arithmetic, Dempster-Shafer theory and probability bounds. Reliability and Safety Engineering also highlights advances in system reliability and safety assessment including dynamic system modeling and uncertainty management. Case studies from typical nuclear power plants, as well as from structural, software, and electronic systems are also discussed. Reliability and Safety Engineering combines discussions of the existing literature on basic concepts and applications with state-of-the-art methods used in reliability and risk assessment of engineering systems. It is designed to assist practicing engineers, students and researchers in the areas of reliability engineering and risk analysis.

Prof. Ajit Kumar Verma is Director of the International Institute of Information Technology Pune, India.  He is also a professor in the Department of Electrical Engineering at Indian Institute of Technology Bombay with a research focus on reliability engineering and quality management.  He has over 180 papers in journals and in conference proceedings. He is the editor-in-chief of OPSEARCH (published by Springer) and of the International Journal of Systems Assurance Engineering and Management (also published by Springer). He is on the editorial board of various international journals. He has been a guest editor of IJRQSE, IJPE, CDQM, IJAC, etc., and has supervised 23 PhDs. His area of research is reliability and maintainability engineering. Prof. Srividya Ajit received her BE degree in 1982, her MTech in Reliability Engineering in 1985 and her PhD in 1994, from IIT Bombay. She has been with IIT Bombay since 1988 and is currently a professor in the Department of Civil Engineering at IIT Bombay with a research focus on reliability in engineering design, structural reliability and environmental effects on system reliability. Over 50 of her papers have been published in various national and international journals, and over 100 have been part of national or international conferences. She has also co-authored a book entitled Fuzzy Reliability Engineering: Concepts and Applications. She was conference chairperson of the International Conference on Reliability, Safety & Hazard 2005 (Advances in Risk Informed Technology), for which she also edited the proceedings; the International Conference on Quality, Reliability and Infocom 2006; and the International Conference on Reliability, Safety and Quality Engineering 2008 (for which she also edited the proceedings). She has been instrumental in editing and reviewing the proceedings of various international conferences, such as the International Conference on Quality Reliability and Control 2001, the International Conference on Multimedia and Design 2002, and the International Conference on Quality Reliability and Information Technology 2003. She is a recipient of SREQOM’s Leadership in Reliability Engineering Education & Research award. Dr. Durga Rao Karanki is presently working as a scientist at the Paul Scherrer Institute, Switzerland. He graduated in Electrical and Electronics Engineering from the Nagarjuna University, India, and holds MTech (Reliability Engineering) and PhD (Engg.) degrees from the Indian Institute of Technology Kharagpur and Bombay respectively. He also completed an OCEP course in Nuclear Science and Engineering at the Bhabha Atomic Research Centre (BARC), India. He was with BARC as a scientist in the Reactor Safety Division during 2002-2008. He was also a visiting faculty member at the training school for the Department of Atomic Energy, India. He has been actively involved in probabilistic safety assessment (PSA) of nuclear reactors, and risk informed decision-making and its implementation in chemical and nuclear facilities. His research interests are uncertainty management in PSA, accident dynamics for integrated safety analysis, and application of Monte Carlo simulation and genetic algorithms in reliability/risk management. He has published several research papers in leading international journals and conferences, as well as being an organizing committee member of reliability and safety conferences: ICRESH 2005, ICQRIT 2006, ICRSQE 2008, and ICQRIT 2009. He is a member of the editorial board of IJSAEM. He is a recipient of SREQOM’s researcher award for his contribution to uncertainty management in PSA of NPPs.

Autoren/Hrsg.

