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INTEGRATE RELIABILITY ASSESSMENT AND RISK ANALYSISINTO PLANNING, DESIGN, AND MANAGEMENT
This comprehensive text is the first to integrate reliability analysis and risk assessment into the planning, design, and management of hydrosystems. Written by internationally respected authorities, Hydrosystems Engineering Reliability Assessment and Risk Analysis provides the tools for designing safer, more reliable dams, storm sewer networks, water treatment plants, and pollution control systems.
Offering example problems that demonstrate the prediction of safety and reliability under different design scenarios, the authors illustrate the application of mathematical tools that quantify reliability and risk. With this book readers can improve the performance, durability (through maintenance scheduling/time to failure analysis), and predictability of hydrosystem designs.
Hydrosystems Engineering Reliability Assessment and Risk Analysis:
Brings together in a single resource mathematical risk and reliability analysis methods needed to improve planning, design, and performance of hydrosystems Demonstrates statistical and probability tools for solving a broad range of hydrosystem engineering problems Provides the tools needed to predict hydrosystem project behavior and lifespan under various risk scenarios Shows engineers and students how to conduct risk and reliability assessments Offers examples of each application, in both U.S. and international units Provides sets of Q & A's for self-testing after every chapterAuthor Notes
Yeou-Koung Tung, Ph.D., is a Professor of Civil Engineering at Hong Kong University of Science and Technology. The author of numerous technical papers on hydrology and risk analysis, he has won several awards for his research on these topics including the Walter L. Huber Research Prize, ASCE; the Arthur T. Ippen Award, IAHR; and the Collingwood Prize, ASCE. Dr. Tung received his B.S. in Hydraulic Engineering from Tamkang University, Taiwan and his M.S. and Ph.D. in civil engineering from the University of Texas at Austin.
Ben-Chie Yen, Ph.D., (deceased) was a Professor of Civil and Environmental Engineering at the University of Illinois at Champaign-Urbana. He worked with surface water and urban hydrology problems, risk and reliability analysis, and open channel and river hydraulics for more than 30 years, and was author of over 200 published technical papers and co-author of eight books. He won a number of lifetime achievement awards from various professional societies focusing on hydraulics and civil engineering including the Hunter Rouse Hydraulic Engineering Lecture, ASCE; the Ven Te Chow Memorial Lecture Award, IWRA; and Honorary Membership in IAHR. He held a B.S. in civil engineering from National Taiwan University and M.S. and Ph.D. degrees in civil engineering from the University of Iowa.
Charles Steve Melching, Ph.D., P.E., is an Associate Professor of Civil and Environmental Engineering at Marquette University, Milwaukee, Wisconsin. He worked for the U.S. Geological Survey, Water Resources Division, for seven years prior to joining the Marquette faculty in 1999. Much of his research has been centered on the application of reliability and uncertainty analysis to water resources modeling and design. He has been honored for his research with the Walter L. Huber Research Prize, ASCE. He received his B.S. in civil engineering from Arizona State University and his M.S. and Ph.D. in civil engineering from the University of Illinois at Urbana-Champaign.
Table of Contents
Preface | p. xi |
Acknowledgments | p. xv |
Chapter 1 Reliability in Hydrosystems Engineering | p. 1 |
1.1 Reliability Engineering | p. 1 |
1.2 Reliability of Hydrosystem Engineering Infrastructure | p. 2 |
1.3 Brief History of Engineering Reliability Analysis | p. 6 |
1.4 Concept of Reliability Engineering | p. 7 |
1.5 Definitions of Reliability and Risk | p. 10 |
1.6 Measures of Reliability | p. 13 |
1.7 Overall View of Reliability Analysis Methods | p. 15 |
References | p. 16 |
Chapter 2 Fundamentals of Probability and Statistics for Reliability Analysis | p. 19 |
2.1 Terminology | p. 19 |
2.2 Fundamental Rules of Probability Computations | p. 21 |
2.2.1 Basic axioms of probability | p. 21 |
2.2.2 Statistical independence | p. 22 |
2.2.3 Conditional probability | p. 23 |
2.2.4 Total probability theorem and Bayes' theorem | p. 24 |
2.3 Random Variables and their Distributions | p. 27 |
2.3.1 Cumulative distribution function and probability density function | p. 27 |
