Statistics in Engineering With Examples in MATLAB r and R 2nd edition by Andrew Metcalfe, David Green, Tony Greenfield, Mayhayaudin Mansor, Andrew Smith, Jonathan Tuke ISBN 1439895474 9781439895474

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ISBN 10: 1439895474
ISBN 13: 9781439895474
Author: Andrew Metcalfe, David Green, Tony Greenfield, Mayhayaudin Mansor, Andrew Smith, Jonathan Tuke

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.

Statistics in Engineering With Examples in MATLAB(r) and R 2nd Table of contents:

1 Why understand statistics?

1.1 Introduction

1.2 Using the book

1.3 Software

2 Probability and making decisions

2.1 Introduction

2.2 Random digits

2.2.1 Concepts and uses

2.2.2 Generating random digits

2.2.3 Pseudo random digits

2.3 Defining probabilities

2.3.1 Defining probabilities – Equally likely outcomes

2.3.2 Defining probabilities – Relative frequencies

2.3.3 Defining probabilities – Subjective probability and expected monetary value

2.4 Axioms of probability

2.5 The addition rule of probability

2.5.1 Complement

2.6 Conditional probability

2.6.1 Conditioning on information

2.6.2 Conditional probability and the multiplicative rule

2.6.3 Independence

2.6.4 Tree diagrams

2.7 Bayes’ theorem

2.7.1 Law of total probability

2.7.2 Bayes’ theorem for two events

2.7.3 Bayes’ theorem for any number of events

2.8 Decision trees

2.9 Permutations and combinations

2.10 Simple random sample

2.11 Summary

2.11.1 Notation

2.11.2 Summary of main results

2.11.3 MATLAB® and R commands

2.12 Exercises

3 Graphical displays of data and descriptive statistics

3.1 Types of variables

3.2 Samples and populations

3.3 Displaying data

3.3.1 Stem-and-leaf plot

3.3.2 Time series plot

3.3.3 Pictogram

3.3.4 Pie chart

3.3.5 Bar chart

3.3.6 Rose plot

3.3.7 Line chart for discrete variables

3.3.8 Histogram and cumulative frequency polygon for continuous variables

3.3.9 Pareto chart

3.4 Numerical summaries of data

3.4.1 Population and sample

3.4.2 Measures of location

3.4.3 Measures of spread

3.5 Box-plots

3.6 Outlying values and robust statistics

3.6.1 Outlying values

3.6.2 Robust statistics

3.7 Grouped data

3.7.1 Calculation of the mean and standard deviation for discrete data

3.7.2 Grouped continuous data [Mean and standard deviation for grouped continuous data]

3.7.3 Mean as center of gravity

3.7.4 Case study of wave stress on offshore structure

3.8 Shape of distributions

3.8.1 Skewness

3.8.2 Kurtosis

3.8.3 Some contrasting histograms

3.9 Multivariate data

3.9.1 Scatter plot

3.9.2 Histogram for bivariate data

3.9.3 Parallel coordinates plot

3.10 Descriptive time series

3.10.1 Definition of time series

3.10.2 Missing values in time series

3.10.3 Decomposition of time series

3.10.3.1 Trend – Centered moving average

3.10.3.2 Seasonal component – Additive monthly model

3.10.3.3 Seasonal component – Multiplicative monthly model

3.10.3.4 Seasonal adjustment

3.10.3.5 Forecasting

3.10.4 Index numbers

3.11 Summary

3.11.1 Notation

3.11.2 Summary of main results

3.11.3 MATLAB and R commands

3.12 Exercises

4 Discrete probability distributions

4.1 Discrete random variables

4.1.1 Definition of a discrete probability distribution

4.1.2 Expected value

4.2 Bernoulli trial

4.2.1 Introduction

4.2.2 Defining the Bernoulli distribution

4.2.3 Mean and variance of the Bernoulli distribution

4.3 Binomial distribution

4.3.1 Introduction

4.3.2 Defining the Binomial distribution

4.3.3 A model for conductivity

4.3.4 Mean and variance of the binomial distribution

4.3.5 Random deviates from binomial distribution

4.3.6 Fitting a binomial distribution

4.4 Hypergeometric distribution

4.4.1 Defining the hypergeometric distribution

4.4.2 Random deviates from the hypergeometric distribution

4.4.3 Fitting the hypergeometric distribution

4.5 Negative binomial distribution

4.5.1 The geometric distribution

4.5.2 Defining the negative binomial distribution

4.5.3 Applications of negative binomial distribution

4.5.4 Fitting a negative binomial distribution

4.5.5 Random numbers from a negative binomial distribution

4.6 Poisson process

4.6.1 Defining a Poisson process in time

4.6.2 Superimposing Poisson processes

4.6.3 Spatial Poisson process

4.6.4 Modifications to Poisson processes

4.6.5 Poisson distribution

4.6.6 Fitting a Poisson distribution