Ajit, Srividya

Inhaltsverzeichnis

1;Foreword;7
2;Preface;8
3;Acknowledgments;10
4;Contents;11
5;1 Introduction;18
5.1;1.1 Need for Reliability and Safety Engineering;18
5.2;1.2 Failures Inevitable;19
5.3;1.3 Improving Reliability and Safety;21
5.4;1.4 Definitions and Explanation of Some Relevant Terms;21
5.4.1;1.4.1 Quality;21
5.4.2;1.4.2 Reliability;22
5.4.3;1.4.3 Maintainability;22
5.4.3.1;1.4.3.1 Corrective Maintenance;23
5.4.3.2;1.4.3.2 Preventive Maintenance;23
5.4.3.3;1.4.3.3 Predictive Maintenance;23
5.4.4;1.4.4 Availability;23
5.4.5;1.4.5 Safety/Risk;24
5.4.6;1.4.6 Probabilistic Risk Assessment/Probabilistic Safety Assessment;24
5.5;1.5 Resources;24
5.6;1.6 History;26
5.7;1.7 Present Challenges and Future Needs for the Practice of Reliability and Safety Engineering;28
5.8;References;29
6;2 Basic Reliability Mathematics;31
6.1;2.1 Classical Set Theory and Boolean Algebra;31
6.1.1;2.1.1 Operations on Sets;32
6.1.2;2.1.2 Laws of Set Theory;33
6.1.3;2.1.3 Boolean Algebra;33
6.2;2.2 Concepts of Probability Theory;35
6.2.1;2.2.1 Axioms of Probability;36
6.2.2;2.2.2 Calculus of Probability Theory;36
6.2.2.1;2.2.2.1 Independent Events and Mutually Exclusive Events;36
6.2.2.2;2.2.2.2 Conditional Probability;37
6.2.2.3;2.2.2.3 Probability for Intersection of Events;37
6.2.2.4;2.2.2.4 Probability for Union of Events;38
6.2.2.5;2.2.2.5 Total Probability Theorem;39
6.2.2.6;2.2.2.6 Bayes’ Theorem;39
6.2.3;2.2.3 Random Variables and Probability Distributions;40
6.2.3.1;2.2.3.1 Discrete Probability Distribution;41
6.2.3.2;2.2.3.2 Continuous Probability Distributions;42
6.2.3.3;2.2.3.3 Characteristics of Random Variables;43
6.3;2.3 Reliability and Hazard Functions;44
6.4;2.4 Distributions Used in Reliability and Safety Studies;47
6.4.1;2.4.1 Discrete Probability Distributions;47
6.4.1.1;2.4.1.1 Binomial Distribution;47
6.4.1.2;2.4.1.2 Poisson Distribution;50
6.4.1.3;2.4.1.3 Hypergeometric Distribution;51
6.4.1.4;2.4.1.4 Geometric Distribution;52
6.4.2;2.4.2 Continuous Probability Distributions;53
6.4.2.1;2.4.2.1 Exponential Distribution;53
6.4.2.2;2.4.2.2 Normal Distribution;56
6.4.2.3;2.4.2.3 Lognormal Distribution;60
6.4.2.4;2.4.2.4 Weibull Distribution;62
6.4.2.5;2.4.2.5 Gamma Distribution;65
6.4.2.6;2.4.2.6 Erlangian Distribution;67
6.4.2.7;2.4.2.7 Chi-square Distribution;68
6.4.2.8;2.4.2.8 F-distribution;69
6.4.2.9;2.4.2.9 t-distribution;70
6.4.3;2.4.3 Summary;72
6.5;2.5 Failure Data Analysis;72
6.5.1;2.5.1 Nonparametric Methods;72
6.5.2;2.5.2 Parametric Methods;77
6.5.2.1;2.5.2.1 Identifying Candidate Distributions;77
6.5.2.2;2.5.2.2 Estimating the Parameters of Distribution;81
6.5.2.3;2.5.2.3 Goodness-of-fit Tests;84
6.6;Exercise Problems;85
6.7;References;86
7;3 System Reliability Modeling;87
7.1;3.1 Reliability Block Diagram;87
7.1.1;3.1.1 Procedure for System Reliability Prediction Using Reliability Block Diagram;87
7.1.1.1;3.1.1.1 Important Points to be Considered while Constructing RBDs;89
7.1.2;3.1.2 Different Types of Models;90
