Statistics in Engineering: With Examples in MATLAB® and R, Second Edition, 2nd Edition (Hardback) book cover

Statistics in Engineering

With Examples in MATLAB® and R, Second Edition, 2nd Edition

By Andrew Metcalfe, David Green, Tony Greenfield, Mayhayaudin Mansor, Andrew Smith, Jonathan Tuke

Chapman and Hall/CRC

792 pages | 100 B/W Illus.

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Description

Engineers are expected to design structures and machines that can operate in challenging and volatile environments, while allowing for variation in materials and noise in measurements and signals. Statistics in Engineering, Second Edition: With Examples in MATLAB and R covers the fundamentals of probability and statistics and explains how to use these basic techniques to estimate and model random variation in the context of engineering analysis and design in all types of environments.

The first eight chapters cover probability and probability distributions, graphical displays of data and descriptive statistics, combinations of random variables and propagation of error, statistical inference, bivariate distributions and correlation, linear regression on a single predictor variable, and the measurement error model. This leads to chapters including multiple regression; comparisons of several means and split-plot designs together with analysis of variance; probability models; and sampling strategies. Distinctive features include: 

  • All examples based on work in industry, consulting to industry, and research for industry 
  • Examples and case studies include all engineering disciplines
  • Emphasis on probabilistic modeling including decision trees, Markov chains and processes, and structure functions
  • Intuitive explanations are followed by succinct mathematical justifications
  • Emphasis on random number generation that is used for stochastic simulations of engineering systems, demonstration of key concepts, and implementation of bootstrap methods for inference
  • Use of MATLAB and the open source software R, both of which have an extensive range of statistical functions for standard analyses and also enable programing of specific applications
  • Use of multiple regression for times series models and analysis of factorial and central composite designs 
  • Inclusion of topics such as Weibull analysis of failure times and split-plot designs that are commonly used in industry but are not usually included in introductory textbooks
  • Experiments designed to show fundamental concepts that have been tested with large classes working in small groups
  • Website with additional materials that is regularly updated

Andrew Metcalfe, David Green, Andrew Smith, and Jonathan Tuke have taught probability and statistics to students of engineering at the University of Adelaide for many years and have substantial industry experience. Their current research includes applications to water resources engineering, mining, and telecommunications. Mahayaudin Mansor worked in banking and insurance before teaching statistics and business mathematics at the Universiti Tun Abdul Razak Malaysia and is currently a researcher specializing in data analytics and quantitative research in the Health Economics and Social Policy Research Group at the Australian Centre for Precision Health, University of South Australia. Tony Greenfield, formerly Head of Process Computing and Statistics at the British Iron and Steel Research Association, is a statistical consultant. He has been awarded the Chambers Medal for outstanding services to the Royal Statistical Society; the George Box Medal by the European Network for Business and Industrial Statistics for Outstanding Contributions to Industrial Statistics; and the William G. Hunter Award by the American Society for Quality.

 

 

Reviews

"Statistics in Engineering: With Examples in MATLAB and R" is an ideal and unreservedly recommended textbook for college and university library collections."

John Burroughs, Reviewer's Bookwatch

Table of Contents

I Foundations

  1. Why Understand Statistics?
  2. Introduction

    Using the book

    Software

  3. Probability and Making Decisions
  4. Introduction

    Random digits

    Concepts and uses

    Generating random digits

    Pseudo random digits

    Defining probabilities

    Defining probabilities {Equally likely outcomes

    Defining probabilities {relative frequencies

    Defining probabilities {subjective probability and expected monetary value

    Axioms of Probability

    The addition rule of probability

    Complement

    Conditional probability

    Conditioning on information

    Conditional probability and the multiplicative rule

    Independence

    Tree diagrams

    Bayes' theorem

    Law of total probability

    Bayes' theorem for two events

    Bayes' theorem for any number of events

    Decision trees

    Permutations and combinations

    Simple random sample

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  5. Graphical Displays of Data and Descriptive Statistics
  6. Types of variables