4.6.7 Times between events

4.7 Summary

4.7.1 Notation

4.7.2 Summary of main results

4.7.3 MATLAB and R commands

4.8 Exercises

5 Continuous probability distributions

5.1 Continuous random variables

5.1.1 Definition of a continuous random variable

5.1.2 Definition of a continuous probability distribution

5.1.3 Moments of a continuous probability distribution

5.1.4 Median and mode of a continuous probability distribution

5.1.5 Parameters of probability distributions

5.2 Uniform distribution

5.2.1 Definition of a uniform distribution

5.2.2 Applications of the uniform distribution

5.2.3 Random deviates from a uniform distribution

5.2.4 Distribution of F(X) is uniform

5.2.5 Fitting a uniform distribution

5.3 Exponential distribution

5.3.1 Definition of an exponential distribution

5.3.2 Markov property

5.3.2.1 Poisson process

5.3.2.2 Lifetime distribution

5.3.3 Applications of the exponential distribution

5.3.4 Random deviates from an exponential distribution

5.3.5 Fitting an exponential distribution

5.4 Normal (Gaussian) distribution

5.4.1 Definition of a normal distribution

5.4.2 The standard normal distribution Z ~ N (0,1)

5.4.3 Applications of the normal distribution

5.4.4 Random numbers from a normal distribution

5.4.5 Fitting a normal distribution

5.5 Probability plots

5.5.1 Quantile-quantile plots

5.5.2 Probability plot

5.6 Lognormal distribution

5.6.1 Definition of a lognormal distribution

5.6.2 Applications of the lognormal distribution

5.6.3 Random numbers from lognormal distribution

5.6.4 Fitting a lognormal distribution

5.7 Gamma distribution

5.7.1 Definition of a gamma distribution

5.7.2 Applications of the gamma distribution

5.7.3 Random deviates from gamma distribution

5.7.4 Fitting a gamma distribution

5.8 Gumbel distribution

5.8.1 Definition of a Gumbel distribution

5.8.2 Applications of the Gumbel distribution

5.8.3 Random deviates from a Gumbel distribution

5.8.4 Fitting a Gumbel distribution

5.9 Summary

5.9.1 Notation

5.9.2 Summary of main results

5.9.3 MATLAB and R commands

5.10 Exercises

6 Correlation and functions of random variables

6.1 Introduction

6.2 Sample covariance and correlation coefficient

6.2.1 Defining sample covariance

6.3 Bivariate distributions, population covariance and correlation coefficient

6.3.1 Population covariance and correlation coefficient

6.3.2 Bivariate distributions – Discrete case

6.3.3 Bivariate distributions – Continuous case

6.3.3.1 Marginal distributions

6.3.3.2 Bivariate histogram

6.3.3.3 Covariate and correlation

6.3.3.4 Bivariate probability distributions

6.3.4 Copulas

6.4 Linear combination of random variables (propagation of error)

6.4.1 Mean and variance of a linear combination of random variables

6.4.1.1 Bounds for correlation coefficient

6.4.2 Linear combination of normal random variables

6.4.3 Central Limit Theorem and distribution of the sample mean

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

6.6 Summary

6.6.1 Notation

6.6.2 Summary of main results

6.6.3 MATLAB and R commands

6.7 Exercises

7 Estimation and inference

7.1 Introduction

7.2 Statistics as estimators

7.2.1 Population parameters

7.2.2 Sample statistics and sampling distributions

7.2.3 Bias and MSE

7.3 Accuracy and precision

7.4 Precision of estimate of population mean

7.4.1 Confidence interval for population mean when σ known

7.4.2 Confidence interval for mean when σ unknown

7.4.2.1 Construction of confidence interval and rationale for the t-distribution

7.4.2.2 The t-distribution

7.4.3 Robustness

7.4.4 Bootstrap methods

7.4.4.1 Bootstrap resampling

7.4.4.2 Basic bootstrap confidence intervals

7.4.4.3 Percentile bootstrap confidence intervals

7.4.5 Parametric bootstrap

7.5 Hypothesis testing

7.5.1 Hypothesis test for population mean when σ known

7.5.2 Hypothesis test for population mean when σ unknown

7.5.3 Relation between a hypothesis test and the confidence interval

7.5.4 p-value

7.5.5 One-sided confidence intervals and one-sided tests

7.6 Sample size

7.7 Confidence interval for a population variance and standard deviation

7.8 Comparison of means

7.8.1 Independent samples

7.8.1.1 Population standard deviations differ

7.8.1.2 Population standard deviations assumed equal

7.8.2 Matched pairs

7.9 Comparing variances

7.10 Inference about proportions

7.10.1 Single sample