7.1.2.1;3.1.2.1 Series Model;91
7.1.2.2;3.1.2.2 Parallel Model;91
7.1.2.3;3.1.2.3 M-out-of-N Models (Identical Items);94
7.1.2.4;3.1.2.4 Standby Redundancy Models;96
7.1.3;3.1.3 Solving the Reliability Block Diagram;100
7.1.3.1;3.1.3.1 Truth Table Method;100
7.1.3.2;3.1.3.2 Cut-set and Tie-set Method;101
7.1.3.3;3.1.3.3 Bounds Method;104
7.2;3.2 Markov Models;105
7.2.1;3.2.1 State Space Method – Principles;105
7.2.1.1;3.2.1.1 Steps;106
7.2.1.2;3.2.1.2 Basic Analysis;106
7.2.1.3;3.2.1.3 State Frequencies and Durations;111
7.2.1.4;3.2.1.4 Two-component System with Repair;112
7.2.2;3.2.2 Safety Modeling;116
7.2.2.1;3.2.2.1 Imperfect Coverage – Two-component Parallel System;118
7.2.2.2;3.2.2.2 Modeling of Fault-tolerant Systems;123
7.3;3.3 Fault Tree Analysis;125
7.3.1;3.3.1 Procedure for Carrying out Fault Tree Analysis;126
7.3.1.1;3.3.1.1 System Awareness and Details;126
7.3.1.2;3.3.1.2 Defining Objectives, Top Event, and Scope of Fault Tree Analysis;126
7.3.1.3;3.3.1.3 Construction of the Fault Tree;127
7.3.1.4;3.3.1.4 Qualitative Evaluation of the Fault Tree;127
7.3.1.5;3.3.1.5 Data Assessment and Parameter Estimation;127
7.3.1.6;3.3.1.6 Quantitative Evaluation of the Fault Tree;128
7.3.1.7;3.3.1.7 Interpretation and Presentation of the Results;128
7.3.1.8;3.3.1.8 Important Points to Be Considered while Constructing Fault Trees;128
7.3.2;3.3.2 Elements of Fault Tree;130
7.3.3;3.3.3 Evaluation of Fault Tree;133
7.3.3.1;3.3.3.1 AND Gate;133
7.3.3.2;3.3.3.2 OR Gate;135
7.3.4;3.3.4 Case Study;137
7.3.4.1;3.3.4.1 Step 1 – Defining Top Event;137
7.3.4.2;3.3.4.2 Step 2 – Construction of the Fault Tree;137
7.3.4.3;3.3.4.3 Step 3 – Qualitative Evaluation;138
7.3.4.4;3.3.4.4 Step 4 – Quantitative Evaluation;140
7.4;3.4 Monte Carlo Simulation;142
7.4.1;3.4.1 Analytical versus Simulation Approaches for System Reliability Modeling;142
7.4.1.1;3.4.1.2 Benefits/Applications of Simulation-based Reliability Evaluation;144
7.4.2;3.4.2 Elements of Monte Carlo Simulation;144
7.4.3;3.4.3 Repairable Series and Parallel Systems;146
7.4.3.1;3.4.3.1 Reliability Evaluation with Analytical Approach;148
7.4.4;3.4.4 Simulation Procedure for Complex Systems;151
7.4.4.1;3.4.4.1 Case Study – AC Power Supply System of Indian Nuclear Power Plant;152
7.4.5;3.4.5 Increasing Efficiency of Simulation;159
7.4.5.1;3.4.5.1 Importance Sampling;160
7.4.5.2;3.4.5.2 Latin Hypercube Sampling;161
7.5;3.5 Dynamic Reliability Analysis;162
7.5.1;3.5.1 Dynamic Fault Tree Gates;162
7.5.1.1;3.5.1.1 PAND Gate;163
7.5.1.2;3.5.1.2 SEQ Gate;164
7.5.1.3;3.5.1.3 SPARE Gate;164
7.5.1.4;3.5.1.4 FDEP Gate;165
7.5.2;3.5.2 Modular Solution for Dynamic Fault Trees;167
7.5.3;3.5.3 Numerical Method;168
7.5.3.1;3.5.3.1 PAND Gate;168
7.5.3.2;3.5.3.2 SEQ Gate;169
7.5.3.3;3.5.3.3 SPARE Gate;170
7.5.4;3.5.4 Monte Carlo Simulation;170
7.5.4.1;3.5.4.1 PAND Gate;170
7.5.4.2;3.6.4.2 SPARE Gate;171
7.5.4.3;3.5.4.3 FDEP Gate;172
7.5.4.4;3.5.4.4 SEQ Gate;173
7.5.4.5;3.5.4.5 Case Study 1 – Simplified Electrical (AC) Power Supply System of Nuclear Power Plant;174
