Reliability and Safety Engineering (eBook)

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.

Foreword 7
Preface 8
Acknowledgments 10
Contents 11
1 Introduction 18
1.1 Need for Reliability and Safety Engineering 18
1.2 Failures Inevitable 19
1.3 Improving Reliability and Safety 21
1.4 Definitions and Explanation of Some Relevant Terms 21
1.4.1 Quality 21
1.4.2 Reliability 22
1.4.3 Maintainability 22
1.4.3.1 Corrective Maintenance 23
1.4.3.2 Preventive Maintenance 23
1.4.3.3 Predictive Maintenance 23
1.4.4 Availability 23
1.4.5 Safety/Risk 24
1.4.6 Probabilistic Risk Assessment/Probabilistic Safety Assessment 24
1.5 Resources 24
1.6 History 26
1.7 Present Challenges and Future Needs for the Practice of Reliability and Safety Engineering 28
References 29
2 Basic Reliability Mathematics 31
2.1 Classical Set Theory and Boolean Algebra 31
2.1.1 Operations on Sets 32
2.1.2 Laws of Set Theory 33
2.1.3 Boolean Algebra 33
2.2 Concepts of Probability Theory 35
2.2.1 Axioms of Probability 36
2.2.2 Calculus of Probability Theory 36
2.2.2.1 Independent Events and Mutually Exclusive Events 36
2.2.2.2 Conditional Probability 37
2.2.2.3 Probability for Intersection of Events 37
2.2.2.4 Probability for Union of Events 38
2.2.2.5 Total Probability Theorem 39
2.2.2.6 Bayes’ Theorem 39
2.2.3 Random Variables and Probability Distributions 40
2.2.3.1 Discrete Probability Distribution 41
2.2.3.2 Continuous Probability Distributions 42
2.2.3.3 Characteristics of Random Variables 43
2.3 Reliability and Hazard Functions 44
2.4 Distributions Used in Reliability and Safety Studies 47
2.4.1 Discrete Probability Distributions 47
2.4.1.1 Binomial Distribution 47
2.4.1.2 Poisson Distribution 50
2.4.1.3 Hypergeometric Distribution 51
2.4.1.4 Geometric Distribution 52
2.4.2 Continuous Probability Distributions 53
2.4.2.1 Exponential Distribution 53
2.4.2.2 Normal Distribution 56
2.4.2.3 Lognormal Distribution 60
2.4.2.4 Weibull Distribution 62
2.4.2.5 Gamma Distribution 65
2.4.2.6 Erlangian Distribution 67
2.4.2.7 Chi-square Distribution 68
2.4.2.8 F-distribution 69
2.4.2.9 t-distribution 70
2.4.3 Summary 72
2.5 Failure Data Analysis 72
2.5.1 Nonparametric Methods 72
2.5.2 Parametric Methods 77
2.5.2.1 Identifying Candidate Distributions 77
2.5.2.2 Estimating the Parameters of Distribution 81
2.5.2.3 Goodness-of-fit Tests 84
Exercise Problems 85
References 86
3 System Reliability Modeling 87
3.1 Reliability Block Diagram 87
3.1.1 Procedure for System Reliability Prediction Using Reliability Block Diagram 87
3.1.1.1 Important Points to be Considered while Constructing RBDs 89
3.1.2 Different Types of Models 90
3.1.2.1 Series Model 91
3.1.2.2 Parallel Model 91
3.1.2.3 M-out-of-N Models (Identical Items) 94
3.1.2.4 Standby Redundancy Models 96
3.1.3 Solving the Reliability Block Diagram 100
3.1.3.1 Truth Table Method 100
3.1.3.2 Cut-set and Tie-set Method 101
3.1.3.3 Bounds Method 104
3.2 Markov Models 105
3.2.1 State Space Method – Principles 105
3.2.1.1 Steps 106
3.2.1.2 Basic Analysis 106
3.2.1.3 State Frequencies and Durations 111
3.2.1.4 Two-component System with Repair 112
3.2.2 Safety Modeling 116
3.2.2.1 Imperfect Coverage – Two-component Parallel System 118
3.2.2.2 Modeling of Fault-tolerant Systems 123
3.3 Fault Tree Analysis 125
3.3.1 Procedure for Carrying out Fault Tree Analysis 126
3.3.1.1 System Awareness and Details 126
3.3.1.2 Defining Objectives, Top Event, and Scope of Fault Tree Analysis 126
3.3.1.3 Construction of the Fault Tree 127
3.3.1.4 Qualitative Evaluation of the Fault Tree 127
3.3.1.5 Data Assessment and Parameter Estimation 127
