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Random Phenomena
Fundamentals of Probability and Statistics for Engineers
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Book Description
Many of the problems that engineers face involve randomly varying phenomena of one sort or another. However, if characterized properly, even such randomness and the resulting uncertainty are subject to rigorous mathematical analysis.
Taking into account the uniquely multidisciplinary demands of 21stcentury science and engineering, Random Phenomena: Fundamentals of Probability and Statistics for Engineers provides students with a working knowledge of how to solve engineering problems that involve randomly varying phenomena. Basing his approach on the principle of theoretical foundations before application, Dr. Ogunnaike presents a classroomtested course of study that explains how to master and use probability and statistics appropriately to deal with uncertainty in standard problems and those that are new and unfamiliar.
Giving students the tools and confidence to formulate practical solutions to problems, this book offers many useful features, including:
As classic scientific boundaries continue to be restructured, the use of engineering is spilling over into more nontraditional areas, ranging from molecular biology to finance. This book emphasizes fundamentals and a "first principles" approach to deal with this evolution. It illustrates theory with practical examples and case studies, equipping readers to deal with a wide range of problems beyond those in the book.
About the Author:
Professor Ogunnaike is Interim Dean of Engineering at the University of Delaware. He is the recipient of the 2008 American Automatic Control Council's Control Engineering Practice Award, the ISA's Donald P. Eckman Education Award, the Slocomb Excellence in Teaching Award, and was elected into the US National Academy of Engineering in 2012.
Table of Contents
Prelude
Approach Philosophy
Four Basic Principles
I Foundations
Two Motivating Examples
Yield Improvement in a Chemical Process
Quality Assurance in a Glass Sheet Manufacturing Process
Outline of a Systematic Approach
Random Phenomena, Variability, and Uncertainty
Two Extreme Idealizations of Natural Phenomena
Random Mass Phenomena
Introducing Probability
The Probabilistic Framework
II Probability
Fundamentals of Probability Theory
Building Blocks
Operations
Probability
Conditional Probability
Independence
Random Variables and Distributions
Distributions
Mathematical Expectation
Characterizing Distributions
Special Derived Probability Functions
Multidimensional Random Variables
Distributions of Several Random Variables
Distributional Characteristics of Jointly Distributed Random Variables
Random Variable Transformations
Single Variable Transformations
Bivariate Transformations
General Multivariate Transformations
Application Case Studies I: Probability
Mendel and Heredity
World War II Warship Tactical Response Under Attack
III Distributions
Ideal Models of Discrete Random Variables
The Discrete Uniform Random Variable
The Bernoulli Random Variable
The Hypergeometric Random Variable
The Binomial Random Variable
Extensions and Special Cases of the Binomial Random Variable
The Poisson Random Variable
Ideal Models of Continuous Random Variables
Gamma Family Random Variables
Gaussian Family Random Variables
Ratio Family Random Variables
Information, Entropy, and Probability Models
Uncertainty and Information
Entropy
Maximum Entropy Principles for Probability Modeling
Some Maximum Entropy Models
Maximum Entropy Models from General Expectations
Application Case Studies II: InVitro Fertilization
InVitro Fertilization and Multiple Births
Probability Modeling and Analysis
Binomial Model Validation
Problem Solution: ModelBased IVF Optimization and Analysis
Sensitivity Analysis
IV Statistics
Introduction to Statistics
From Probability to Statistics
Variable and Data Types
Graphical Methods of Descriptive Statistics
Numerical Descriptions
Sampling
The Distribution of Functions of Random Variables
Sampling Distribution of the Mean
Sampling Distribution of the Variance
Estimation
Criteria for Selecting Estimators
Point Estimation Methods
Precision of Point Estimates
Interval Estimates
Bayesian Estimation
Hypothesis Testing
Basic Concepts
Concerning Single Mean of a Normal Population
Concerning Two Normal Population Means
Determining β, Power, and Sample Size
Concerning Variances of Normal Populations
Concerning Proportions
Concerning NonGaussian Populations
Likelihood Ratio Tests
Discussion
Regression Analysis
Simple Linear Regression
"Intrinsically" Linear Regression
Multiple Linear Regression
Polynomial Regression
Probability Model Validation
Probability Plots
ChiSquared GoodnessofFit Test
Nonparametric Methods
Single Population
Two Populations
Probability Model Validation
A Comprehensive Illustrative Example
Design of Experiments
Analysis of Variance
Single Factor Experiments
TwoFactor Experiments
General Multifactor Experiments
2k Factorial Experiments and Design
Screening Designs: Fractional Factorial
Screening Designs: PlackettBurman
1Response Surface Methodology
Introduction to Optimal Designs
Application Case Studies III: Statistics
Prussian Army DeathbyHorse Kicks
WW II Aerial Bombardment of London
US Population Dynamics: 1790–2000
Process Optimization
V Applications
Reliability and Life Testing
System Reliability
System Lifetime and FailureTime Distributions
The Exponential Reliability Model
The Weibull Reliability Model
Life Testing