7.5.4.6;3.5.4.6 Case Study 2 – Reactor Regulation System of Nuclear Power Plant;179
7.6;Exercise Problems;182
7.7;References;183
8;4 Electronic System Reliability;185
8.1;4.1 Importance of Electronic Industry;185
8.2;4.2 Various Components Used and Their Failure Mechanisms;186
8.2.1;4.2.1 Resistors;186
8.2.2;4.2.2 Capacitors;187
8.2.3;4.2.3 Inductors;187
8.2.4;4.2.4 Relays;187
8.2.5;4.2.5 Semiconductor Devices;188
8.2.6;4.2.6 Integrated Circuits;188
8.3;4.3 Reliability Prediction of Electronic Systems;190
8.3.1;4.3.1 Part-count Method;190
8.3.2;4.3.2 Part-stress Method;191
8.4;4.4 PRISM;192
8.5;4.5 Sneak Circuit Analysis;193
8.5.1;4.5.1 Definition;194
8.5.2;4.5.2 Network Tree Production;194
8.5.3;4.5.3 Topological Pattern Identification;195
8.6;4.6 Case Study;195
8.6.1;4.6.1 Total Failure Rate;198
8.7;4.7 Physics of Failure Mechanisms of Electronic Components;198
8.7.1;4.7.1 Physics of Failures;198
8.7.2;4.7.2 Failure Mechanisms for Resistors;199
8.7.2.1;4.7.2.1 Failure Due to Excessive Heating;199
8.7.2.2;4.7.2.2 Failure Due to Metal Diffusion and Oxidation;200
8.7.3;4.7.3 Failure Mechanisms for Capacitors;200
8.7.3.1;4.7.3.1 Dielectric Breakdown;200
8.7.4;4.7.4 Failure Mechanisms for Metal Oxide Semiconductors;201
8.7.4.1;4.7.4.1 Electromigration;201
8.7.4.2;4.7.4.2 Time-dependent Dielectric Breakdown;202
8.7.4.3;4.7.4.3 Hot-carrier Injection;204
8.7.4.4;4.7.4.4 Negative Bias Temperature Instability;204
8.7.5;4.7.5 Field Programmable Gate Array;205
8.7.5.1;4.7.5.1 Hierarchical Model;205
8.7.5.2;4.7.5.2 Optimal Model;206
8.7.5.3;4.7.5.3 Coarse Model;206
8.7.5.4;4.7.5.4 Tile-based Model;206
8.8;References;207
9;5 Software Reliability;208
9.1;5.1 Introduction to Software Reliability;208
9.2;5.2 Past Incidences of Software Failures in Safety Critical Systems;209
9.2.1;5.2.1 Therac-25 Failure;210
9.2.2;5.2.2 Ariane 5 Failure;211
9.2.3;5.2.3 Patriot Failure;211
9.3;5.3 The Need for Reliable Software;212
9.4;5.4 Difference Between Hardware Reliability and Software Reliability;213
9.5;5.5 Software Reliability Modeling;216
9.5.1;5.5.1 Software Reliability Growth Models;216
9.5.2;5.5.2 Black-box Software Reliability Models;216
9.5.3;5.5.3 White-box Software Reliability Models;217
9.6;5.6 How to Implement Software Reliability;218
9.6.1;5.6.1 Example – Operational Profile Model;219
9.6.2;5.6.2 Case Study;220
9.6.2.1;5.6.2.1 Step 1 – Determine All Possible Modules, Submodules and Scenarios;220
9.6.2.2;5.6.2.2 Step 2 – Create n × n Matrix;220
9.6.2.3;5.6.2.3 Step 3 – Add the Possible Scenarios from n × n Matrix to the List of Scenarios;221
9.6.2.4;5.6.2.4 Step 4 – Assign Probability of Modules;222
9.6.2.5;5.6.2.5 Step 5 – Assign Probability of Submodules;222
9.6.2.6;5.6.2.6 Step 6 – Assign Probability of Scenarios;223
9.6.2.7;5.6.2.7 Step 7 – Generate Random Numbers;224
9.6.3;5.6.3 Benefits;224
9.7;5.7 Emerging Techniques in Software Reliability Modeling – Soft Computing Technique;225