3.3.1.6 Quantitative Evaluation of the Fault Tree 128
3.3.1.7 Interpretation and Presentation of the Results 128
3.3.1.8 Important Points to Be Considered while Constructing Fault Trees 128
3.3.2 Elements of Fault Tree 130
3.3.3 Evaluation of Fault Tree 133
3.3.3.1 AND Gate 133
3.3.3.2 OR Gate 135
3.3.4 Case Study 137
3.3.4.1 Step 1 – Defining Top Event 137
3.3.4.2 Step 2 – Construction of the Fault Tree 137
3.3.4.3 Step 3 – Qualitative Evaluation 138
3.3.4.4 Step 4 – Quantitative Evaluation 140
3.4 Monte Carlo Simulation 142
3.4.1 Analytical versus Simulation Approaches for System Reliability Modeling 142
3.4.1.2 Benefits/Applications of Simulation-based Reliability Evaluation 144
3.4.2 Elements of Monte Carlo Simulation 144
3.4.3 Repairable Series and Parallel Systems 146
3.4.3.1 Reliability Evaluation with Analytical Approach 148
3.4.4 Simulation Procedure for Complex Systems 151
3.4.4.1 Case Study – AC Power Supply System of Indian Nuclear Power Plant 152
3.4.5 Increasing Efficiency of Simulation 159
3.4.5.1 Importance Sampling 160
3.4.5.2 Latin Hypercube Sampling 161
3.5 Dynamic Reliability Analysis 162
3.5.1 Dynamic Fault Tree Gates 162
3.5.1.1 PAND Gate 163
3.5.1.2 SEQ Gate 164
3.5.1.3 SPARE Gate 164
3.5.1.4 FDEP Gate 165
3.5.2 Modular Solution for Dynamic Fault Trees 167
3.5.3 Numerical Method 168
3.5.3.1 PAND Gate 168
3.5.3.2 SEQ Gate 169
3.5.3.3 SPARE Gate 170
3.5.4 Monte Carlo Simulation 170
3.5.4.1 PAND Gate 170
3.6.4.2 SPARE Gate 171
3.5.4.3 FDEP Gate 172
3.5.4.4 SEQ Gate 173
3.5.4.5 Case Study 1 – Simplified Electrical (AC) Power Supply System of Nuclear Power Plant 174
3.5.4.6 Case Study 2 – Reactor Regulation System of Nuclear Power Plant 179
Exercise Problems 182
References 183
4 Electronic System Reliability 185
4.1 Importance of Electronic Industry 185
4.2 Various Components Used and Their Failure Mechanisms 186
4.2.1 Resistors 186
4.2.2 Capacitors 187
4.2.3 Inductors 187
4.2.4 Relays 187
4.2.5 Semiconductor Devices 188
4.2.6 Integrated Circuits 188
4.3 Reliability Prediction of Electronic Systems 190
4.3.1 Part-count Method 190
4.3.2 Part-stress Method 191
4.4 PRISM 192
4.5 Sneak Circuit Analysis 193
4.5.1 Definition 194
4.5.2 Network Tree Production 194
4.5.3 Topological Pattern Identification 195
4.6 Case Study 195
4.6.1 Total Failure Rate 198
4.7 Physics of Failure Mechanisms of Electronic Components 198
4.7.1 Physics of Failures 198
4.7.2 Failure Mechanisms for Resistors 199
4.7.2.1 Failure Due to Excessive Heating 199
4.7.2.2 Failure Due to Metal Diffusion and Oxidation 200
4.7.3 Failure Mechanisms for Capacitors 200
4.7.3.1 Dielectric Breakdown 200
4.7.4 Failure Mechanisms for Metal Oxide Semiconductors 201
4.7.4.1 Electromigration 201
4.7.4.2 Time-dependent Dielectric Breakdown 202
4.7.4.3 Hot-carrier Injection 204
4.7.4.4 Negative Bias Temperature Instability 204
4.7.5 Field Programmable Gate Array 205
4.7.5.1 Hierarchical Model 205
4.7.5.2 Optimal Model 206
4.7.5.3 Coarse Model 206
4.7.5.4 Tile-based Model 206
References 207
5 Software Reliability 208
5.1 Introduction to Software Reliability 208
5.2 Past Incidences of Software Failures in Safety Critical Systems 209
5.2.1 Therac-25 Failure 210
5.2.2 Ariane 5 Failure 211
5.2.3 Patriot Failure 211
5.3 The Need for Reliable Software 212
5.4 Difference Between Hardware Reliability and Software Reliability 213
5.5 Software Reliability Modeling 216
5.5.1 Software Reliability Growth Models 216
5.5.2 Black-box Software Reliability Models 216
5.5.3 White-box Software Reliability Models 217
5.6 How to Implement Software Reliability 218
5.6.1 Example – Operational Profile Model 219