2.3.2 Joint, conditional, and marginal distributions | p. 31 |
2.4 Statistical Properties of Random Variables | p. 35 |
2.4.1 Statistical moments of random variables | p. 35 |
2.4.2 Mean, mode, median, and quantiles | p. 40 |
2.4.3 Variance, standard deviation, and coefficient of variation | p. 43 |
2.4.4 Skewness coefficient and kurtosis | p. 44 |
2.4.5 Covariance and correlation coefficient | p. 47 |
2.5 Discrete Univariate Probability Distributions | p. 49 |
2.5.1 Binomial distribution | p. 51 |
2.5.2 Poisson distribution | p. 53 |
2.6 Some Continuous Univariate Probability Distributions | p. 55 |
2.6.1 Normal (Gaussian) distribution | p. 56 |
2.6.2 Lognormal distribution | p. 60 |
2.6.3 Gamma distribution and variations | p. 63 |
2.6.4 Extreme-value distributions | p. 66 |
2.6.5 Beta distributions | p. 71 |
2.6.6 Distributions related to normal random variables | p. 72 |
2.7 Multivariate Probability Distributions | p. 75 |
2.7.1 Multivariate normal distributions | p. 77 |
2.7.2 Computation of multivariate normal probability | p. 81 |
2.7.3 Determination of bounds on multivariate normal probability | p. 88 |
2.7.4 Multivariate lognormal distributions | p. 91 |
Problems | p. 92 |
References | p. 101 |
Chapter 3 Hydrologic Frequency Analysis | p. 103 |
3.1 Types of Geophysical Data Series | p. 104 |
3.2 Return Period | p. 108 |
3.3 Probability Estimates for Data Series: Plotting Positions (Rank-order Probability) | p. 109 |
3.4 Graphic Approach | p. 111 |
3.5 Analytical Approaches | p. 114 |
3.6 Estimation of Distributional Parameters | p. 119 |
3.6.1 Maximum-likelihood (ML) method | p. 119 |
3.6.2 Product-moments-based method | p. 121 |
3.6.3 L-moments-based method | p. 122 |
3.7 Selection of Distribution Model | p. 125 |
3.7.1 Probability plot correlation coefficients | p. 125 |
3.7.2 Model reliability indices | p. 126 |
3.7.3 Moment-ratio diagrams | p. 126 |
3.7.4 Summary | p. 129 |
3.8 Uncertainty Associated with a Frequency Relation | p. 129 |
3.9 Limitations of Hydrologic Frequency Analysis | p. 135 |
3.9.1 Distribution selection: practical considerations | p. 135 |
3.9.2 Extrapolation problems | p. 136 |
3.9.3 The stationarity assumption | p. 139 |
3.9.4 Summary comments | p. 139 |
Problems | p. 140 |
References | p. 142 |
Chapter 4 Reliability Analysis Considering Load-Resistance Interference | p. 145 |
4.1 Basic Concept | p. 145 |
4.2 Performance Functions and Reliability Index | p. 147 |
4.3 Direct Integration Method | p. 149 |
4.4 Mean-Value First-Order Second-Moment (MFOSM) Method | p. 156 |
4.5 Advanced First-Order Second-Moment (AFOSM) Method | p. 164 |
4.5.1 Definitions of stochastic parameter spaces | p. 164 |
4.5.2 Determination of design point (most probable failure point) | p. 165 |
4.5.3 First-order approximation of performance function at the design point | p. 169 |
4.5.4 Algorithms of AFOSM for independent normal parameters | p. 173 |
4.5.5 Treatment of nonnormal stochastic variables | p. 180 |
4.5.6 Treatment of correlated normal stochastic variables | p. 185 |
4.5.7 AFOSM reliability analysis for nonnormal correlated stochastic variables | p. 190 |
4.5.8 Overall summary of AFOSM reliability method | p. 200 |
4.6 Second-Order Reliability Methods | p. 203 |
4.6.1 Quadratic approximations of the performance function | p. 204 |
4.6.2 Breitung's formula | p. 208 |
4.7 Time-Dependent Reliability Models | p. 211 |
4.7.1 Time-dependent resistance | p. 213 |
4.7.2 Time-dependent load | p. 214 |
4.7.3 Classification of time-dependent reliability models | p. 214 |
4.7.4 Modeling intensity and occurrence of loads | p. 215 |
4.7.5 Time-dependent reliability models | p. 217 |
4.7.6 Time-dependent reliability models for hydrosystems | p. 218 |
Appendix 4A Some One-Dimensional Numerical Integration Formulas | p. 221 |
Appendix 4B Cholesky Decomposition | p. 223 |
Appendix 4C Orthogonal Transformation Techniques | p. 224 |
Appendix 4D Gram-Schmid Ortho Normalization | p. 229 |
Problems | p. 231 |
References | p. 240 |
Chapter 5 Time-to-Failure Analysis | p. 245 |
5.1 Basic Concept | p. 245 |
5.2 Failure Characteristics | p. 246 |
5.2.1 Failure density function | p. 246 |
5.2.2 Failure rate and hazard function | p. 247 |
5.2.3 Cumulative hazard function and average failure rate | p. 251 |
5.2.5 Typical hazard functions | p. 254 |
5.2.6 Relationships among failure density function, failure rate, and reliability | p. 255 |
5.2.7 Effect of age on reliability | p. 257 |
5.2.8 Mean time to failure | p. 259 |
5.3 Repairable Systems | p. 259 |
