Engineers commonly encounter problems that require them to make decisions under conditions of uncertainty. The uncertainty can be in the definition of the problem, the available information, the alternative solutions and their results, or the random nature of the solution outcomes. As engineers are required to solve increasingly complex design problems with limited resources, they must rely more and more on the proper treatment of uncertainty to make the best decisions. Probability, Statistics, and Reliability for Engineers will assist both engineering students and practicing engineers in understanding the fundamentals of probability, statistics, and reliability methods, especially their applications, limitations, and potentials. Using examples, this practical guide allows engineers to model very complex situations and predict an array of possible outcomes. It will also show readers how to write computational algorithms to solve probability and statistical problems.
Table of Contents:
Introduction: Introduction. - Types of Uncertainty. - Taylor Series Expansion. - Applications. - Problems. - Data Description and Treatment: Introduction.- Classification of Data. - Graphical Description of Data. - Histograms and Frequency Diagrams. - Descriptive Measures. - Applications. - Problems. - Fundamentals Of Probability: Introduction. - Sample Spaces, Sets, and Events. - Mathematics of Probability. - Random Variables and Their Probability Distributions. - Moment.- Common Discrete Probability Distributions. - Common Continuous Probability Distributions. - Applications. - Problems. - Multiple Random Variables: Introduction. - Joint Random Variables and Their Probability Distributions. - Functions of Random Variables. - Applications. - Problems. - Fundamentals of Statistical Analysis: Introduction. - Estimation of Parameters. - Sampling Distributions. - Hypothesis Testing: Procedure. - Hypothesis Tests of Means. - Hypothesis Tests of Variances. - Confidence Intervals. - Sample-Size Determination. - Selection of Model Probability Distributions. - Applications. Problems. - Curve Fitting and Regression Analysis: Introduction. - Correlation Analysis. - Introduction to Regression. - Principle of Least Squares. - Reliability of the Regression Equation. - Reliability of Point Estimates of the Regression Coefficients. - Confidence Intervals of the Regression Equation. - Correlation Versus Regression. - Applications of Bivariate Regression Analysis. - Multiple Regression Analysis. - Regression Analysis of Nonlinear Models. - Applications. Problems. - Simulation: Introduction. - Monte Carlo Simulation. - Random Numbers. - Generation of Random Variables. - Generation of Selected Discrete Random Variables. - Generation of Selected Continuous Random Variables. - Applications. - Problems. - Reliability and Risk Analysis: Introduction. - Time to Failure. - Reliability of Components. - Reliability of Systems. - Risk-Based Decision Analysis. - Applications. - Problems. - Bayesian Methods: Introduction. - Bayesian Probabilities. - Bayesian Estimation of Parameters. - Bayesian Statistics. - Applications. - Problems. - Appendix A: Probability and Statistics Tables. - Appendix B: Values of the Gamma Function. - Subject Index.
Table of Contents:
Introduction: Introduction. - Types of Uncertainty. - Taylor Series Expansion. - Applications. - Problems. - Data Description and Treatment: Introduction.- Classification of Data. - Graphical Description of Data. - Histograms and Frequency Diagrams. - Descriptive Measures. - Applications. - Problems. - Fundamentals Of Probability: Introduction. - Sample Spaces, Sets, and Events. - Mathematics of Probability. - Random Variables and Their Probability Distributions. - Moment.- Common Discrete Probability Distributions. - Common Continuous Probability Distributions. - Applications. - Problems. - Multiple Random Variables: Introduction. - Joint Random Variables and Their Probability Distributions. - Functions of Random Variables. - Applications. - Problems. - Fundamentals of Statistical Analysis: Introduction. - Estimation of Parameters. - Sampling Distributions. - Hypothesis Testing: Procedure. - Hypothesis Tests of Means. - Hypothesis Tests of Variances. - Confidence Intervals. - Sample-Size Determination. - Selection of Model Probability Distributions. - Applications. Problems. - Curve Fitting and Regression Analysis: Introduction. - Correlation Analysis. - Introduction to Regression. - Principle of Least Squares. - Reliability of the Regression Equation. - Reliability of Point Estimates of the Regression Coefficients. - Confidence Intervals of the Regression Equation. - Correlation Versus Regression. - Applications of Bivariate Regression Analysis. - Multiple Regression Analysis. - Regression Analysis of Nonlinear Models. - Applications. Problems. - Simulation: Introduction. - Monte Carlo Simulation. - Random Numbers. - Generation of Random Variables. - Generation of Selected Discrete Random Variables. - Generation of Selected Continuous Random Variables. - Applications. - Problems. - Reliability and Risk Analysis: Introduction. - Time to Failure. - Reliability of Components. - Reliability of Systems. - Risk-Based Decision Analysis. - Applications. - Problems. - Bayesian Methods: Introduction. - Bayesian Probabilities. - Bayesian Estimation of Parameters. - Bayesian Statistics. - Applications. - Problems. - Appendix A: Probability and Statistics Tables. - Appendix B: Values of the Gamma Function. - Subject Index.