5.6.2 Case Study 220
5.6.2.1 Step 1 – Determine All Possible Modules, Submodules and Scenarios 220
5.6.2.2 Step 2 – Create n × n Matrix 220
5.6.2.3 Step 3 – Add the Possible Scenarios from n × n Matrix to the List of Scenarios 221
5.6.2.4 Step 4 – Assign Probability of Modules 222
5.6.2.5 Step 5 – Assign Probability of Submodules 222
5.6.2.6 Step 6 – Assign Probability of Scenarios 223
5.6.2.7 Step 7 – Generate Random Numbers 224
5.6.3 Benefits 224
5.7 Emerging Techniques in Software Reliability Modeling – Soft Computing Technique 225
5.7.1 Need for Soft Computing Methods 226
5.7.2 Environmental Parameters 227
5.7.2.1 Defect Rating 227
5.7.2.2 Project Risk Index 230
5.7.2.3 Process Compliance Index 231
5.7.2.4 Group Maturity Rating 232
5.7.3 Anil–Verma Model 235
5.7.3.1 Results Obtained from Anil–Verma Model 235
5.7.3.2 Implementation Guidelines for Anil–Verma Model 240
5.8 Future Trends of Software Reliability 242
References 242
6 Mechanical Reliability 244
6.1 Reliability versus Durability 245
6.2 Failure Modes in Mechanical Systems 247
6.2.1 Failures Due to Operating Load 247
6.2.2 Failures Due to Environment 251
6.2.3 Failures Due to Poor Manufacturing Quality 251
6.3 Reliability Circle 251
6.3.1 Specify Reliability 253
6.3.1.1 Quality Function Deployment – Capturing the Voice of the Customer 253
6.3.1.2 Reliability Measures 254
6.3.1.3 Environment and Usage 255
6.3.1.4 Reliability Apportionment 255
6.3.2 Design for Reliability 256
6.3.2.1 Reliability Analysis and Prediction 258
6.3.2.2 Stress-Strength Interference Theory 267
6.3.3 Test for Reliability 270
6.3.3.1 Reliability Test Objectives 270
6.3.3.2 Types of Testing 271
6.3.3.3 Reliability Test Program 271
6.3.3.4 Degradation Data Analysis 275
6.3.4 Maintain Manufacturing Reliability 276
6.3.4.1 Process Control Methods 276
6.3.4.2 Online Quality Control 277
6.3.5 Operational Reliability 278
6.3.5.1 Weibull Analysis 278
References 281
7 Structural Reliability 282
7.1 Deterministic versus Probabilistic Approach in Structural Engineering 282
7.2 The Basic Reliability Problem 283
7.2.1 First-order Second-moment Method 284
7.2.2 Advanced First-order Second-moment Method 288
7.3 First-order Reliability Method 289
7.4 Reliability Analysis for Correlated Variables 294
7.4.1 Reliability Analysis for Correlated Normal Variables 294
7.4.2 Reliability Analysis for Correlated Non-normal Variables 295
7.4.2.1 Rosenblatt Transformation 295
7.4.2.2 Nataf Transformation 296
7.5 Second-order Reliability Methods 296
7.6 System Reliability 307
7.6.1 Classification of Systems 307
7.6.1.1 Series System 308
7.6.1.2 Parallel System 308
7.6.1.3 Combined Series–Parallel Systems 309
7.6.2 Evaluation of System Reliability 310
7.6.2.1 Numerical Integration 310
7.6.2.2 Bounding Techniques 311
7.6.2.3 Approximate Methods 311
References 317
8 Power System Reliability 319
8.1 Introduction 319
8.2 Basics of Power System Reliability 321
8.2.1 Functional Zones and Hierarchical Levels 321
8.2.2 Adequacy Evaluation in Hierarchical Level I Studies 322
8.2.2.1 Construction of Capacity Outage Probability Table 323
8.2.2.2 Loss of Load Probability and Expected Energy Not Supplied 323
8.2.3 Adequacy Evaluation in Hierarchical Level II Studies 327
8.2.3.1 Basic Adequacy Indices 329
8.2.3.2 IEEE Proposed Adequacy Indices 330
8.2.4 Distribution System Reliability 331
8.3 Reliability Test Systems 333
8.4 Advances in Power System Reliability – Power System Reliability in the Deregulated Scenario 334
References 335
9 Probabilistic Safety Assessment 336
9.1 Introduction 336
9.2 Concept of Risk and Safety 337