Quality Assurance and Control
Acceptance Sampling
Process and Quality Control
Chemical Process Control
Process and Parameter Design
Introduction to Multivariate Analysis
Multivariate Probability Models
Multivariate Data Analysis
Principal Components Analysis
Appendix
Index
Featured Author Profiles
Reviews
The author does an excellent job presenting the material in an interesting way, making connections between theoretical and experimental statistics and between deterministic and probabilistic models. … a good book for engineers. … an excellent introductory mathematical statistics textbook for engineers. I like the fact that the theory is well developed throughout the chapters and that the transition between chapters is smooth. Compared with another introductory statistics resource for engineering (Probability and Statistics for Engineering and the Sciences by Jay Devore), I would choose this text … . I recommend this textbook with full confidence for engineering students who have the strong mathematical background, specifically differential and integral calculus. This book is distinguished from the crowded field by the wellexplained theory of statistics and how it provides interesting applications. The big plus about this text is the variety and large amount of review questions, exercises, and application problems that the author provides, which in my opinion is crucial to the understanding of the theoretical concepts.
—Walid K. Sharabati, The American Statistician, August 2011This book offers many unique features in a crowded field of statistics books for engineers. ... The core concepts are written in an easytounderstand format and students from various engineering disciplines can easily follow the theoretical concepts presented. The examples and application problems are selected from a wide range that spans catalysts in a chemical reactor, invitro fertilization, molecular biology, reliability of parallel computer systems, population demographics, polymers, and finance. … I highly recommend this book for engineering students, professional engineers and applied statisticians dealing with systems involving random phenomena. Instructors who are looking for an alternative textbook should give a serious consideration to adopting this book.
—Ali Cinar, Technometrics, August 2011The theory is built up from reallife examples from which the first principles are deduced. This works well as it becomes immediately clear that these principles are relevant and useful in practical situations. … The book clearly explains both probabilistic and statistical concepts in minute detail and none of the essentials seem to be missing. All this is done without ever resorting to abstract mathematics, which is quite an achievement. … As an engineer involved in statistical data analysis, I would have loved to be taught from a book like this and I heartily recommend this book as a classroom textbook for both the clarity of the explanations and the amount of material covered. The book further accommodates such use with a large amount of review questions, exercises, application problems, and project assignments. However, the book is also suitable for selfstudy … . It will allow engineers who have to deal with statistics, but lack sufficient statistical background, to easily gain fundamental insights that are readily applicable in their working environment.
—Pieter Bastiaan Ober, Journal of Applied Statistics, 2011Introduces the theory by starting from well described engineering examples such that the resulting probability equations appear as the natural outcomes from engineering first principles and not as esoteric mathematics. Engineering significance is then reinforced with discussion of how the results apply to other problems… provide[s] an understanding of why and when statistical methods apply, and equally importantly, when pitfalls lurk. The continual relating of probability and statistics throughout the book is one of its strongest features. … Concepts are clearly explained. A good balance is struck between the providing critical theoretical underpinnings without overwhelming mathematical detail….
Examples from many engineering and science fields illustrate ideas and methods throughout the book, especially in the statistics material. …[presented] examples allow the reader to obtain a sense of the limitations of theory and methods and of the practical judgments required in applications to move to a problem resolution. A useful pedagogical feature is the repeated use of some data sets [on an accompanying CD], allowing students to see how new material provides new understanding.
Although aimed at the textbook market (several syllabus suggestions for 1 and 2semester undergraduate and graduate courses are given in the Preface), Random Phenomena has much to offer the industrial practitioner. As a chemical engineer who came to statistics out of industrial necessity and not from formal training or a career plan, I found new insights despite more than 20 years of practice, which includes providing internal statistics consulting and training
…all the fundamentals needed for further study in any of its topics are certainly provided. In summary, Random Phenomena is an excellent choice for anyone, educator or practitioner, wishing to impart or gain a fundamental understanding of probability and statistics from an engineering perspective.
—Dennis C. Williams, LyondellBasell Industries, The American Institute of Chemical Engineers Journal (AIChE Journal)
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