1st Edition

Random Phenomena Fundamentals of Probability and Statistics for Engineers

By Babatunde A. Ogunnaike Copyright 2010
    1064 Pages 193 B/W Illustrations
    by CRC Press

    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 21st-century 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 classroom-tested 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:

  • Unique case studies to illustrate the fundamentals and applications of probability and foster understanding of the random variable and its distribution

  • Examples of development, selection, and analysis of probability models for specific random variables

  • Presentation of core concepts and ideas behind statistics and design of experiments

  • Selected "special topics," including reliability and life testing, quality assurance and control, and multivariate analysis
  • As classic scientific boundaries continue to be restructured, the use of engineering is spilling over into more non-traditional 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.

    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
    Conditional Probability
    Random Variables and 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
    Maximum Entropy Principles for Probability Modeling
    Some Maximum Entropy Models
    Maximum Entropy Models from General Expectations
    Application Case Studies II: In-Vitro Fertilization
    In-Vitro Fertilization and Multiple Births
    Probability Modeling and Analysis
    Binomial Model Validation
    Problem Solution: Model-Based 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
    The Distribution of Functions of Random Variables
    Sampling Distribution of the Mean
    Sampling Distribution of the Variance
    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 Non-Gaussian Populations
    Likelihood Ratio Tests
    Regression Analysis
    Simple Linear Regression
    "Intrinsically" Linear Regression
    Multiple Linear Regression
    Polynomial Regression
    Probability Model Validation
    Probability Plots
    Chi-Squared Goodness-of-Fit Test
    Nonparametric Methods
    Single Population
    Two Populations
    Probability Model Validation
    A Comprehensive Illustrative Example
    Design of Experiments
    Analysis of Variance
    Single Factor Experiments
    Two-Factor Experiments
    General Multi-factor Experiments
    2k Factorial Experiments and Design
    Screening Designs: Fractional Factorial
    Screening Designs: Plackett-Burman
    1Response Surface Methodology
    Introduction to Optimal Designs
    Application Case Studies III: Statistics
    Prussian Army Death-by-Horse 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 Failure-Time 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


    Babatunde A. Ogunnaike

    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 well-explained 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 2011

    This book offers many unique features in a crowded field of statistics books for engineers. ... The core concepts are written in an easy-to-understand 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, in-vitro 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 2011 

    The theory is built up from real-life 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 self-study … . 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, 2011

    Introduces 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 2-semester 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)