Risk Analysis in Engineering and Economics

Risk Analysis in Engineering and Economics......Page 2
Dedication......Page 4
Preface......Page 5
Structure, Format, and Main Features......Page 7
Acknowledgments......Page 10
About the Author......Page 12
Books by Bilal M. Ayyub......Page 13
Table of Contents......Page 14
Appendix A: Fundamentals of Probability and Statistics......Page 469
Appendix B: Failure Data......Page 527
References and Bibliography......Page 555
Table of Contents......Page 1
1.1 Societal Needs......Page 22
1.2 Risk Analysis......Page 23
1.3 System Framework......Page 29
1.4.1 Knowledge......Page 31
1.4.2 Cognition and Cognitive Science......Page 35
1.4.3 Human Knowledge and Ignorance......Page 37
1.4.4 Classifying Ignorance......Page 39
1.4.5 Ignorance Hierarchy......Page 42
1.4.6 Mathematical Models for Ignorance Types......Page 45
1.4.7.1 Abstraction and Modeling of Engineering Systems......Page 47
1.4.7.2 Ignorance and Uncertainty in Abstracted Aspects of a System......Page 48
1.4.7.4 Ignorance Due to Unknown Aspects of a System......Page 50
1.5 Exercise Problems......Page 52
2.1 Introduction......Page 53
2.2.2 Reliability......Page 54
2.2.4 Risks......Page 55
2.2.6 Risk-Based Technology......Page 59
2.2.7 Safety......Page 60
2.2.8 Systems for Risk Analysis......Page 62
2.3.2 Risk Assessment Methodologies......Page 63
2.3.3 Risk Events and Scenarios......Page 66
2.3.4 Identification of Risk Events and Scenarios......Page 69
2.3.5 Risk Breakdown Structure......Page 73
2.3.6 System Definition for Risk Assessment......Page 74
2.3.7.2 Failure Mode and Effects Analysis......Page 78
2.3.7.3 Risk Matrices......Page 90
2.3.7.4.1 Event-Tree Analysis......Page 92
2.3.7.4.2 Fault-Tree and Success-Tree Analyses......Page 94
2.3.7.4.4 Sensitivity Factors......Page 103
2.3.7.5 Qualitative vs. Quantitative Risk Assessment......Page 104
2.3.8 Human-Related Risks......Page 105
2.3.8.2 Human Error Modeling......Page 106
2.3.8.4 Reducing Human Errors......Page 107
2.3.8.5 Game Theory for Intelligent Threats......Page 108
2.3.9.1 Market Risks......Page 112
2.3.9.4 Reputation Risks......Page 113
2.3.10 Data Needs for Risk Assessment......Page 114
2.4.1 Risk Acceptance......Page 115
2.4.1.1 Risk Conversion Factors......Page 118
2.4.1.3 Method of Revealed Preferences......Page 121
2.4.1.4 Magnitudes of Risk Consequence......Page 123
2.4.1.6 Risk Comparisons......Page 124
2.4.2 Rankings Based on Risk Results......Page 125
2.4.4 Benefit–Cost Analysis......Page 126
2.4.5 Risk Mitigation......Page 127
2.4.5.1 Risk Reduction or Elimination......Page 128
2.4.5.5 Uncertainty Characterization......Page 129
2.5 Risk Communication......Page 131
2.6 Exercise Problems......Page 133
3.2.1 Perspectives for System Definition......Page 138
3.2.2.1 Requirements Analysis......Page 142
3.2.3 Contributing Factor Diagrams......Page 144
3.2.4.1 Decision Trees......Page 146
3.2.4.2 Decision Variables......Page 147
3.2.4.4 Associated Probabilities and Consequences......Page 148
3.2.4.5 Tree Construction......Page 149
3.2.4.6 Influence Diagrams......Page 151
3.2.5 Bayesian Networks......Page 152
3.2.5.2 Relationships in a Bayesian Model......Page 154
3.2.5.4 Network Creation......Page 155
3.2.6.1 System Engineering Process......Page 169
3.2.6.2 Lifecycle of Engineering Systems......Page 172
Phase B. Concept Definition......Page 175
Phase C. Design and Development......Page 176
3.2.6.3 Technical Maturity Model......Page 177
3.2.6.4 Spiral Development Process......Page 178
3.2.7 Black-Box Method......Page 179
3.2.8 State-Based Method......Page 181
3.2.9 Component Integration Method......Page 184
3.3.1 Introduction......Page 185
3.3.2 Knowledge and Information Hierarchy......Page 186
3.3.2.2 Data Systems......Page 187
3.3.2.5 Metasystems......Page 188
3.4 System Complexity......Page 189
3.5 Exercise Problems......Page 193
4.2 Analytical Performance-Based Reliability Assessment......Page 197
4.2.1 Advanced Second-Moment Method......Page 198
4.2.1.1 Reliability Index......Page 199
4.2.1.2 Nonlinear Performance Functions......Page 200
4.2.1.3 Equivalent Normal Distributions......Page 202
