Title:
Probability concepts in engineering planning and design
Personal Author:
Publication Information:
New York : J. Wiley, 1975
ISBN:
9780471032007
Added Author:
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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000001649429 | TA340 A54 1975 | Open Access Book | Book | Searching... |
Searching... | 30000001649437 | TA340 A54 1975 | Open Access Book | Book | Searching... |
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Table of Contents
| 1 Role of Probability in Engineering |
| 1.1 Introduction |
| 1.2 Uncertainty in Real-World Information |
| 1.2.1 Uncertainty Associated with Randomness |
| 1.2.2 Uncertainty Associated with Imperfect Modeling and Estimation |
| 1.3 Design and Decision-Making Under Uncertainty |
| 1.3.1 Planning and Design of Airport Pavement |
| 1.3.2 Hydrologic Design |
| 1.3.3 Design of Structures and Machines |
| 1.3.4 Geotechnical Design |
| 1.3.5 Construction Planning and Management |
| 1.3.6 Photogrammetric, Geodetic, and Surveying Measurements |
| 1.4 Control and Standards |
| 1.5 Concluding Remarks |
| 2 Basic Probability Concepts |
| 2.1 Events and Probability |
| 2.1.1 Characteristics of Probability Problems |
| 2.1.2 Calculation of Probability |
| 2.2 Elements of Set Theory |
| 2.2.1 Definitions |
| 2.2.2 Combination of Events |
| 2.2.3 Operational Rules |
| 2.3 Mathematics of Probability |
| 2.3.1 Basic Axioms of Probability Addition Rule |
| 2.3.2 Conditional Probability Multiplication Rule |
| 2.3.3 Theorem of Total Probability |
| 2.3.4 Bayes' Theorem |
| 2.4 Concluding Remarks Problems |
| 3 Analytical Models of Random Phenomena |
| 3.1 Random Variables |
| 3.1.1 Probability Distribution of a Random Variable |
| 3.1.2 Main Descriptors of a Random Variable |
| 3.2 Useful Probability Distributions |
| 3.2.1 The Normal Distribution |
| 3.2.2 The Logarithmic Normal Distribution |
| 3.2.3 Bernoulli Sequence and the Binomial Distribution |
| 3.2.4 The Geometric Distribution |
| 3.2.5 The Negative Binomial Distribution |
| 3.2.6 The Poisson Process and Poisson Distribution |
| 3.2.7 The Exponential Distribution |
| 3.2.8 The Gamma Distribution |
| 3.2.9 The Hypergeometric Distribution |
| 3.2.10 The Beta Distribution |
| 3.2.11 Other Distributions |
| 3.3 Multiple Random Variables |
| 3.3.1 Joint and Conditional Probability Distributions |
| 3.3.2 Covariance and Correlation |
| 3.3.3 Conditional Mean and Variance |
| 3.4 Concluding Remarks Problems |
| 4 Functions of Random Variables |
| 4.1 Introduction |
| 4.2 Derived Probability Distributions |
| 4.2.1 Function of Single Random Variable |
| 4.2.2 Function of Multiple Random Variables |
| 4.3 Moments of Functions of Random Variables |
| 4.3.1 Introduction |
| 4.3.2 Mean and Variance of a Linear Function |
| 4.3.3 Product of Independent Variates |
| 4.3.4 Mean and Variance of a General Function |
| 4.4 Concluding Remarks Problems |
| 5 Estimating Parameters from Observational Data |
| 5.1 The Role of Statistical Inference in Engineering |
| 5.1.1 Inherent Variability and Estimation Error |
| 5.2 Classical Approach to Estimation of Parameters |
| 5.2.1 Random Sampling and Point Estimation |
| 5.2.2 Interval Estimation of the Mean |
| 5.2.3 Problems of Measurement Theory |
| 5.2.4 Interval Estimation of the Variance |
| 5.2.5 Estimation of Proportion |
| 5.3 Concluding Remarks Problems |
| 6 Empirical Determination of Distribution Models |
| 6.1 Introduction |
| 6.2 Probability Paper |
| 6.2.1 The Normal Probability Paper |
| 6.2.2 The Log-Normal Probability Paper |
| 6.2.3 Construction of General Probability Paper |
| 6.3 Testing Validity of Assumed Distribution |
| 6.3.1 Chi-Square Test for Distribution |
| 6.3.2 Kolmogorov-Smirnov Test for Distribution |
| 6.4 Concluding Remarks Problems |
| 7 Regression and Correlation Analyses |
| 7.1 Basic Formulation of Linear Regression |
| 7.1.1 Regression with Constant Variance |
| 7.1.2 Regression with Nonconstant Variance |
| 7.2 Multiple Linear Regression |
| 7.3 Nonlinear Regression |
| 7.4 Applications of Regression Analysis in Engineering |
| 7.5 Correlation Analysis |
| 7.5.1 Estimation of Correlation Coefficient |
| 7.6 Concluding Remarks Problems |
| 8 The Bayesian Approach |
| 8.1 Introduction |
| 8.2 Basic Concepts-The Discrete Case |
| 8.3 The Continuous Case |
| 8.3.1 General Formulation |
| 8.3.2 A Special Application of Bayesian Up-dating Process |
| 8.4 Bayesian Concepts in Sampling Theory |
| 8.4.1 General Formulation |
| 8.4.2 Sampling from Normal Population |
| 8.4.3 Error in Estimation |
| 8.4.4 Use of Conjugate Distributions |
| 8.5 Concluding Remarks Problems |
| 9 Elements of Quality Assurance and Acceptance Sampling |
| 9.1 Acceptance Sampling by Attributes |
| 9.1.1 The Operating Characteristic (OC) Curve |
| 9.1.2 The Success Run |
| 9.1.3 The Average Outgoing Quality Curve |
| 9.2 Acceptance Sampling by Variables |
| 9.2.1 Average Quality Criterion, sigma Known |
| 9.2.2 Average Quality Criterion, sigma Unknown |
| 9.2.3 Fraction Defective Criterion |
| 9.3 Multiple-Stage Sampling |
| 9.4 Concluding Remarks Problems |
| Appendix A Probability Tables |
| Table A.1 Table of Standard Normal Probability |
| Table A.2 p-Percentile Values of the t-Distribution |
| Table A.3 p-Percentile Values of the x 2 -Distribution |
| Table A.4 Critical Values of D alpha; in the Kolmogorov-Smirnov Test |
| Appendix B Combinatorial Formulas |
| Appendix C Derivation of the Poisson Distribution |
| References |
| Index |