    Samples and populations

    Displaying data

    Stem-and-leaf plot

    Time series plot

    Pictogram

    Pie chart

    Bar chart

    Rose plot

    Line chart for discrete variables

    Histogram and cumulative frequency polygon for continuous variables

    Pareto chart

    Numerical summaries of data

    Population and sample

    Measures of location

    Measures of spread

    Box-plots

    Outlying values and robust statistics

    Outlying values

    Robust statistics

    Grouped data

    Calculation of the mean and standard deviation for discrete data

    Grouped continuous data [mean and sd for grouped continuous data]

    Mean as center of gravity

    Case study of wave stress on offshore structure

    Shape of distributions

    Skewness

    Kurtosis

    Some contrasting histograms

    Multivariate data

    Scatter plot

    Histogram for bivariate data

    Parallel coordinates plot

    Descriptive time series

    Definition of time series

    Missing values in time series

    Decomposition of time series

    Centered moving average

    Additive monthly model

    Multiplicative monthly model

    Seasonal adjustment

    Forecasting

    Index numbers

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  7. Discrete Probability Distributions
  8. Discrete random variables

    Definition of a discrete probability distribution

    Expected value

    Bernoulli trial

    Binomial distribution

    Introduction

    Defining the Binomial distribution

    A model for conductivity

    Random deviates from binomial distribution

    Fitting a binomial distribution

    Hypergeometric distribution

    Defining the hypergeometric distribution

    Random deviates from the hypergeometric distribution

    Fitting the hypergeometric distribution

    Negative binomial distribution

    The geometric distribution

    Defining the negative binomial distribution

    Applications of negative binomial distribution

    Fitting a negative binomial distribution

    Random numbers from a negative binomial distribution

    Poisson process

    Defining a Poisson process in time

    Superimposing Poisson processes

    Spatial Poisson Process

    Modifications to Poisson processes

    Poisson distribution

    Fitting a Poisson distribution

    Times between events

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  9. Continuous Probability Distributions
  10. Continuous probability distributions

    Definition of a continuous random variable

    Definition of a continuous probability distribution

    Moments of a continuous probability distribution

    Median and mode of a continuous probability distribution

    Parameters of probability distributions

    Uniform distribution

    Definition of a uniform distribution

    Applications of the uniform distribution

    Random deviates from a uniform distribution

    Distribution of F(X) is uniform

    Fitting a uniform distribution

    Exponential distribution

    Definition of an exponential distribution

    Markov property

    Poisson process

    Lifetime distribution

    Applications of the exponential distribution

    Random deviates from an exponential distribution

    Fitting an exponential distribution

    Normal (Gaussian) distribution

    Definition of a normal distribution

    The standard normal distribution

    Applications of the normal distribution

    Random numbers from a normal distribution

    Fitting a normal distribution

    Probability plots

    Quantile-quantile plots

    Probability plot

    Lognormal distribution

    Definition of a lognormal distribution

    Applications of the lognormal distribution

    Random numbers from lognormal distribution

    Fitting a lognormal distribution

    Gamma distribution

    Definition of a gamma distribution

    Applications of the gamma distribution

    Random deviates from gamma distribution

    Fitting a gamma distribution

    Gumbel distribution

    Definition of a Gumbel distribution

    Applications of the Gumbel distribution

    Random deviates from a Gumbel distribution

    Fitting a Gumbel distribution

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  11. Correlation and Functions of Random Variables
  12. Introduction

    Sample covariance and correlation coefficient

    Defining sample covariance

    Bivariate distributions, population covariance and correlation coefficient

    Population covariance and correlation coefficient

    Bivariate distributions - discrete case

    Bivariate distributions - continuous case

    Marginal distributions

    Bivariate histogram

    Covariate and correlation

    Bivariate probability distributions

    Copulas

    Linear combination of random variables (propagation of error)