4.2.1.4 Correlated Random Variables......Page 203
4.2.1.5 Numerical Algorithms......Page 205
4.2.2.2 Conditional Expectation......Page 210
4.2.2.3 Importance Sampling......Page 212
4.2.2.4 Correlated Random Variables......Page 213
4.2.3 Time-Dependent Reliability Analysis......Page 214
4.3.1 Failure and Repair......Page 215
4.3.2 Types of Data......Page 216
4.3.3 Availability......Page 218
4.3.4 Reliability, Failure Rates, and Hazard Functions......Page 219
4.3.4.2 Weibull Distribution......Page 220
4.3.5 Hazard Functions......Page 221
4.3.6 Selection and Fitting Reliability Models......Page 223
4.3.6.1 Complete Data without Censoring......Page 224
4.3.6.2 Samples with Censoring......Page 228
4.3.6.3 Parametric Reliability Functions......Page 231
4.3.6.4 Parameter Estimation Using Loglinear Transformation......Page 232
4.3.6.5 Nonlinear Model Estimation......Page 235
4.3.6.6 Probability Plotting......Page 237
4.3.6.7 Assessment of Hazard Functions......Page 240
4.3.7 Case Study: Reliability Data Analysis of Hydropower Equipment......Page 242
4.3.7.1 Reliability Data......Page 243
4.3.7.2 Fitting Reliability Models......Page 244
4.3.7.2.1 Individual Univariate Models for the 12 Plant-on-Line and Power Combinations......Page 246
4.3.7.2.2 Bivariate Models Using Average Plant-on-Line Dates......Page 248
4.4 Bayesian Methods......Page 249
4.4.1 Bayes’ Theorem......Page 250
4.4.2 Estimating Binomial Distribution......Page 251
4.4.3 Parameter Estimation for the Exponential Distribution......Page 256
4.5 Reliability Analysis of Systems......Page 260
4.5.2 Series Systems......Page 261
4.5.3 Parallel Systems......Page 264
4.5.4 Series–Parallel Systems......Page 272
4.5.5 k-out-of-n Systems......Page 275
4.6 Exercise Problems......Page 281
5.1 Introduction......Page 290
5.2.1 Cause–Consequence Diagrams......Page 292
5.2.2 Functional Modeling......Page 296
5.3 Real Property Damage......Page 298
5.3.1 Microeconomic Modeling......Page 299
5.3.2 Expert Opinions......Page 301
Levee Failure and Consequent Flooding......Page 302
Flood Characteristics......Page 303
Content Depth–Damage Relationships......Page 304
Content-to-Structure Value Ratios......Page 305
Vehicle Depth–Damage Relationships......Page 308
5.4 Loss of Human Life......Page 312
5.4.2 Human Capital Method......Page 313
5.4.3 Typical Human Life Values......Page 314
5.4.4.2 Floodplains......Page 316
5.4.4.3 Demographics......Page 317
5.4.4.4 Simulating Dam Breach Inundation......Page 319
5.4.4.5 Dam Failure and Flood Fatalities......Page 320
5.5 Injuries......Page 324
5.6 Indirect Losses......Page 326
5.7 Public Health and Ecological Damages......Page 327
Exercise Problems......Page 330
6.1.1 Need for Economics......Page 333
6.1.3 Engineering and Economic Studies......Page 336
6.2 Fundamental Economic Concepts......Page 337
6.4.1 Types of Interest......Page 339
6.4.2 Discrete Compounding and Discrete Payments......Page 341
6.4.2.2 Single-Payment, Present-Worth Factor......Page 342
6.4.2.3 Equal-Payment-Series, Compound-Amount Factor......Page 345
6.4.2.4 Equal-Payment-Series, Sinking-Fund Factor......Page 346
6.4.2.5 Equal-Payment-Series, Capital-Recovery Factor......Page 347
6.4.2.6 Equal-Payment-Series, Present-Worth Factor......Page 348
6.4.2.7 Uniform-Gradient-Series Factor......Page 349
6.4.3.2 Continuous Compounding......Page 351
6.4.4 Summary of Interest Formulae......Page 352
6.5.2 Equivalence Calculations......Page 353
6.5.3 Amortization Schedule for Loans......Page 355
6.6.2 Annual Inflation Rate......Page 356
6.6.3 Purchasing Power of Money......Page 357
6.7.1 Present, Annual, and Future-Worth Amounts......Page 358
6.7.2 Internal Rate of Return......Page 359
6.7.3 Payback Period......Page 360
6.8 Exercise Problems......Page 361
7.1 Introduction......Page 367
7.2 Philosophies of Risk Control......Page 368
7.3 Risk Aversion in Investment Decisions......Page 370
7.4 Risk Homeostasis......Page 383
7.5.1 Loss Control......Page 385
7.5.2 Risk Actuaries and Insurance-Claim Models......Page 386
7.5.2.1 Modeling Loss Accumulation......Page 388
7.5.2.2 Subjective Severity Assessment......Page 390
