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Engineering Uncertainty and Risk Analysis : A Balanced Approach to Probability, Statistics, Stochastic Modeling, and Stochastic Differential Equations

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ISBN-10: 096556438X

ISBN-13: 9780965564380

Edition: 2001

Authors: Sergio E. Serrano

List price: $89.00
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Book details

List price: $89.00
Copyright year: 2001
Publisher: HydroScience, Incorporated
Publication date: 1/1/2001
Binding: Perfect 
Pages: 472
Size: 9.00" wide x 7.00" long
Weight: 1.870
Language: English

Engineering Uncertainty Analysisp. 1
Probabilistic Analysis of Engineering Systemsp. 1
The Engineering Methodp. 1
The Origins of Uncertaintyp. 3
Deterministic Versus Probabilistic Analysis of Engineering Systemsp. 5
Method of Uncertainty Analysisp. 12
Questions and Problemsp. 19
The Concept of Probabilityp. 21
Chance Experiments and Their Outcomesp. 21
Estimation of the Number of Possible Outcomesp. 22
Simple Enumerationp. 22
Permutations: Sampling in a Specific Order Without Replacementp. 24
Combinations: Sampling Without a Specific Order and Without Replacementp. 25
Sample Space and Eventsp. 27
Quantitative Evaluation of Probabilityp. 28
The Frequency Definition of probabilityp. 28
Fundamental Axioms of Probabilityp. 31
Additional Probability Relationshipsp. 38
Independence and Conditioning of Probabilistic Eventsp. 38
Statistical Independencep. 40
The Total Probability and Bayes' Theoremsp. 51
Problemsp. 54
Random Variables and Probability Distributionsp. 57
Random Variable: A Function of Probabilityp. 57
Discrete Random Variablesp. 59
The Probability Mass Functionp. 59
The Cumulative Distribution Functionp. 61
Expected Value of a Random Variablep. 63
The Variance of a Random Variablep. 65
The Binomial Random Variablep. 69
The Geometric Random Variablep. 73
The Pascal Random Variablep. 74
The Hypergeometric Random Variablep. 75
The Poisson Random Variablep. 76
Approximation to the Poisson Random Variablep. 79
Continuous Random Variablesp. 80
The Probability Density Functionp. 80
The Cumulative Distribution Functionp. 85
Mean, Variance, and other Moments of Continuous Random Variablesp. 87
The Exponential Random Variablep. 91
The Uniform Random Variablep. 93
The Gaussian Random Variablep. 96
The Lognormal Random Variablep. 101
The Gamma Random Variablep. 103
Other Probability Distributionsp. 106
Problemsp. 107
Simulation of Random Systemsp. 111
Derivation of a System Output Density Functionp. 111
Monte Carlo Simulationp. 116
Generation of Random Numbers from a Specified Density Functionp. 117
Analytical Decomposition of the Transformation Equationp. 122
Numerical Solution of the Transformation Equationp. 125
The Heart of Monte Carlo Simulations: Generation of Uniform Random Numbersp. 128
Generation of Gaussian Random Numbersp. 131
Application of the Transformation Equation: Generation of Random Numbers of Other Probability Distributionsp. 133
Simulation of Systems with Several Random Variablesp. 135
System Sensitivity to Uncertainty in One or More Variablesp. 135
Systems with Several Independent Random Variablesp. 136
Analytical Derivation of Second-Order Statisticsp. 141
Problemsp. 144
Systems with Jointly-Distributed Random Variablesp. 147
Two Discrete Random Variablesp. 147
The Joint Probability Mass Functionp. 147
The Joint Cumulative Distribution Functionp. 150
Marginal Distributionp. 152
Conditional Joint Functionsp. 153
Two Continuous Random Variablesp. 155
The Joint Probability Density Functionp. 155
The Joint Cumulative Distribution Functionp. 157
The Marginal Probability Density Functionsp. 159
Conditional Joint Functionsp. 160
Statistically Independent Random Variablesp. 162
Special Moments of Two Random Variablesp. 162
The Covariance of Two Random Variablesp. 163
The Correlation Coefficient of Two Random Variablesp. 164
The Bivariate Gaussian Density Functionp. 166
System s Forced by Jointly-Distributed Random Variablesp. 168
Output of Sums of Random Variables: The Central Limit Theoremp. 169
Problemsp. 174
Estimation Theory in Engineeringp. 177
Statistics and Uncertainty Analysisp. 177
Population Parameters versus Sample Statisticsp. 178
Probability Distribution of the Sample Meanp. 181
Point Estimatorsp. 182
Estimation with the Method of Momentsp. 183
Estimation with the Method of Maximum Likelihoodp. 183
Interval Estimatorsp. 186
Confidence Intervalsp. 186
Confidence Interval for the Mean (Variance Known)p. 187
Confidence Interval for the Mean (Variance Unknown)p. 191
Confidence Interval for the Variance (Mean Known)p. 195
Confidence Interval for the Variance (Mean Unknown)p. 199
Statistical Testsp. 200
Test for the Population Mean (Variance Known)p. 202
Test for the Population Mean (Variance unknown and N[greater than or equal]60)p. 205
Test for the Population Mean (Variance Unknown and N[60)p. 205
Test for the Population Variance (N[less than or equal]100)p. 207
Test for the Population Variance (N]100)p. 210
Problemsp. 212
Fitting Probability Models to Datap. 215
Empirical Distributionsp. 215
The Frequency Histogram from Observed Datap. 215
The Expected Frequency Histogram from a Theoretical Distributionp. 218
The Empirical Cumulative Distribution Functionp. 222
Statistical Tests for Goodness of Fitp. 226