    Mean and variance of a linear combination of random variables

    Bounds for correlation coefficient

    Linear combination of normal random variables

    Central Limit Theorem and distribution of the sample mean

    Non-linear functions of random variables (propagation of error)

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  13. Estimation and Inference
  14. Introduction

    Statistics as estimators

    Population parameters

    Sample statistics and sampling distributions

    Bias and MSE

    Accuracy and precision

    Precision of estimate of population mean

    Confidence interval for population mean when _ known

    Confidence interval for mean when _ unknown

    Construction of confidence interval and rationale for the t-

    distribution

    The t-distribution

    Robustness

    Bootstrap methods

    Bootstrap resampling

    Basic bootstrap confidence intervals

    Percentile bootstrap confidence intervals

    Parametric bootstrap

    Hypothesis testing

    Hypothesis test for population mean when _ known

    Hypothesis test for population mean when _ unknown

    Relation between a hypothesis test and the confidence interval

    p-value

    One-sided confidence intervals and one-sided tests

    Sample size

    Confidence interval for a population variance and standard deviation

    Comparison of means

    Independent Samples

    Population standard deviations differ

    Population standard deviations assumed equal

    Matched pairs

    Comparing variances

    Inference about proportions

    Single sample

    Comparing two proportions

    McNemar's test

    Prediction intervals and statistical tolerance intervals

    Prediction interval

    Statistical tolerance interval

    Goodness of _t tests

    Chi-square test

    Empirical distribution function tests

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  15. Linear Regression and Linear Relationships
  16. Linear regression

    Introduction

    The model

    Fitting the model

    Fitting the regression line

    Identical forms for the least squares estimate of the slope

    Relation to correlation

    Alternative form for the fitted regression line

    Residuals

    Identities satisfied by the residuals

    Estimating the standard deviation of the errors

    Checking assumptions A, A and A

    Properties of the estimators

    Estimator of the slope

    Estimator of the intercept

    Predictions

    Confidence interval for mean value of Y given x

    Limits of Prediction

    Plotting confidence intervals and prediction limits

    Summarizing the algebra

    Coefficient of determination R

    Regression for a bivariate normal distribution

    The bivariate normal distribution

    Regression towards the mean

    Relationship between correlation and regression

    Values of x are assumed to be measured without error and can be

    preselected

    The data pairs are assumed to be a random sample from a bivariate

    normal distribution

    Fitting a linear relationship when both variables are measured with error

    Calibration lines

    Intrinsically linear models

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

    II Developments

  17. Multiple Regression
  18. Introduction

    Multivariate data

    Multiple regression model

    The linear model

    Random vectors

    Definition

    Linear transformations of a random vector

    Multivariate normal distribution

    Matrix formulation of the linear model

    Geometrical interpretation

    Fitting the model

    Principle of least squares

    Multivariate calculus - three basic results

    The least squares estimator of the coefficients

    Estimating the coefficients

    Estimating the standard deviation of the errors

    Standard errors of the estimators of the coefficients

    Assessing the fit

    The residuals

    R-squared

    F-statistic

    Cross validation

    Predictions

    Building multiple regression models

    Interactions

    Categorical variables

    F-test for an added set of variables

    Quadratic terms

    Guidelines formatting regression models

    Time series

    Introduction

    Aliasing and sampling intervals

    Fitting a trend and seasonal variation with regression

    Autocovariance and autocorrelation

    Defining autocovariance for a stationary times series model

    Defining sample autocovariance and the correlogram

    Autoregressive models

    AR() and AR() models

    Non-linear least squares

    Generalized linear model

    Logistic regression

    Poisson regression

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  19. Statistical Quality Control
  20. Continuous improvement

