| Engineering Uncertainty Analysis | p. 1 |
| Probabilistic Analysis of Engineering Systems | p. 1 |
| The Engineering Method | p. 1 |
| The Origins of Uncertainty | p. 3 |
| Deterministic Versus Probabilistic Analysis of Engineering Systems | p. 5 |
| Method of Uncertainty Analysis | p. 12 |
| Questions and Problems | p. 19 |
| The Concept of Probability | p. 21 |
| Chance Experiments and Their Outcomes | p. 21 |
| Estimation of the Number of Possible Outcomes | p. 22 |
| Simple Enumeration | p. 22 |
| Permutations: Sampling in a Specific Order Without Replacement | p. 24 |
| Combinations: Sampling Without a Specific Order and Without Replacement | p. 25 |
| Sample Space and Events | p. 27 |
| Quantitative Evaluation of Probability | p. 28 |
| The Frequency Definition of probability | p. 28 |
| Fundamental Axioms of Probability | p. 31 |
| Additional Probability Relationships | p. 38 |
| Independence and Conditioning of Probabilistic Events | p. 38 |
| Statistical Independence | p. 40 |
| The Total Probability and Bayes' Theorems | p. 51 |
| Problems | p. 54 |
| Random Variables and Probability Distributions | p. 57 |
| Random Variable: A Function of Probability | p. 57 |
| Discrete Random Variables | p. 59 |
| The Probability Mass Function | p. 59 |
| The Cumulative Distribution Function | p. 61 |
| Expected Value of a Random Variable | p. 63 |
| The Variance of a Random Variable | p. 65 |
| The Binomial Random Variable | p. 69 |
| The Geometric Random Variable | p. 73 |
| The Pascal Random Variable | p. 74 |
| The Hypergeometric Random Variable | p. 75 |
| The Poisson Random Variable | p. 76 |
| Approximation to the Poisson Random Variable | p. 79 |
| Continuous Random Variables | p. 80 |
| The Probability Density Function | p. 80 |
| The Cumulative Distribution Function | p. 85 |
| Mean, Variance, and other Moments of Continuous Random Variables | p. 87 |
| The Exponential Random Variable | p. 91 |
| The Uniform Random Variable | p. 93 |
| The Gaussian Random Variable | p. 96 |
| The Lognormal Random Variable | p. 101 |
| The Gamma Random Variable | p. 103 |
| Other Probability Distributions | p. 106 |
| Problems | p. 107 |
| Simulation of Random Systems | p. 111 |
| Derivation of a System Output Density Function | p. 111 |
| Monte Carlo Simulation | p. 116 |
| Generation of Random Numbers from a Specified Density Function | p. 117 |
| Analytical Decomposition of the Transformation Equation | p. 122 |
| Numerical Solution of the Transformation Equation | p. 125 |
| The Heart of Monte Carlo Simulations: Generation of Uniform Random Numbers | p. 128 |
| Generation of Gaussian Random Numbers | p. 131 |
| Application of the Transformation Equation: Generation of Random Numbers of Other Probability Distributions | p. 133 |
| Simulation of Systems with Several Random Variables | p. 135 |
| System Sensitivity to Uncertainty in One or More Variables | p. 135 |
| Systems with Several Independent Random Variables | p. 136 |
| Analytical Derivation of Second-Order Statistics | p. 141 |
| Problems | p. 144 |
| Systems with Jointly-Distributed Random Variables | p. 147 |
| Two Discrete Random Variables | p. 147 |
| The Joint Probability Mass Function | p. 147 |
| The Joint Cumulative Distribution Function | p. 150 |
| Marginal Distribution | p. 152 |
| Conditional Joint Functions | p. 153 |
| Two Continuous Random Variables | p. 155 |
| The Joint Probability Density Function | p. 155 |
| The Joint Cumulative Distribution Function | p. 157 |
| The Marginal Probability Density Functions | p. 159 |
| Conditional Joint Functions | p. 160 |
| Statistically Independent Random Variables | p. 162 |
| Special Moments of Two Random Variables | p. 162 |
| The Covariance of Two Random Variables | p. 163 |
| The Correlation Coefficient of Two Random Variables | p. 164 |
| The Bivariate Gaussian Density Function | p. 166 |
| System s Forced by Jointly-Distributed Random Variables | p. 168 |
| Output of Sums of Random Variables: The Central Limit Theorem | p. 169 |
| Problems | p. 174 |
| Estimation Theory in Engineering | p. 177 |
| Statistics and Uncertainty Analysis | p. 177 |
| Population Parameters versus Sample Statistics | p. 178 |
| Probability Distribution of the Sample Mean | p. 181 |
| Point Estimators | p. 182 |
| Estimation with the Method of Moments | p. 183 |