9.3 Probabilistic Safety Assessment Procedure 339
9.4 Identification of Hazards and Initiating Events 342
9.4.1 Preliminary Hazard Analysis 342
9.4.2 Master Logic Diagram 342
9.5 Event Tree Analysis 343
9.5.1 Procedure for Event Tree Analysis 343
9.6 Importance Measures 350
9.6.1 Birnbaum Importance 351
9.6.2 Inspection Importance 352
9.6.3 Fussell–Vesely Importance 352
9.7 Common-cause Failure Analysis 355
9.7.1 Treatment of Dependent Failures 355
9.7.1.1 Functional Dependences 356
9.7.1.2 Physical Dependences 356
9.7.1.3 Human Interaction Dependence 357
9.7.1.4 Defense Against Common-cause Failure 357
9.7.2 Procedural Framework for Common-cause Failure Analysis 358
9.7.3 Treatment of Common-cause Failures in Fault Tree Models 358
9.7.4 Common-cause Failure Models 363
9.7.4.1 Non-shock Models 363
9.7.4.2 Shock Models 370
9.8 Human Reliability Analysis 374
9.8.1 Human Behavior and Errors 374
9.8.2 Categorization of Human Interactions in Probabilistic Safety Assessment 376
9.8.2.1 Category A: Pre-initiators 376
9.8.2.2 Category B: Initiators 376
9.8.2.3 Category C: Post-initiators 376
9.8.3 Steps in Human Reliability Analysis 377
9.8.3.1 Definition 377
9.8.3.2 Screening 378
9.8.3.3 Qualitative Analysis 378
9.8.3.4 Representation and Model Integration 378
9.8.3.5 Quantification 381
References 381
10 Applications of Probabilistic Safety Assessment 383
10.1 Objectives of Probabilistic Safety Assessment 383
10.2 Probabilistic Safety Assessment of Nuclear Power Plants 384
10.2.1 Description of Pressurized Heavy-water Reactors 384
10.2.1.1 Reactor Process System 385
10.2.1.2 Reactor Protection System 385
10.2.1.3 Electrical Power System 386
10.2.2 Probabilistic Safety Assessment of Indian Nuclear Power Plants (Pressurized Heavy-water Reactor Design) 386
10.2.2.1 Dominating Initiating Events 387
10.2.2.2 Reliability Analysis 392
10.2.2.3 Accident Sequence Identification 394
10.2.2.4 Event Trees 396
10.2.2.5 Dominating Accident Sequences 399
10.2.2.6 Risk Importance Measures 400
10.3 Technical Specification Optimization 401
10.3.1 Traditional Approaches for Technical Specification Optimization 402
10.3.1.1 Measures Applicable for Allowed Outage Time Evaluations 402
10.3.1.2 Measures Applicable for Surveillance Test Interval Evaluations 405
10.3.2 Advanced Techniques for Technical Specification Optimization 405
10.3.2.1 Mathematical Modeling of Problem 406
10.3.2.2 Genetic Algorithm as Optimization Method 407
10.3.2.3 Case Studies: Test Interval Optimization for Emergency Core Cooling System of Pressurized Heavy-water Reactor 409
10.4 Risk Monitor 412
10.4.1 Necessity of Risk Monitor? 413
10.4.2 Different Modules of Risk Monitor 413
10.4.3 Applications of Risk Monitor 414
10.4.3.1 Decision-making in Operations 415
10.4.3.2 Maintenance Strategies 416
10.4.3.3 Risk-based In-Service Inspection 416
10.4.3.4 Incident Severity Assessment 417
10.4.3.5 Review of Technical Specification 417
10.4.3.6 Emergency Operating Procedures and Risk Management 417
10.5 Risk-informed In-service Inspection 417
10.5.1 Risk-informed In-service Inspection Models 418
10.5.1.1 American Society of Mechanical Engineers/Westinghouse Owners Group Model 418
10.5.1.2 Electric Power Research Institute Model 421
10.5.1.3 Comparison of Risk-informed In-service Inspection Models 424
10.5.2 In-service Inspection and Piping Failure Frequency 426
10.5.2.1 In-service Inspection 426
10.5.2.2 Models for Including In-service Inspection Effect on Piping Failure Frequency 427
10.5.3 Case Study 435
10.5.3.1 Assumptions 435
10.5.3.2 Consequence Analysis of Feeder Failure 436
10.5.3.3 Using the Three-state Markov Model 437
