Statistics in Engineering

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/

• I Foundations Why Understand Statistics? Introduction Using the book Software Probability and Making Decisions 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 Graphical Displays of Data and Descriptive Statistics 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 Discrete Probability Distributions 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 Continuous Probability Distributions 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 Correlation and Functions of Random Variables 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 Estimation and Inference 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 fit tests Chi-square test Empirical distribution function tests Summary Notation Summary of main results MATLAB and R commands Exercises Linear Regression and Linear Relationships 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 Multiple Regression 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 Statistical Quality Control 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 Design of Experiments with Regression Analysis 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 Design of Experiments and Analysis of Variance 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 Probability Models 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 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

"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"Distinctive features of this new second edition of Statistics in Engineering iinclude: All examples being based on work in industry, consulting to industry, and research for industry; 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 an extensive range of statistical functions for standard analyses and also enable programming of specific applications; Use of multiple regression for times series models and analysis of factorial and central composite for time 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."~Midwest Book Review