9.7.1;5.7.1 Need for Soft Computing Methods;226
9.7.2;5.7.2 Environmental Parameters;227
9.7.2.1;5.7.2.1 Defect Rating;227
9.7.2.2;5.7.2.2 Project Risk Index;230
9.7.2.3;5.7.2.3 Process Compliance Index;231
9.7.2.4;5.7.2.4 Group Maturity Rating;232
9.7.3;5.7.3 Anil–Verma Model;235
9.7.3.1;5.7.3.1 Results Obtained from Anil–Verma Model;235
9.7.3.2;5.7.3.2 Implementation Guidelines for Anil–Verma Model;240
9.8;5.8 Future Trends of Software Reliability;242
9.9;References;242
10;6 Mechanical Reliability;244
10.1;6.1 Reliability versus Durability;245
10.2;6.2 Failure Modes in Mechanical Systems;247
10.2.1;6.2.1 Failures Due to Operating Load;247
10.2.2;6.2.2 Failures Due to Environment;251
10.2.3;6.2.3 Failures Due to Poor Manufacturing Quality;251
10.3;6.3 Reliability Circle;251
10.3.1;6.3.1 Specify Reliability;253
10.3.1.1;6.3.1.1 Quality Function Deployment – Capturing the Voice of the Customer;253
10.3.1.2;6.3.1.2 Reliability Measures;254
10.3.1.3;6.3.1.3 Environment and Usage;255
10.3.1.4;6.3.1.4 Reliability Apportionment;255
10.3.2;6.3.2 Design for Reliability;256
10.3.2.1;6.3.2.1 Reliability Analysis and Prediction;258
10.3.2.2;6.3.2.2 Stress-Strength Interference Theory;267
10.3.3;6.3.3 Test for Reliability;270
10.3.3.1;6.3.3.1 Reliability Test Objectives;270
10.3.3.2;6.3.3.2 Types of Testing;271
10.3.3.3;6.3.3.3 Reliability Test Program;271
10.3.3.4;6.3.3.4 Degradation Data Analysis;275
10.3.4;6.3.4 Maintain Manufacturing Reliability;276
10.3.4.1;6.3.4.1 Process Control Methods;276
10.3.4.2;6.3.4.2 Online Quality Control;277
10.3.5;6.3.5 Operational Reliability;278
10.3.5.1;6.3.5.1 Weibull Analysis;278
10.4;References;281
11;7 Structural Reliability;282
11.1;7.1 Deterministic versus Probabilistic Approach in Structural Engineering;282
11.2;7.2 The Basic Reliability Problem;283
11.2.1;7.2.1 First-order Second-moment Method;284
11.2.2;7.2.2 Advanced First-order Second-moment Method;288
11.3;7.3 First-order Reliability Method;289
11.4;7.4 Reliability Analysis for Correlated Variables;294
11.4.1;7.4.1 Reliability Analysis for Correlated Normal Variables;294
11.4.2;7.4.2 Reliability Analysis for Correlated Non-normal Variables;295
11.4.2.1;7.4.2.1 Rosenblatt Transformation;295
11.4.2.2;7.4.2.2 Nataf Transformation;296
11.5;7.5 Second-order Reliability Methods;296
11.6;7.6 System Reliability;307
11.6.1;7.6.1 Classification of Systems;307
11.6.1.1;7.6.1.1 Series System;308
11.6.1.2;7.6.1.2 Parallel System;308
11.6.1.3;7.6.1.3 Combined Series–Parallel Systems;309
11.6.2;7.6.2 Evaluation of System Reliability;310
11.6.2.1;7.6.2.1 Numerical Integration;310
11.6.2.2;7.6.2.2 Bounding Techniques;311
11.6.2.3;7.6.2.3 Approximate Methods;311
11.7;References;317
12;8 Power System Reliability;319
12.1;8.1 Introduction;319
12.2;8.2 Basics of Power System Reliability;321
12.2.1;8.2.1 Functional Zones and Hierarchical Levels;321
12.2.2;8.2.2 Adequacy Evaluation in Hierarchical Level I Studies;322
12.2.2.1;8.2.2.1 Construction of Capacity Outage Probability Table;323