10.5.3.4 Using the Four-state Markov Model 441
10.5.4 Remarks on Risk-informed In-service Inspection 444
References 445
11 Uncertainty Managementin Reliability/Safety Assessment 447
11.1 Mathematical Models and Uncertainties 447
11.1.1 Example for Understanding of Epistemic and Aleatory Uncertainties 449
11.2 Uncertainty Analysis: an Important Task of Probabilistic Risk/Safety Assessment 450
11.3 Methods of Characterizing Uncertainties 452
11.3.1 The Probabilistic Approach 452
11.3.2 Interval and Fuzzy Representation 452
11.3.2.1 Interval Representation 452
11.3.2.2 Fuzzy Representation 453
11.3.3 Dempster–Shafer-theory-based Representation 453
11.3.3.1 Frame of Discernment – X or O 454
11.3.3.2 Basic Belief Assignment 454
11.3.3.3 Belief and Plausibility Functions 456
11.4 Uncertainty Propagation 457
11.4.1 Method of Moments 458
11.4.1.1 Approximation from the Taylor Series 458
11.4.1.2 Consideration of Correlation Using Method of Moments 460
11.4.2 Monte Carlo Simulation 463
11.4.2.1 Crude Monte Carlo Sampling 464
11.4.2.2 Latin Hypercube Sampling 466
11.4.3 Interval Arithmetic 467
11.4.4 Fuzzy Arithmetic 469
11.4.4.1 Probability to Possibility Transformations 471
11.5 Uncertainty Importance Measures 471
11.5.1 Probabilistic Approach to Ranking Uncertain Parameters in System Reliability Models 472
11.5.1.1 Correlation Coefficient Method 473
11.5.1.2 Variance-based Method 473
11.5.2 Method Based on Fuzzy Set Theory 474
11.5.3 Application to a Practical System 477
11.6 Treatment of Aleatory and Epistemic Uncertainties 481
11.6.1 Epistemic and Aleatory Uncertainty in Reliability Calculations 481
11.6.2 Need to Separate Epistemic and Aleatory Uncertainties 483
11.6.3 Methodology for Uncertainty Analysis in Reliability Assessment Based on Monte Carlo Simulation 484
11.6.3.1 Methodology 486
11.7 Dempster–Shafer Theory 488
11.7.1 Belief and Plausibility Function of Real Numbers 490
11.7.2 Dempster’s Rule of Combination 491
11.7.3 Sampling Technique for the Evidence Theory 493
11.8 Probability Bounds Approach 497
11.8.1 Computing with Probability Bounds 497
11.8.1.1 Basic Calculations for Construction of P-box 500
11.8.2 Two-phase Monte Carlo Simulation 504
11.8.3 Uncertainty Propagation Considering Correlation Between Variables 506
11.9 Bayesian Approach 507
11.9.1 Bayes’ Theorem 508
11.9.2 Identification of Parameter 509
11.9.3 Development of Prior Distribution 509
11.9.4 Construction of Likelihood Function 510
11.9.5 Derivation of Posterior Distribution 510
11.9.6 Characteristic Parameters of Posterior Distribution 510
11.9.7 Estimation of Parameters from Multiple Sources of Information 511
11.9.8 The Hierarchical Bayes Method 512
11.10 Expert Elicitation Methods 513
11.10.1 Definition and Uses of Expert Elicitation 513
11.10.2 Treatment of Expert Elicitation Process 514
11.10.3 Methods of Treatment 514
11.10.3.1 Indirect Elicitation Method 515
11.10.3.2 Direct Elicitation Methods 515
11.10.3.3 Geometric Averaging Technique 516
11.10.3.4 Percentiles for Combining Expert Opinions 517
11.11 Case Study to Compare Uncertainty Analysis Methods 518
11.11.1 Availability Assessment of Main Control Power Supply Using Fault Tree Analysis 519
11.11.2 Uncertainty Propagation in Main Control Power Supply with Different Methods 521
11.11.2.1 Interval Analysis 521
11.11.2.2 Fuzzy Arithmetic 521
11.11.2.3 Monte Carlo Simulation 523
11.11.2.4 Dempster–Shafer Theory 524
11.11.2.5 Probability Bounds Analysis 525
11.11.3 Observations from Case Study 527
11.11.3.1 Remarks 527
Exercise Problems 528
References 531
Appendix: Distribution Tables 535
Index 543