5.3.1 Repair density and repair probability | p. 261 |
5.3.2 Repair rate and its relationship with repair density and repair probability | p. 263 |
5.3.3 Mean time to repair, mean time between failures, and mean time between repairs | p. 263 |
5.3.4 Preventive maintenance | p. 264 |
5.3.5 Supportability | p. 272 |
5.4 Determinations of Availability and Unavailability | p. 272 |
5.4.1 Terminology | p. 272 |
5.4.2 Determinations of availability and unavailability | p. 275 |
Appendix 5A Laplace Transform | p. 282 |
Problems | p. 283 |
References | p. 286 |
Chapter 6 Monte Carlo Simulation | p. 289 |
6.1 Introduction | p. 289 |
6.2 Generation of Random Numbers | p. 291 |
6.3 Classifications of Random Variates Generation Algorithms | p. 294 |
6.3.1 CDF-inverse method | p. 294 |
6.3.2 Acceptance-rejection methods | p. 296 |
6.3.3 Variable transformation method | p. 298 |
6.4 Generation of Univariate Random Numbers for Some Distributions | p. 299 |
6.4.1 Normal distribution | p. 299 |
6.4.2 Lognormal distribution | p. 301 |
6.4.3 Exponential distribution | p. 301 |
6.4.4 Gamma distribution | p. 302 |
6.4.5 Poisson distribution | p. 302 |
6.4.6 Other univariate distributions and computer programs | p. 303 |
6.5 Generation of Vectors of Multivariate Random Variables | p. 303 |
6.5.1 CDF-inverse method | p. 304 |
6.5.2 Generating multivariate normal random variates | p. 307 |
6.5.3 Generating multivariate random variates with known marginal PDFs and correlations | p. 311 |
6.5.4 Generating multivariate random variates subject to linear constraints | p. 312 |
6.6 Monte Carlo Integration | p. 314 |
6.6.1 The hit-and-miss method | p. 316 |
6.6.2 The sample-mean method | p. 319 |
6.6.3 Directional Monte Carlo simulation algorithm | p. 321 |
6.6.4 Efficiency of the Monte Carlo algorithm | p. 327 |
6.7 Variance-Reduction Techniques | p. 327 |
6.7.1 Importance sampling technique | p. 328 |
6.7.2 Antithetic-variates technique | p. 330 |
6.7.3 Correlated-sampling techniques | p. 333 |
6.7.4 Stratified sampling technique | p. 335 |
6.7.5 Latin hypercube sampling technique | p. 338 |
6.7.6 Control-variate method | p. 342 |
6.8 Resampling Techniques | p. 344 |
Problems | p. 348 |
References | p. 352 |
Chapter 7 Reliability of Systems | p. 357 |
7.1 Introduction | p. 357 |
7.2 General View of System Reliability Computation | p. 358 |
7.2.1 Classification of systems | p. 359 |
7.2.2 Basic probability rules for system reliability | p. 360 |
7.2.3 Bounds for system reliability | p. 363 |
7.3 Reliability of Simple Systems | p. 371 |
7.3.1 Series systems | p. 371 |
7.3.2 Parallel systems | p. 376 |
7.3.3 K-out-of-M parallel systems | p. 379 |
7.3.4 Standby redundant systems | p. 380 |
7.4 Methods for Computing Reliability of Complex Systems | p. 381 |
7.4.1 State enumeration method | p. 381 |
7.4.2 Path enumeration method | p. 385 |
7.4.3 Conditional probability approach | p. 389 |
7.4.4 Fault-tree analysis | p. 391 |
7.5 Summary and Conclusions | p. 398 |
Appendix 7A Derivation of Bounds for Bivariate Normal Probability | p. 399 |
Problems | p. 402 |
References | p. 404 |
Chapter 8 Integration of Reliability in Optimal Hydrosystems Design | p. 407 |
8.1 Introduction | p. 407 |
8.1.1 General framework of optimization models | p. 408 |
8.1.2 Single-objective versus multiobjective programming | p. 409 |
8.1.3 Optimization techniques | p. 411 |
8.2 Optimization of System Reliability | p. 422 |
8.2.1 Reliability design with redundancy | p. 422 |
8.2.2 Determination of optimal maintenance schedule | p. 425 |
8.3 Optimal Risk-Based Design of Hydrosystem Infrastructures | p. 427 |
8.3.1 Basic concept | p. 428 |
8.3.2 Historical development of hydraulic design methods | p. 429 |
8.3.3 Tangible costs in risk-based design | p. 431 |
8.3.4 Evaluations of annual expected flood damage cost | p. 433 |
8.3.5 Risk-based design without flood damage information | p. 436 |
8.3.6 Risk-based design considering intangible factors | p. 438 |
8.4 Applications of Risk-Based Hydrosystem Design | p. 439 |
8.4.1 Optimal risk-based pipe culvert for roadway drainage | p. 440 |
8.4.2 Risk-based analysis for flood-damage-reduction projects | p. 445 |
8.5 Optimization of Hydrosystems by Chance-Constrained Methods | p. 449 |
8.6 Chance-Constrained Method to ASSESS Water-Quality Management | p. 454 |
8.6.1 Optimal stochastic waste-load allocation | p. 455 |
8.6.2 Multiobjective stochastic waste-load allocation | p. 465 |
Appendix 8A Derivation of Water-Quality Constraints | p. 470 |
Problems | p. 472 |
References | p. 477 |
Index | p. 483 |