12.2.2.2;8.2.2.2 Loss of Load Probability and Expected Energy Not Supplied;323
12.2.3;8.2.3 Adequacy Evaluation in Hierarchical Level II Studies;327
12.2.3.1;8.2.3.1 Basic Adequacy Indices;329
12.2.3.2;8.2.3.2 IEEE Proposed Adequacy Indices;330
12.2.4;8.2.4 Distribution System Reliability;331
12.3;8.3 Reliability Test Systems;333
12.4;8.4 Advances in Power System Reliability – Power System Reliability in the Deregulated Scenario;334
12.5;References;335
13;9 Probabilistic Safety Assessment;336
13.1;9.1 Introduction;336
13.2;9.2 Concept of Risk and Safety;337
13.3;9.3 Probabilistic Safety Assessment Procedure;339
13.4;9.4 Identification of Hazards and Initiating Events;342
13.4.1;9.4.1 Preliminary Hazard Analysis;342
13.4.2;9.4.2 Master Logic Diagram;342
13.5;9.5 Event Tree Analysis;343
13.5.1;9.5.1 Procedure for Event Tree Analysis;343
13.6;9.6 Importance Measures;350
13.6.1;9.6.1 Birnbaum Importance;351
13.6.2;9.6.2 Inspection Importance;352
13.6.3;9.6.3 Fussell–Vesely Importance;352
13.7;9.7 Common-cause Failure Analysis;355
13.7.1;9.7.1 Treatment of Dependent Failures;355
13.7.1.1;9.7.1.1 Functional Dependences;356
13.7.1.2;9.7.1.2 Physical Dependences;356
13.7.1.3;9.7.1.3 Human Interaction Dependence;357
13.7.1.4;9.7.1.4 Defense Against Common-cause Failure;357
13.7.2;9.7.2 Procedural Framework for Common-cause Failure Analysis;358
13.7.3;9.7.3 Treatment of Common-cause Failures in Fault Tree Models;358
13.7.4;9.7.4 Common-cause Failure Models;363
13.7.4.1;9.7.4.1 Non-shock Models;363
13.7.4.2;9.7.4.2 Shock Models;370
13.8;9.8 Human Reliability Analysis;374
13.8.1;9.8.1 Human Behavior and Errors;374
13.8.2;9.8.2 Categorization of Human Interactions in Probabilistic Safety Assessment;376
13.8.2.1;9.8.2.1 Category A: Pre-initiators;376
13.8.2.2;9.8.2.2 Category B: Initiators;376
13.8.2.3;9.8.2.3 Category C: Post-initiators;376
13.8.3;9.8.3 Steps in Human Reliability Analysis;377
13.8.3.1;9.8.3.1 Definition;377
13.8.3.2;9.8.3.2 Screening;378
13.8.3.3;9.8.3.3 Qualitative Analysis;378
13.8.3.4;9.8.3.4 Representation and Model Integration;378
13.8.3.5;9.8.3.5 Quantification;381
13.9;References;381
14;10 Applications of Probabilistic Safety Assessment;383
14.1;10.1 Objectives of Probabilistic Safety Assessment;383
14.2;10.2 Probabilistic Safety Assessment of Nuclear Power Plants;384
14.2.1;10.2.1 Description of Pressurized Heavy-water Reactors;384
14.2.1.1;10.2.1.1 Reactor Process System;385
14.2.1.2;10.2.1.2 Reactor Protection System;385
14.2.1.3;10.2.1.3 Electrical Power System;386
14.2.2;10.2.2 Probabilistic Safety Assessment of Indian Nuclear Power Plants (Pressurized Heavy-water Reactor Design);386
14.2.2.1;10.2.2.1 Dominating Initiating Events;387
14.2.2.2;10.2.2.2 Reliability Analysis;392
14.2.2.3;10.2.2.3 Accident Sequence Identification;394
14.2.2.4;10.2.2.4 Event Trees;396
14.2.2.5;10.2.2.5 Dominating Accident Sequences;399
14.2.2.6;10.2.2.6 Risk Importance Measures;400
14.3;10.3 Technical Specification Optimization;401
