MARVIN RAUSAND is Professor Emeritus in the department of Mechanical and Industrial Engineering at the Norwegian University of Science and Technology (NTNU), Norway, and author of Risk Assessment: Theory, Methods, and Applications and Reliability of Safety-Critical Systems: Theory and Applications, both published by Wiley.

ANNE BARROS, PHD, is Professor in reliability and maintenance engineering at Ecole CentraleSupélec, University of Paris-Saclay, France. Her research focus is on degradation modeling, prognostics, condition based and predictive maintenance. She got a PHD then a professorship position at University of Technology of Troyes, France (2003 ? 2014) and spent five years as a full-time professor at NTNU, Norway (2014 ? 2019). She is currently heading a research group and holds an industrial chair at CentraleSupélec with the ambition to provide reliability assessment and maintenance modeling methods for systems of systems.

The late ARNLJOT HØYLAND, PHD, was a Professor in the Department of Mathematical Sciences at the Norwegian University of Science and Technology.

Preface xxiii

About the Companion Website xxix

1 Introduction 1

1.1 What is Reliability? 1

1.1.1 Service Reliability 2

1.1.2 Past and Future Reliability 3

1.2 The Importance of Reliability 3

1.2.1 Related Applications 4

1.3 Basic Reliability Concepts 6

1.3.1 Reliability 6

1.3.2 Maintainability and Maintenance 8

1.3.3 Availability 8

1.3.4 Quality 9

1.3.5 Dependability 9

1.3.6 Safety and Security 10

1.3.7 RAM and RAMS 10

1.4 Reliability Metrics 11

1.4.1 Reliability Metrics for a Technical Item 11

1.4.2 Reliability Metrics for a Service 12

1.5 Approaches to Reliability Analysis 12

1.5.1 The Physical Approach to Reliability 13

1.5.2 Systems Approach to Reliability 13

1.6 Reliability Engineering 15

1.6.1 Roles of the Reliability Engineer 16

1.6.2 Timing of Reliability Studies 17

1.7 Objectives, Scope, and Delimitations of the Book 17

1.8 Trends and Challenges 19

1.9 Standards and Guidelines 20

1.10 History of System Reliability 20

1.11 Problems 26

References 27

2 The Study Object and its Functions 31

2.1 Introduction 31

2.2 System and System Elements 31

2.2.1 Item 32

2.2.2 Embedded Item 33

2.3 Boundary Conditions 33

2.3.1 Closed and Open Systems 34

2.4 Operating Context 35

2.5 Functions and Performance Requirements 35

2.5.1 Functions 35

2.5.2 Performance Requirements 36

2.5.3 Classification of Functions 37

2.5.4 Functional Modeling and Analysis 38

2.5.5 Function Trees 38

2.5.6 SADT and IDEF 0 39

2.6 System Analysis 41

2.6.1 Synthesis 41

2.7 Simple, Complicated, and Complex Systems 42

2.8 System Structure Modeling 44

2.8.1 Reliability Block Diagram 44

2.8.2 Series Structure 46

2.8.3 Parallel Structure 46

2.8.4 Redundancy 47

2.8.5 Voted Structure 47

2.8.6 Standby Structure 48

2.8.7 More Complicated Structures 48

2.8.8 Two Different System Functions 49

2.8.9 Practical Construction of RBDs 50

2.9 Problems 51

References 52

3 Failures and Faults 55

3.1 Introduction 55

3.1.1 States and Transitions 56

3.1.2 Operational Modes 56

3.2 Failures 57

3.2.1 Failures in a State 58

3.2.2 Failures During Transition 59

3.3 Faults 60

3.4 Failure Modes 60

3.5 Failure Causes and Effects 62

3.5.1 Failure Causes 62

3.5.2 Proximate Causes and Root Causes 63

3.5.3 Hierarchy of Causes 64

3.6 Classification of Failures and Failure Modes 64

3.6.1 Classification According to Local Consequence 65

3.6.2 Classification According to Cause 65

3.6.3 Failure Mechanisms 70

3.6.4 Software Faults 71

3.6.5 Failure Effects 71

3.7 Failure/Fault Analysis 72

3.7.1 Cause and Effect Analysis 73

3.7.2 Root Cause Analysis 74

3.8 Problems 76

References 77

4 Qualitative System Reliability Analysis 79

4.1 Introduction 79

4.1.1 Deductive Versus Inductive Analysis 80

4.2 FMEA/FMECA 80

4.2.1 Types of FMECA 81

4.2.2 Objectives of FMECA 82

4.2.3 FMECA Procedure 83

4.2.4 Applications 87

4.3 Fault Tree Analysis 88

4.3.1 Fault Tree Symbols and Elements 88

4.3.2 Definition of the Problem and the Boundary Conditions 91

4.3.3 Constructing the Fault Tree 92

4.3.4 Identification of Minimal Cut and Path Sets 95

4.3.5 MOCUS 96

4.3.6 Qualitative Evaluation of the Fault Tree 98

4.3.7 Dynamic Fault Trees 101

4.4 Event Tree Analysis 103

4.4.1 Initiating Event 104

4.4.2 Safety Functions 105

4.4.3 Event Tree Construction 106

4.4.4 Description of Resulting Event Sequences 106

4.5 Fault Trees versus Reliability Block Diagrams 109

4.5.1 Recommendation 111

4.6 Structure Function 111

4.6.1 Series Structure 112

4.6.2 Parallel Structure 112

4.6.3 koon:G Structure 113

4.6.4 Truth Tables 114

4.7 System Structure Analysis 114

4.7.1 Single Points of Failure 115