| Estimation with the Method of Maximum Likelihood | p. 183 |
| Interval Estimators | p. 186 |
| Confidence Intervals | p. 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 Tests | p. 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 |
| Problems | p. 212 |
| Fitting Probability Models to Data | p. 215 |
| Empirical Distributions | p. 215 |
| The Frequency Histogram from Observed Data | p. 215 |
| The Expected Frequency Histogram from a Theoretical Distribution | p. 218 |
| The Empirical Cumulative Distribution Function | p. 222 |
| Statistical Tests for Goodness of Fit | p. 226 |
| The Chi Squared Goodness of Fit Test | p. 226 |
| Problems | p. 234 |
| Regression Analysis | p. 237 |
| Statistical Measures Between Two Random Variables | p. 237 |
| The Sample Covariance and Sample Correlation Coefficient | p. 237 |
| The Least-Squares Straight Line | p. 239 |
| Fitting a Straight Line through the Scatter Diagram | p. 239 |
| Non-Linear Curves Reducible to Straight Lines | p. 243 |
| Confidence Intervals of the Regression Model | p. 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 |
| Problems | p. 255 |
| Reliability of Engineering Systems | p. 257 |
| The Concept of Reliability | p. 257 |
| Time Reliability | p. 259 |
| Reliability of Systems | p. 267 |
| Systems in Series | p. 267 |
| Systems in Parallel | p. 270 |
| Hybrid Systems | p. 272 |
| Engineering Models of Failure | p. 272 |
| The Weibull Failure Model | p. 272 |
| Fitting Data to a Weibull Failure Model | p. 275 |
| Problems | p. 278 |
| Design of Engineering Experiments | p. 281 |
| The Concept of Statistical Experiment Design | p. 281 |
| Estimating the Population Mean from Limited Sampling | p. 283 |
| Estimating the Required Number of Measurements | p. 286 |
| Pre-Specified Variance | p. 287 |
| Pre-Specified Margin of Error | p. 288 |
| Problems | p. 292 |
| Experiments and Tests for Two or More Populations | p. 293 |
| Comparison of Parameters of Two Populations | p. 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 Populations | p. 299 |
| Comparison of Means of Two or More Populations: Single Factor Analysis of Variance (Anova) | p. 302 |
| Box Plots and the Logic Behind Anova | p. 302 |
| Test for the Comparison of Means of More than Two Normal Populations | p. 307 |
| Problems | p. 314 |
| Stochastic Processes | p. 317 |
| The Concept of a Stochastic Process | p. 317 |
| First and Second-Order Statistics | p. 322 |
| Density Function and Cumulative Distribution Function | p. 322 |
| Mean, and Correlation Functions | p. 324 |
| Stationarity | p. 334 |
| The Correlogram | p. 335 |
| Transformations of the Correlation Function: The Spectral Density | p. 340 |
| Some Theoretical Stochastic Processes | p. 347 |
| The Random Walk Process | p. 347 |
| The Brownian Motion Process | p. 348 |
| The White Gaussian Noise Process | p. 351 |
| Time Series Analysis | p. 353 |
| Time Average Versus Ensemble Properties | p. 354 |
| Deterministic Trend | p. 355 |
| Periodicity | p. 356 |
| Models for the Random Component | p. 357 |
| Problems | p. 362 |
| Stochastic Differential Equations | p. 365 |
| The Origin of Stochastic Differential Equations | p. 365 |
| Stochastic Continuity, Differentiation, and Integration | p. 368 |
| Mean Square Continuity | p. 368 |
| Stochastic Differentiation | p. 369 |
| Stochastic Integrals | p. 373 |
| Solving Applied Stochastic Differential Equations | p. 376 |
| Differential Equations with Random Initial Conditions | p. 379 |
| Differential Equations with Random Forcing Functions | p. 391 |
| Solution of Random Equations with Decomposition | p. 398 |
| Solving Non-Linear Differential Equations | p. 402 |
| Differential Equations with Random Coefficients | p. 409 |
| Problems | p. 412 |
| Conclusion | p. 415 |
| Tables | p. 417 |
| Cumulative Areas under the Standard Normal Probability Density Function | p. 417 |
| Abscissa Values Corresponding to Areas under the Student's t Density Function with m Degrees of Freedom | p. 418 |
| Abscissa Values Corresponding to Areas under the Chi-Squared Density Function with m Degrees of Freedom | p. 420 |
| Abscissa Values Corresponding to Areas under the F Density Function with and Degrees of Freedom | p. 422 |
| Answers to Problems | p. 430 |
| Bibliography | p. 444 |
| Index | p. 450 |
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