| |
| |
Role of Probability in Engineering | |
| |
| |
Introduction | |
| |
| |
Uncertainty in Real-World Information | |
| |
| |
Uncertainty Associated with Randomness | |
| |
| |
Uncertainty Associated with Imperfect Modeling and Estimation | |
| |
| |
Design and Decision-Making Under Uncertainty | |
| |
| |
Planning and Design of Airport Pavement | |
| |
| |
Hydrologic Design | |
| |
| |
Design of Structures and Machines | |
| |
| |
Geotechnical Design | |
| |
| |
Construction Planning and Management | |
| |
| |
Photogrammetric, Geodetic, and Surveying Measurements | |
| |
| |
Control and Standards | |
| |
| |
Concluding Remarks | |
| |
| |
Basic Probability Concepts | |
| |
| |
Events and Probability | |
| |
| |
Characteristics of Probability Problems | |
| |
| |
Calculation of Probability | |
| |
| |
Elements of Set Theory | |
| |
| |
Definitions | |
| |
| |
Combination of Events | |
| |
| |
Operational Rules | |
| |
| |
Mathematics of Probability | |
| |
| |
Basic Axioms of Probability Addition Rule | |
| |
| |
Conditional Probability Multiplication Rule | |
| |
| |
Theorem of Total Probability | |
| |
| |
Bayes' Theorem | |
| |
| |
Concluding Remarks Problems | |
| |
| |
Analytical Models of Random Phenomena | |
| |
| |
Random Variables | |
| |
| |
Probability Distribution of a Random Variable | |
| |
| |
Main Descriptors of a Random Variable | |
| |
| |
Useful Probability Distributions | |
| |
| |
The Normal Distribution | |
| |
| |
The Logarithmic Normal Distribution | |
| |
| |
Bernoulli Sequence and the Binomial Distribution | |
| |
| |
The Geometric Distribution | |
| |
| |
The Negative Binomial Distribution | |
| |
| |
The Poisson Process and Poisson Distribution | |
| |
| |
The Exponential Distribution | |
| |
| |
The Gamma Distribution | |
| |
| |
The Hypergeometric Distribution | |
| |
| |
The Beta Distribution | |
| |
| |
Other Distributions | |
| |
| |
Multiple Random Variables | |
| |
| |
Joint and Conditional Probability Distributions | |
| |
| |
Covariance and Correlation | |
| |
| |
Conditional Mean and Variance | |
| |
| |
Concluding Remarks Problems | |
| |
| |
Functions of Random Variables | |
| |
| |
Introduction | |
| |
| |
Derived Probability Distributions | |
| |
| |
Function of Single Random Variable | |
| |
| |
Function of Multiple Random Variables | |
| |
| |
Moments of Functions of Random Variables | |
| |
| |
Introduction | |
| |
| |
Mean and Variance of a Linear Function | |
| |
| |
Product of Independent Variates | |
| |
| |
Mean and Variance of a General Function | |
| |
| |
Concluding Remarks Problems | |
| |
| |
Estimating Parameters from Observational Data | |
| |
| |
The Role of Statistical Inference in Engineering | |
| |
| |
Inherent Variability and Estimation Error | |
| |
| |
Classical Approach to Estimation of Parameters | |
| |
| |
Random Sampling and Point Estimation | |
| |
| |
Interval Estimation of the Mean | |
| |
| |
Problems of Measurement Theory | |
| |
| |
Interval Estimation of the Variance | |
| |
| |
Estimation of Proportion | |
| |
| |
Concluding Remarks Problems | |
| |
| |
Empirical Determination of Distribution Models | |
| |
| |
Introduction | |
| |
| |
Probability Paper | |
| |
| |
The Normal Probability Paper | |
| |
| |
The Log-Normal Probability Paper | |
| |
| |
Construction of General Probability Paper | |
| |
| |
Testing Validity of Assumed Distribution | |
| |
| |
Chi-Square Test for Distribution | |
| |
| |
Kolmogorov-Smirnov Test for Distribution | |
| |
| |
Concluding Remarks Problems | |
| |
| |
Regression and Correlation Analyses | |
| |
| |
Basic Formulation of Linear Regression | |
| |
| |
Regression with Constant Variance | |
| |
| |
Regression with Nonconstant Variance | |
| |
| |
Multiple Linear Regression | |
| |
| |
Nonlinear Regression | |
| |
| |
Applications of Regression Analysis in Engineering | |
| |
| |
Correlation Analysis | |
| |
| |
Estimation of Correlation Coefficient | |
| |
| |
Concluding Remarks Problems | |
| |
| |
The Bayesian Approach | |
| |
| |
Introduction | |
| |
| |
Basic Concepts-The Discrete Case | |
| |
| |
The Continuous Case | |
| |
| |
General Formulation | |
| |
| |
A Special Application of Bayesian Up-dating Process | |
| |
| |
Bayesian Concepts in Sampling Theory | |
| |
| |
General Formulation | |
| |
| |
Sampling from Normal Population | |
| |
| |
Error in Estimation | |
| |
| |
Use of Conjugate Distributions | |
| |
| |
Concluding Remarks Problems | |
| |
| |
Elements of Quality Assurance and Acceptance Sampling | |
| |
| |
Acceptance Sampling by Attributes | |
| |
| |
The Operating Characteristic (OC) Curve | |
| |
| |
The Success Run | |
| |
| |
The Average Outgoing Quality Curve | |
| |
| |
Acceptance Sampling by Variables | |
| |
| |
Average Quality Criterion, sigma Known | |
| |
| |
Average Quality Criterion, sigma Unknown | |
| |
| |
Fraction Defective Criterion | |
| |
| |
Multiple-Stage Sampling | |
| |
| |
Concluding Remarks Problems | |
| |
| |
Probability Tables | |
| |
| |
Table of Standard Normal Probability | |
| |
| |
p-Percentile Values of the t-Distribution | |
| |
| |
p-Percentile Values of the x 2 -Distribution | |
| |
| |
Critical Values of D alpha; in the Kolmogorov-Smirnov Test | |
| |
| |
Combinatorial Formulas | |
| |
| |
Derivation of the Poisson Distribution | |
| |
| |
References | |
| |
| |
Index | |