Preface	7
	Contents	10
	1 Basic Concepts	13
	Abstract	13
	1.1…Introduction	13
	1.2…Hydrosystem	14
	1.3…Risk and Reliability	14
	1.4…Risk Assessment and Management	15
	1.5…Uncertainty	16
	1.5.1 Purpose of Uncertainty Analysis	17
	1.5.2 Measurement of Risk and Uncertainty	17
	References	19
	2 Probability Theories	20
	Abstract	20
	2.1…Review of Probability Theory	20
	2.2…Probability Concepts	21
	2.3…Random Variables	23
	2.4…Moments of Distribution	25
	2.4.1 Estimate Moments From Data Series	29
	2.5…Two Random Variables	32
	2.6…Commonly Used Probability Distributions in Hydrosystem Engineering	37
	2.6.1 Binomial Distribution	37
	2.6.2 Poisson Distribution	41
	2.6.3 Normal Distribution	42
	2.6.4 Log-Normal Distribution	45
	2.6.5 Exponential Distribution	48
	2.6.6 Gamma Distribution	50
	2.6.7 Beta Distribution	53
	2.6.8 Uniform DistributionUniform Distribution	54
	References	55
	3 Risk and Uncertainty Analysis	56
	Abstract	56
	3.1…Basic Concept of Uncertainty	56
	3.2…Uncertainty Analysis	57
	3.2.1 Analytical Techniques	58
	3.2.1.1 Derived Distribution Technique	58
	3.2.1.2 Fourier Transforms Techniques	59
	3.3…Basic Concepts of Risk and Reliability	62
	3.4…Safety Factor and Safety Margin	63
	3.5…Performance Function	64
	3.6…Reliability Index	66
	3.7…First-Order Second-Moment Method	72
	3.7.1 Mean-Value First-Order Second-Moment Method	72
	3.8…Probabilistic Point Estimation Methods	76
	3.8.1 Rosenblueth’s Point Estimation Method	76
	3.8.2 Bivariate RPEM	79
	3.9…Reliability Analysis of Complex System	82
	3.9.1 Event-Tree	82
	3.9.2 Fault-Tree	84
	References	86
	4 Monte Carlo Simulation	88
	Abstract	88
	4.1…Introduction	88
	4.2…Basics of Monte Carlo Simulation	89
	4.3…Generation of Random Numbers	89
	4.4…CDF-inverse Method (Continuous Case)	91
	4.5…Acceptance-Rejection Method	95
	4.6…Generation Random Variates from Probability Distributions	97
	4.6.1 Normal Distribution	97
	4.6.1.1 Box-Muller Algorithm	97
	4.6.1.2 The Polar Method	98
	4.6.2 Lognormal Distribution	99
	4.6.3 Exponential Distribution	101
	4.7…Monte Carlo Integration	102
	4.7.1 One-Dimensional Monte Carlo Integration	102
	4.7.2 Two-Dimensional Monte Carlo Integration	104
	4.8… Hit-and-Miss Method	105
	4.9…Variance-Reduction Techniques	110
	References	111
	5 Evaluation of Dam Overtopping Risk Based on Univariate Frequency Analysis	112
	Abstract	112
	5.1…Introduction	112
	5.2…Dam Risk Model	115
	5.2.1 Risk Modeling for Flood and Wind Overtopping	116
	5.3…Reservoir Routing	117
	5.4…Wind Model	117
	5.5…Uncertainty Analysis	119
	5.5.1 Monte Carlo Simulation	119
	5.5.2 Latin Hypercube Sampling	120
	5.6…Overtopping Risk for an Existing Dam	121
	5.6.1 Study Area and Data Collection	121
	5.6.2 Flood Frequency Analysis	122
	5.6.3 Wind Frequency Analysis	123
	5.6.4 Uncertain Variables	124
	5.6.5 Overtopping Risk Due to Different Floods	125
	5.6.6 Overtopping Risk Due to Flood and Wind	126
	5.7…Conclusions	128
	5.8…Future Studies	131
	References	131
	6 Evaluation of Dam Overtopping Risk Based on Univariate and Bivariate Flood Frequency Analyses	133
	Abstract	133
	6.1…Introduction	133
	6.2…Bivariate Frequency Analysis	135
	6.3…Reservoir Routing Analysis	137
	6.4…Risk and Uncertainty Analysis	137
	6.5…Case Study	138
	6.6…Outlier Test	139
	6.7…Determination of Uncertainty Factors	139
	6.8…Univariate Flood Frequency Analysis	141
	6.9…Bivariate Flood Frequency Analysis	143
	6.10…Overtopping Risk Based on Univariate Flood Frequency	145
	6.11…Overtopping Risk Based on Bivariate Flood Frequency	145
	6.12…Conclusion	148
	References	150
	Appendix A	152
	Appendix A	152
	Appendix B	158
	Appendix C	161
	Index	163