The Chi Squared Goodness of Fit Testp. 226
Problemsp. 234
Regression Analysisp. 237
Statistical Measures Between Two Random Variablesp. 237
The Sample Covariance and Sample Correlation Coefficientp. 237
The Least-Squares Straight Linep. 239
Fitting a Straight Line through the Scatter Diagramp. 239
Non-Linear Curves Reducible to Straight Linesp. 243
Confidence Intervals of the Regression Modelp. 245
Confidence Interval of the Slope a ([sigma superscript 2 subscript X] Unknown, N[60)p. 246
Confidence Interval of the Slope a ([sigma superscript 2 subscript X] Unknown, 60[less than or equal]N)p. 247
Confidence Interval of the Predicted Y ([sigma superscript 2 subscript X] Unknown, N[60)p. 247
Confidence Interval of the Predicted Y ([sigma superscript 2 subscript X] Unknown, 60[less than or equal]N)p. 248
Confidence Interval of the Intercept b ([sigma superscript 2 subscript X] Unknown, 60[less than or equal]N)p. 249
Confidence Interval of the Intercept b ([sigma superscript 2 subscript X] Unknown, 60[less than or equal]N)p. 249
Problemsp. 255
Reliability of Engineering Systemsp. 257
The Concept of Reliabilityp. 257
Time Reliabilityp. 259
Reliability of Systemsp. 267
Systems in Seriesp. 267
Systems in Parallelp. 270
Hybrid Systemsp. 272
Engineering Models of Failurep. 272
The Weibull Failure Modelp. 272
Fitting Data to a Weibull Failure Modelp. 275
Problemsp. 278
Design of Engineering Experimentsp. 281
The Concept of Statistical Experiment Designp. 281
Estimating the Population Mean from Limited Samplingp. 283
Estimating the Required Number of Measurementsp. 286
Pre-Specified Variancep. 287
Pre-Specified Margin of Errorp. 288
Problemsp. 292
Experiments and Tests for Two or More Populationsp. 293
Comparison of Parameters of Two Populationsp. 293
Test for the Comparison of Means of Two Populations (Variances [sigma superscript 2 subscript X subscript 1] and [sigma superscript 2 subscript X subscript 2] are Known)p. 293
Test for the Comparison of Means of Two Populations ([sigma superscript 2 subscript X subscript 1] and [sigma superscript 2 subscript X subscript 2] are Unknown, [sigma superscript 2 subscript X subscript 1] =[sigma superscript 2 subscript X subscript 2], 60[less than or equal]N[subscript 1] and 60[less than or equal]N[subscript 2])p. 295
Test for the Comparison of Means of Two Populations ([sigma superscript 2 subscript X subscript 1] and [sigma superscript 2 subscript X subscript 2] are Unknown, [sigma superscript 2 subscript X subscript 1] [not equal] [sigma superscript 2 subscript X subscript 2], 60[less than or equal]N[subscript 1] and and 60[less than or equal]N[subscript 2])p. 296
Test for the Comparison of Means of Two Populations ([sigma superscript 2 subscript X subscript 1] and [sigma superscript 2 subscript X subscript 2] are Unknown, [sigma superscript 2 subscript X subscript 1] = [sigma superscript 2 subscript X subscript 2], and N[subscript 1][60 or N[subscript 2][60)p. 296
Test for the Comparison of Means of Two Populations ([sigma superscript 2 subscript X subscript 1] and [sigma superscript 2 subscript X subscript 2] are Unknown, [sigma superscript 2 subscript X subscript 1] [not equal] [sigma superscript 2 subscript X subscript 2], and N[subscript 1][60 or N[subscript 2][60)p. 297
Test for the Comparison of Variances of Two Normal Populationsp. 299
Comparison of Means of Two or More Populations: Single Factor Analysis of Variance (Anova)p. 302
Box Plots and the Logic Behind Anovap. 302
Test for the Comparison of Means of More than Two Normal Populationsp. 307
Problemsp. 314
Stochastic Processesp. 317
The Concept of a Stochastic Processp. 317
First and Second-Order Statisticsp. 322
Density Function and Cumulative Distribution Functionp. 322
Mean, and Correlation Functionsp. 324
Stationarityp. 334
The Correlogramp. 335
Transformations of the Correlation Function: The Spectral Densityp. 340
Some Theoretical Stochastic Processesp. 347
The Random Walk Processp. 347
The Brownian Motion Processp. 348
The White Gaussian Noise Processp. 351
Time Series Analysisp. 353
Time Average Versus Ensemble Propertiesp. 354
Deterministic Trendp. 355
Periodicityp. 356
Models for the Random Componentp. 357
Problemsp. 362
Stochastic Differential Equationsp. 365
The Origin of Stochastic Differential Equationsp. 365
Stochastic Continuity, Differentiation, and Integrationp. 368
Mean Square Continuityp. 368
Stochastic Differentiationp. 369
Stochastic Integralsp. 373
Solving Applied Stochastic Differential Equationsp. 376
Differential Equations with Random Initial Conditionsp. 379
Differential Equations with Random Forcing Functionsp. 391
Solution of Random Equations with Decompositionp. 398
Solving Non-Linear Differential Equationsp. 402
Differential Equations with Random Coefficientsp. 409
Problemsp. 412
Conclusionp. 415
Tablesp. 417
Cumulative Areas under the Standard Normal Probability Density Functionp. 417
Abscissa Values Corresponding to Areas under the Student's t Density Function with m Degrees of Freedomp. 418
Abscissa Values Corresponding to Areas under the Chi-Squared Density Function with m Degrees of Freedomp. 420
Abscissa Values Corresponding to Areas under the F Density Function with and Degrees of Freedomp. 422
Answers to Problemsp. 430
Bibliographyp. 444
Indexp. 450
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