14.3.1;10.3.1 Traditional Approaches for Technical Specification Optimization;402
14.3.1.1;10.3.1.1 Measures Applicable for Allowed Outage Time Evaluations;402
14.3.1.2;10.3.1.2 Measures Applicable for Surveillance Test Interval Evaluations;405
14.3.2;10.3.2 Advanced Techniques for Technical Specification Optimization;405
14.3.2.1;10.3.2.1 Mathematical Modeling of Problem;406
14.3.2.2;10.3.2.2 Genetic Algorithm as Optimization Method;407
14.3.2.3;10.3.2.3 Case Studies: Test Interval Optimization for Emergency Core Cooling System of Pressurized Heavy-water Reactor;409
14.4;10.4 Risk Monitor;412
14.4.1;10.4.1 Necessity of Risk Monitor?;413
14.4.2;10.4.2 Different Modules of Risk Monitor;413
14.4.3;10.4.3 Applications of Risk Monitor;414
14.4.3.1;10.4.3.1 Decision-making in Operations;415
14.4.3.2;10.4.3.2 Maintenance Strategies;416
14.4.3.3;10.4.3.3 Risk-based In-Service Inspection;416
14.4.3.4;10.4.3.4 Incident Severity Assessment;417
14.4.3.5;10.4.3.5 Review of Technical Specification;417
14.4.3.6;10.4.3.6 Emergency Operating Procedures and Risk Management;417
14.5;10.5 Risk-informed In-service Inspection;417
14.5.1;10.5.1 Risk-informed In-service Inspection Models;418
14.5.1.1;10.5.1.1 American Society of Mechanical Engineers/Westinghouse Owners Group Model;418
14.5.1.2;10.5.1.2 Electric Power Research Institute Model;421
14.5.1.3;10.5.1.3 Comparison of Risk-informed In-service Inspection Models;424
14.5.2;10.5.2 In-service Inspection and Piping Failure Frequency;426
14.5.2.1;10.5.2.1 In-service Inspection;426
14.5.2.2;10.5.2.2 Models for Including In-service Inspection Effect on Piping Failure Frequency;427
14.5.3;10.5.3 Case Study;435
14.5.3.1;10.5.3.1 Assumptions;435
14.5.3.2;10.5.3.2 Consequence Analysis of Feeder Failure;436
14.5.3.3;10.5.3.3 Using the Three-state Markov Model;437
14.5.3.4;10.5.3.4 Using the Four-state Markov Model;441
14.5.4;10.5.4 Remarks on Risk-informed In-service Inspection;444
14.6;References;445
15;11 Uncertainty Managementin Reliability/Safety Assessment;447
15.1;11.1 Mathematical Models and Uncertainties;447
15.1.1;11.1.1 Example for Understanding of Epistemic and Aleatory Uncertainties;449
15.2;11.2 Uncertainty Analysis: an Important Task of Probabilistic Risk/Safety Assessment;450
15.3;11.3 Methods of Characterizing Uncertainties;452
15.3.1;11.3.1 The Probabilistic Approach;452
15.3.2;11.3.2 Interval and Fuzzy Representation;452
15.3.2.1;11.3.2.1 Interval Representation;452
15.3.2.2;11.3.2.2 Fuzzy Representation;453
15.3.3;11.3.3 Dempster–Shafer-theory-based Representation;453
15.3.3.1;11.3.3.1 Frame of Discernment – X or O;454
15.3.3.2;11.3.3.2 Basic Belief Assignment;454
15.3.3.3;11.3.3.3 Belief and Plausibility Functions;456
15.4;11.4 Uncertainty Propagation;457
15.4.1;11.4.1 Method of Moments;458
15.4.1.1;11.4.1.1 Approximation from the Taylor Series;458
15.4.1.2;11.4.1.2 Consideration of Correlation Using Method of Moments;460
15.4.2;11.4.2 Monte Carlo Simulation;463
15.4.2.1;11.4.2.1 Crude Monte Carlo Sampling;464
