Statistics and probability theory : in pursuit of engineering decision support

Cover......Page 1
S Title......Page 2
TOPICS IN SAFETY, RISK, RELIABILITY AND QUALITY, Volume 18......Page 3
Statistics and Probability Theory: In Pursuit of Engineering Decision Support......Page 4
DOI 10.1007/978-94-007-4056-3......Page 5
Dedication......Page 6
Preface......Page 8
Acknowledgements......Page 12
Contents......Page 14
1.1 Introduction......Page 18
1.2 Societal Decision Making and Risk......Page 19
1.2.1 Example 1.1-Feasibility of Hydraulic Power Plant......Page 20
1.3 Definition of Risk......Page 23
1.4 Self Assessment Questions/Exercises......Page 24
2.1 Introduction......Page 26
2.2.1 Frequentistic Definition......Page 27
2.2.3 Bayesian Definition......Page 28
2.3 Sample Space and Events......Page 29
2.5 Conditional Probability and Bayes\' Rule......Page 31
2.5.1 Example 2.1-Using Bayes\' Rule for Concrete Assessment......Page 33
2.5.2 Example 2.2-Using Bayes\' Rule for Bridge Upgrading......Page 34
2.6 Self Assessment Questions/Exercises......Page 35
3.1 Introduction......Page 38
3.2.2 Example 3.1-Concrete Compressive Strength Data......Page 39
3.2.3 Example 3.2-Traffic Flow Data......Page 40
3.2.4 Dispersion Measures......Page 41
3.2.5 Other Measures......Page 42
3.2.7 Measures of Correlation......Page 43
3.3 Graphical Representations......Page 44
3.3.2 Histograms......Page 45
3.3.3 Quantile Plots......Page 48
3.3.4 Tukey Box Plots......Page 53
3.3.5 Q-Q Plots and Tukey Mean-Difference Plot......Page 56
3.4 Self Assessment Questions/Exercises......Page 58
4.1 Introduction......Page 60
4.2 Uncertainties in Engineering Problems......Page 61
4.3 Random Variables......Page 63
4.3.1 Cumulative Distribution and Probability Density Functions......Page 64
4.3.2 Moments of Random Variables and the Expectation Operator......Page 65
4.3.3 Example 4.1-Uniform Distribution......Page 66
Lecture 5 (Aim of the Present Lecture)......Page 67
4.3.4 Properties of the Expectation Operator......Page 68
4.3.5 Random Vectors and Joint Moments......Page 69
4.3.6 Example 4.2-Linear Combinations and Random Variables......Page 70
4.3.7 Conditional Distributions and Conditional Moments......Page 71
4.3.8 The Probability Distribution for the Sum of Two Random Variables......Page 72
4.3.9 Example 4.3-Density Function for the Sum of Two Random Variables-Special Case Normal Distribution......Page 74
4.3.10 The Probability Distribution for Functions of Random Variables......Page 75
4.3.11 Example 4.4-Probability Distribution for a Function of Random Variables......Page 76
4.3.12 Probability Density and Distribution Functions......Page 78
4.3.13 The Central Limit Theorem and Derived Distributions......Page 79
4.3.15 The Normal Distribution......Page 81
4.4 Stochastic Processes and Extremes......Page 84
4.4.1 Random Sequences-Bernoulli Trials......Page 85
Lecture 7 (Aim of the Present Lecture)......Page 86
4.4.3 The Poisson Counting Process......Page 87
4.4.4 Continuous Random Processes......Page 88
4.4.5 Stationarity and Ergodicity......Page 91
4.4.6 Statistical Assessment of Extreme Values......Page 92
4.4.7 Extreme Value Distributions......Page 93
4.4.8 Type I Extreme Maximum Value Distribution-Gumbel Max......Page 94
4.4.10 Type II Extreme Maximum Value Distribution-Fréchet Max......Page 96
4.4.11 Type III Extreme Minimum Value Distribution-Weibull Min......Page 97
4.4.13 Example 4.7-A Flood with a 100-Year Return Period......Page 98
4.5 Self Assessment Questions/Exercises......Page 99
Lecture 8 (Aim of the Present Lecture)......Page 102
5.1 Introduction......Page 103
5.2 Selection of Probability Distributions......Page 104
5.2.1 Model Selection by Use of Probability Paper......Page 105
5.3.1 The Method of Moments......Page 108
5.3.2 The Method of Maximum Likelihood......Page 109
5.3.3 Example 5.1-Parameter Estimation......Page 110
Lecture 9 (Aim of the Present Lecture)......Page 112
5.4 Bayesian Estimation Methods......Page 113
5.4.1 Example 5.2-Yield Stress of a Steel Bar......Page 114
5.5 Bayesian Regression Analysis......Page 116
5.5.1 Linear Regression: Prior Model......Page 117
5.5.2 Example 5.3-Tensile Strength of Timber: Prior Model......Page 119
5.5.4 Example 5.4-Updating Regression Coefficients (Determined in Example 5.3)......Page 121
5.6 Probability Distributions in Statistics......Page 123
5.6.1 The Chi-Square (chi2)-Distribution......Page 124
5.7 Estimators for Sample Descriptors-Sample Statistics......Page 125
5.7.1 Statistical Characteristics of the Sample Average......Page 126
5.7.2 Statistical Characteristics of the Sample Variance......Page 128
5.7.3 Confidence Intervals......Page 129
5.8 Testing for Statistical Significance......Page 130
5.8.1 The Hypothesis Testing Procedure......Page 131
5.8.3 Some Remarks on Testing......Page 133
5.9 Model Evaluation by Statistical Testing......Page 134
5.9.1 The Chi-Square (chi2)-Goodness of Fit Test......Page 135
5.9.2 The Kolmogorov-Smirnov Goodness of Fit Test......Page 139
5.9.3 Model Comparison......Page 141
5.10 Self Assessment Questions/Exercises......Page 142
6.1 Introduction......Page 146
6.2 Failure Events and Basic Random Variables......Page 147
6.3 Linear Limit State Functions and Normal Distributed Variables......Page 148
6.3.1 Example 6.1-Reliability of a Steel Rod-Linear Safety Margin......Page 149
6.4 The Error Propagation Law......Page 150
6.4.1 Example 6.2-Error Propagation Law......Page 152
6.5 Non-linear Limit State Functions......Page 153
6.5.1 Example 6.3-FORM-Non-linear Limit State Function......Page 154
6.6 Simulation Methods......Page 156
6.6.1 Example 6.4: Monte Carlo Simulation......Page 157
6.7 Self Assessment Questions/Exercises......Page 159
Lecture 13 (Aim of the Present Lecture)......Page 160
7.2 The Decision/Event Tree......Page 161
7.3 Decisions Based on Expected Values......Page 162
7.5 Decision Analysis with Given Information-Prior Analysis......Page 164
7.6 Decision Analysis with Additional Information-Posterior Analysis......Page 165
7.7 Decision Analysis with `Unknown\' Information-Pre-posterior Analysis......Page 168
7.8 The Risk Treatment Decision Problem......Page 169
7.9 Self Assessment Questions/Exercises......Page 171
A.1 Chapter 1......Page 172
A.2 Chapter 2......Page 173
A.3 Chapter 3......Page 175
A.4 Chapter 4......Page 176
A.5 Chapter 5......Page 178
A.6 Chapter 6......Page 180
A.7 Chapter 7......Page 184
B.1.2 Equation 5.71......Page 188
B.1.3 Examples on Chi-Square Significance Test......Page 189
B.2.2 Example 6.3......Page 190
Appendix C: Tables......Page 194
References......Page 202
Index......Page 204