7.5.2.3 Computational Procedures and Illustrations......Page 391
7.6 Benefit–Cost Analysis......Page 392
7.7.1 Maintenance Methodology......Page 400
7.7.2 Selection of Ship or Fleet System......Page 401
7.7.4 Development of Optimal Maintenance Policy for Components......Page 402
7.7.4.2 Identification of Damage Categories......Page 403
7.7.4.3 Development of Condition States......Page 405
7.7.4.4 Allocation of Component Percentages in Each Condition State......Page 406
7.7.4.8 Transition Probabilities for Cases without Maintenance Actions......Page 409
7.7.4.7 Failure Consequences and Expected Failure Cost......Page 413
7.7.4.8 Transition Probabilities for Cases with Maintenance Actions......Page 414
7.7.4.9 Risk-Based Optimal Maintenance Policy......Page 415
7.7.6 Optimal Maintenance Scheduling for the Overall Vessel......Page 418
7.7.8 An Application: Optimal Maintenance Management of Ship Structures......Page 419
7.8 Exercise Problems......Page 431
8.1 Introduction......Page 436
8.2 Data Sources......Page 437
8.3 Databases......Page 438
8.3.4 Reliability, Availability, and Maintainability Databases......Page 439
8.3.6 Challenges Associated with Data from Other Sources......Page 440
8.4.2 Theoretical Bases and Terminology......Page 442
8.4.3 Classification of Issues, Study Levels, Experts, and Process Outcomes......Page 445
8.4.5 Need Identification for Expert-Opinion Elicitation......Page 447
8.4.7.1 Selection of Peer Reviewers......Page 449
8.4.7.2 Identification and Selection of Experts......Page 450
8.4.7.3 Items Needed by Experts and Reviewers before the Expert-Opinion Elicitation Meeting......Page 451
8.4.8 Identification, Selection, and Development of Technical Issues......Page 452
8.4.9.2 Training of Experts......Page 455
8.4.9.3 Elicitation and Collection of Opinions......Page 456
8.4.9.6 Documentation and Communication......Page 457
Personal Flotation Device Face Plane Angle......Page 459
Personal Flotation Device Chin Support......Page 460
Personal Flotation Device Torso Angle......Page 462
Personal Flotation Device Turning Time from Face Down......Page 463
8.5 Model Modification Based on Available Data......Page 464
8.6 Failure Data Sources......Page 465
8.7 Exercise Problems......Page 466
A.2 Mathematics of Probability......Page 471
A.3.1 Probability for Discrete Random Variables......Page 476
A.3.2 Probability for Continuous Random Variables......Page 477
A.4 Moments......Page 478
A.5.1 Bernoulli Distribution......Page 482
A.5.2 Binomial Distribution......Page 483
A.5.3 Geometric Distribution......Page 484
A.5.4 Poisson Distribution......Page 485
A.5.6 Hypergeometric Distribution......Page 486
A.6.1 Uniform Distribution......Page 487
A.6.2 Normal Distribution......Page 488
A.6.3 Lognormal Distribution......Page 489
A.6.4 Exponential Distribution......Page 491
A.6.5 Triangular Distribution......Page 492
A.6.7 Rayleigh Distribution......Page 493
A.6.9 Statistical Probability Distributions......Page 494
A.6.10 Extreme Value Distributions......Page 497
A.8 Joint Random Variables and Their Probability Distributions......Page 500
A.8.1 Probability for Discrete Random Vectors......Page 502
A.8.2 Probability for Continuous Random Vectors......Page 503
A.8.3 Conditional Moments, Covariance, and Correlation Coefficient......Page 505
A.9.1 Probability Distributions for Functions of Random Variables......Page 508
A.9.2 Approximate Methods for Moments of Functions of Random Variables......Page 510
A.11 Estimation of Parameters......Page 512
A.11.2 Method-of-Moments Estimation......Page 513
A.11.3 Maximum-Likelihood Estimation......Page 514
A.12.1 Sampling Distribution of the Mean......Page 516
A.12.2 Sampling Distribution of the Variance......Page 517
A.13.1 Test of the Mean with Known Population Variance......Page 518
A.13.2 Test of the Mean with Unknown Population Variance......Page 520
A.13.3 Summary......Page 521
A.14.1 One-Sample Chi-Square Test......Page 522
A.14.2 Two-Sample F Test......Page 523
A.15 Confidence Intervals......Page 524
A.15.1 Confidence Interval for the Mean......Page 525
A.15.2 Confidence Interval for the Variance......Page 526