4.7.2 Coherent Structures 115

4.7.3 General Properties of Coherent Structures 117

4.7.4 Structures Represented by Paths and Cuts 119

4.7.5 Pivotal Decomposition 123

4.7.6 Modules of Coherent Structures 124

4.8 Bayesian Networks 127

4.8.1 Illustrative Examples 128

4.9 Problems 131

References 138

5 Probability Distributions in Reliability Analysis 141

5.1 Introduction 141

5.1.1 State Variable 142

5.1.2 Time-to-Failure 142

5.2 A Dataset 143

5.2.1 Relative Frequency Distribution 143

5.2.2 Empirical Distribution and Survivor Function 144

5.3 General Characteristics of Time-to-Failure Distributions 145

5.3.1 Survivor Function 147

5.3.2 Failure Rate Function 148

5.3.3 Conditional Survivor Function 153

5.3.4 Mean Time-to-Failure 154

5.3.5 Additional Probability Metrics 155

5.3.6 Mean Residual Lifetime 157

5.3.7 Mixture of Time-to-Failure Distributions 160

5.4 Some Time-to-Failure Distributions 161

5.4.1 The Exponential Distribution 161

5.4.2 The Gamma Distribution 168

5.4.3 TheWeibull Distribution 173

5.4.4 The Normal Distribution 180

5.4.5 The Lognormal Distribution 183

5.4.6 Additional Time-to-Failure Distributions 188

5.5 Extreme Value Distributions 188

5.5.1 The Gumbel Distribution of the Smallest Extreme 190

5.5.2 The Gumbel Distribution of the Largest Extreme 191

5.5.3 TheWeibull Distribution of the Smallest Extreme 191

5.6 Time-to-Failure Models With Covariates 193

5.6.1 Accelerated Failure Time Models 194

5.6.2 The Arrhenius Model 195

5.6.3 Proportional Hazards Models 198

5.7 Additional Continuous Distributions 198

5.7.1 The Uniform Distribution 198

5.7.2 The Beta Distribution 199

5.8 Discrete Distributions 200

5.8.1 Binomial Situation 200

5.8.2 The Binomial Distribution 201

5.8.3 The Geometric Distribution 201

5.8.4 The Negative Binomial Distribution 202

5.8.5 The Homogeneous Poisson Process 203

5.9 Classes of Time-to-Failure Distributions 205

5.9.1 IFR and DFR Distributions 206

5.9.2 IFRA and DFRA Distributions 208

5.9.3 NBU and NWU Distributions 208

5.9.4 NBUE and NWUE Distributions 209

5.9.5 Some Implications 209

5.10 Summary of Time-to-Failure Distributions 210

5.11 Problems 210

References 218

6 System Reliability Analysis 221

6.1 Introduction 221

6.1.1 Assumptions 222

6.2 System Reliability 222

6.2.1 Reliability of Series Structures 223

6.2.2 Reliability of Parallel Structures 224

6.2.3 Reliability of koon Structures 225

6.2.4 Pivotal Decomposition 226

6.2.5 Critical Component 227

6.3 Nonrepairable Systems 228

6.3.1 Nonrepairable Series Structures 228

6.3.2 Nonrepairable Parallel Structures 230

6.3.3 Nonrepairable 2oo3 Structures 234

6.3.4 A Brief Comparison 235

6.3.5 Nonrepairable koon Structures 236

6.4 Standby Redundancy 237

6.4.1 Passive Redundancy, Perfect Switching, No Repairs 238

6.4.2 Cold Standby, Imperfect Switch, No Repairs 240

6.4.3 Partly Loaded Redundancy, Imperfect Switch, No Repairs 241

6.5 Single Repairable Items 242

6.5.1 Availability 243

6.5.2 Average Availability with Perfect Repair 244

6.5.3 Availability of a Single Item with Constant Failure and Repair Rates 246

6.5.4 Operational Availability 247

6.5.5 Production Availability 248

6.5.6 Punctuality 249

6.5.7 Failure Rate of Repairable Items 249

6.6 Availability of Repairable Systems 252

6.6.1 The MUT and MDT of Repairable Systems 253

6.6.2 Computation Based on Minimal Cut Sets 258

6.6.3 Uptimes and Downtimes for Reparable Systems 260

6.7 Quantitative Fault Tree Analysis 262

6.7.1 Terminology and Symbols 263

6.7.2 Delimitations and Assumptions 263

6.7.3 Fault Trees with a Single AND-Gate 264

6.7.4 Fault Tree with a Single OR-Gate 265

6.7.5 The Upper Bound Approximation Formula for Q0(t) 265

6.7.6 The Inclusion-Exclusion Principle 267

6.7.7 ROCOF of a Minimal Cut Parallel Structure 271

6.7.8 Frequency of the TOP Event 271

6.7.9 Binary Decision Diagrams 273

6.8 Event Tree Analysis 275

6.9 Bayesian Networks 277

6.9.1 Influence and Cause 278

6.9.2 Independence Assumptions 278

6.9.3 Conditional Probability Table 279

6.9.4 Conditional Independence 280

6.9.5 Inference and Learning 282

6.9.6 BN and Fault Tree Analysis 282

6.10 Monte Carlo Simulation 284

6.10.1 Random Number Generation 285

6.10.2 Monte Carlo Next Event Simulation 287

6.10.3 Simulation of Multicomponent Systems 289

6.11 Problems 291

References 296

7 Reliability Importance Metrics 299

7.1 Introduction 299

7.1.1 Objectives of Reliability Importance Metrics 300

7.1.2 Reliability Importance Metrics Considered 300

7.1.3 Assumptions and Notation 301

7.2 Critical Components 302

7.3 Birnbaum's Metric for Structural Importance 304

7.4 Birnbaum's Metric of Reliability Importance 305

7.4.1 Birnbaum's Metric in Fault Tree Analysis 307

7.4.2 A...