    Defining quality

    Taking measurements

    Avoiding rework

    Strategies for quality improvement

    Quality management systems

    Implementing continuous improvement

    Process stability

    Runs chart

    Histograms and boxplots

    Components of variance

    Capability

    Process capability index

    Process performance index

    One-sided process capability indices

    Reliability

    Introduction

    Reliability of components

    Reliability function and the failure rate

    Weibull analysis

    Definition of the Weibull distribution

    Weibull quantile plot

    Censored data

    Maximum likelihood

    Kaplan-Meier estimator of reliability

    Acceptance sampling

    Statistical quality control charts

    Shewhart mean and range chart for continuous variables

    Mean chart

    Range chart

    p-charts for proportions

    c-charts for counts

    Cumulative sum charts

    Multivariate control charts

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  21. Design of Experiments with Regression analysis
  22. Introduction

    Factorial designs with factors at two levels

    Full factorial designs

    Setting up a k design

    Analysis of k design

    Fractional factorial designs

    Central composite designs

    Evolutionary operation (EVOP)

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  23. Design of Experiments and Analysis of Variance
  24. Introduction

    Comparison of several means with one-way ANOVA

    Defining the model

    Multiple comparisons

    One-way ANOVA

    Testing HO

    Follow up procedure

    Two factors at multiple levels

    Two factors without replication (two-way ANOVA)

    Two factors with replication (three-way ANOVA)

    Randomized block design

    Split plot design

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  25. Probability Models
  26. System Reliability

    Series system

    Parallel system

    k-out-of-n system

    Modules

    Duality

    Paths and Cut sets

    Reliability function

    Redundancy

    Non-repairable systems

    Standby systems

    Common cause failures

    Reliability bounds

    Markov chains

    Discrete Markov chain

    Equilibrium Behavior of irreducible Markov Chains

    Methods for solving equilibrium equations

    Absorbing Markov Chains

    Markov chains in continuous time

    Simulation of systems

    The simulation procedure

    Drawing inference from simulation outputs

    Variance reduction

    Summary

    Notation

    Summary of main results

    MATLAB and R commands

    Exercises

  27. Sampling Strategies

Introduction

Simple random sampling from a finite population

Finite population correction

Randomization theory

Defining the simple random sample

Mean and variance of sample mean

Mean and variance of estimator of population total

Model based analysis

Sample size

Stratified sampling

Principle of stratified sampling

Estimating the population mean and total

Optimal allocation of the sample over strata

Multi-stage sampling

Quota sampling

Ratio estimators and regression estimators

Introduction

Regression estimators

Ratio estimator

Calibration of the unit cost data base

Sources of error in an AMP

Calibration factor

Summary

Notation

Summary of main results

MATLAB and R commands

Exercises

A Notation

B Glossary

C Data

D Getting started in R

E Getting started in MATLAB

F Experiments

G Mathematical explanations of key results

H MATLAB code for selected Figures

I Statistical Tables

About the Authors

Andrew Metcalfe, David Green, Andrew Smith, and Jonathan Tuke have taught probability and statistics to students of engineering at the University of Adelaide for many years and have substantial industry experience. Their current research includes applications to water resources engineering, mining, and telecommunications. Mahayaudin Mansor worked in banking and insurance before teaching statistics and business mathematics at the Universiti Tun Abdul Razak Malaysia and is currently a researcher specializing in data analytics and quantitative research in the Health Economics and Social Policy Research Group at the Australian Centre for Precision Health, University of South Australia. Tony Greenfield, formerly Head of Process Computing and Statistics at the British Iron and Steel Research Association, is a statistical consultant. He has been awarded the Chambers Medal for outstanding services to the Royal Statistical Society; the George Box Medal by the European Network for Business and Industrial Statistics for Outstanding Contributions to Industrial Statistics; and the William G. Hunter Award by the American Society for Quality.

Visit their website here:

http://www.maths.adelaide.edu.au/david.green/BookWebsite/

About the Series

Chapman & Hall/CRC Texts in Statistical Science

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Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General