15.4.2.2;11.4.2.2 Latin Hypercube Sampling;466
15.4.3;11.4.3 Interval Arithmetic;467
15.4.4;11.4.4 Fuzzy Arithmetic;469
15.4.4.1;11.4.4.1 Probability to Possibility Transformations;471
15.5;11.5 Uncertainty Importance Measures;471
15.5.1;11.5.1 Probabilistic Approach to Ranking Uncertain Parameters in System Reliability Models;472
15.5.1.1;11.5.1.1 Correlation Coefficient Method;473
15.5.1.2;11.5.1.2 Variance-based Method;473
15.5.2;11.5.2 Method Based on Fuzzy Set Theory;474
15.5.3;11.5.3 Application to a Practical System;477
15.6;11.6 Treatment of Aleatory and Epistemic Uncertainties;481
15.6.1;11.6.1 Epistemic and Aleatory Uncertainty in Reliability Calculations;481
15.6.2;11.6.2 Need to Separate Epistemic and Aleatory Uncertainties;483
15.6.3;11.6.3 Methodology for Uncertainty Analysis in Reliability Assessment Based on Monte Carlo Simulation;484
15.6.3.1;11.6.3.1 Methodology;486
15.7;11.7 Dempster–Shafer Theory;488
15.7.1;11.7.1 Belief and Plausibility Function of Real Numbers;490
15.7.2;11.7.2 Dempster’s Rule of Combination;491
15.7.3;11.7.3 Sampling Technique for the Evidence Theory;493
15.8;11.8 Probability Bounds Approach;497
15.8.1;11.8.1 Computing with Probability Bounds;497
15.8.1.1;11.8.1.1 Basic Calculations for Construction of P-box;500
15.8.2;11.8.2 Two-phase Monte Carlo Simulation;504
15.8.3;11.8.3 Uncertainty Propagation Considering Correlation Between Variables;506
15.9;11.9 Bayesian Approach;507
15.9.1;11.9.1 Bayes’ Theorem;508
15.9.2;11.9.2 Identification of Parameter;509
15.9.3;11.9.3 Development of Prior Distribution;509
15.9.4;11.9.4 Construction of Likelihood Function;510
15.9.5;11.9.5 Derivation of Posterior Distribution;510
15.9.6;11.9.6 Characteristic Parameters of Posterior Distribution;510
15.9.7;11.9.7 Estimation of Parameters from Multiple Sources of Information;511
15.9.8;11.9.8 The Hierarchical Bayes Method;512
15.10;11.10 Expert Elicitation Methods;513
15.10.1;11.10.1 Definition and Uses of Expert Elicitation;513
15.10.2;11.10.2 Treatment of Expert Elicitation Process;514
15.10.3;11.10.3 Methods of Treatment;514
15.10.3.1;11.10.3.1 Indirect Elicitation Method;515
15.10.3.2;11.10.3.2 Direct Elicitation Methods;515
15.10.3.3;11.10.3.3 Geometric Averaging Technique;516
15.10.3.4;11.10.3.4 Percentiles for Combining Expert Opinions;517
15.11;11.11 Case Study to Compare Uncertainty Analysis Methods;518
15.11.1;11.11.1 Availability Assessment of Main Control Power Supply Using Fault Tree Analysis;519
15.11.2;11.11.2 Uncertainty Propagation in Main Control Power Supply with Different Methods;521
15.11.2.1;11.11.2.1 Interval Analysis;521
15.11.2.2;11.11.2.2 Fuzzy Arithmetic;521
15.11.2.3;11.11.2.3 Monte Carlo Simulation;523
15.11.2.4;11.11.2.4 Dempster–Shafer Theory;524
15.11.2.5;11.11.2.5 Probability Bounds Analysis;525
15.11.3;11.11.3 Observations from Case Study;527
15.11.3.1;11.11.3.1 Remarks;527
15.12;Exercise Problems;528
15.13;References;531
16;Appendix: Distribution Tables;535
17;Index;543