7.10.2 Comparing two proportions

7.10.3 McNemar’s test

7.11 Prediction intervals and statistical tolerance intervals

7.11.1 Prediction interval

7.11.2 Statistical tolerance interval

7.12 Goodness of fit tests

7.12.1 Chi-square test

7.12.2 Empirical distribution function tests

7.13 Summary

7.13.1 Notation

7.13.2 Summary of main results

7.13.3 MATLAB and R commands

7.14 Exercises

8 Linear regression and linear relationships

8.1 Linear regression

8.1.1 Introduction

8.1.2 The model

8.1.3 Fitting the model

8.1.3.1 Fitting the regression line

8.1.3.2 Identical forms for the least squares estimate of the slope

8.1.3.3 Relation to correlation

8.1.3.4 Alternative form for the fitted regression line

8.1.3.5 Residuals

8.1.3.6 Identities satisfied by the residuals

8.1.3.7 Estimating the standard deviation of the errors

8.1.3.8 Checking assumptions A3, A4 and A5

8.1.4 Properties of the estimators

8.1.4.1 Estimator of the slope

8.1.4.2 Estimator of the intercept

8.1.5 Predictions

8.1.5.1 Confidence interval for mean value of Y given x

8.1.5.2 Limits of prediction

8.1.5.3 Plotting confidence intervals and prediction limits

8.1.6 Summarizing the algebra

8.1.7 Coefficient of determination R2

8.2 Regression for a bivariate normal distribution

8.2.1 The bivariate normal distribution

8.3 Regression towards the mean

8.4 Relationship between correlation and regression

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

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

8.5 Fitting a linear relationship when both variables are measured with error

8.6 Calibration lines

8.7 Intrinsically linear models

8.8 Summary

8.8.1 Notation

8.8.2 Summary of main results

8.8.3 MATLAB and R commands

8.9 Exercises

9 Multiple regression

9.1 Introduction

9.2 Multivariate data

9.3 Multiple regression model

9.3.1 The linear model

9.3.2 Random vectors

9.3.2.1 Linear transformations of a random vector

9.3.2.2 Multivariate normal distribution

9.3.3 Matrix formulation of the linear model

9.3.4 Geometrical interpretation

9.4 Fitting the model

9.4.1 Principle of least squares

9.4.2 Multivariate calculus – Three basic results

9.4.3 The least squares estimator of the coefficients

9.4.4 Estimating the coefficients

9.4.5 Estimating the standard deviation of the errors

9.4.6 Standard errors of the estimators of the coefficients

9.5 Assessing the fit

9.5.1 The residuals

9.5.2 R-squared

9.5.3 F-statistic

9.5.4 Cross validation

9.6 Predictions

9.7 Building multiple regression models

9.7.1 Interactions

9.7.2 Categorical variables

9.7.3 F-test for an added set of variables

9.7.4 Quadratic terms

9.7.5 Guidelines for fitting regression models

9.8 Time series

9.8.1 Introduction

9.8.2 Aliasing and sampling intervals

9.8.3 Fitting a trend and seasonal variation with regression

9.8.4 Auto-covariance and auto-correlation

9.8.4.1 Defining auto-covariance for a stationary times series model

9.8.4.2 Defining sample auto-covariance and the correlogram

9.8.5 Auto-regressive models

9.8.5.1 AR(1) and AR(2) models

9.9 Non-linear least squares

9.10 Generalized linear model

9.10.1 Logistic regression

9.10.2 Poisson regression

9.11 Summary

9.11.1 Notation

9.11.2 Summary of main results

9.11.3 MATLAB and R commands

9.12 Exercises

10 Statistical quality control

10.1 Continuous improvement

10.1.1 Defining quality

10.1.2 Taking measurements

10.1.3 Avoiding rework

10.1.4 Strategies for quality improvement

10.1.5 Quality management systems

10.1.6 Implementing continuous improvement

10.2 Process stability

10.2.1 Runs chart

10.2.2 Histograms and box plots

10.2.3 Components of variance

10.3 Capability

10.3.1 Process capability index

10.3.2 Process performance index

10.3.3 One-sided process capability indices

10.4 Reliability

10.4.1 Introduction

10.4.1.1 Reliability of components

10.4.1.2 Reliability function and the failure rate

10.4.2 Weibull analysis

10.4.2.1 Definition of the Weibull distribution

10.4.2.2 Weibull quantile plot

10.4.2.3 Censored data

10.4.3 Maximum likelihood

10.4.4 Kaplan-Meier estimator of reliability

10.5 Acceptance sampling

10.6 Statistical quality control charts

10.6.1 Shewhart mean and range chart for continuous variables

10.6.1.1 Mean chart

10.6.1.2 Range chart

10.6.2 p-charts for proportions

10.6.3 c-charts for counts

10.6.4 Cumulative sum charts

10.6.5 Multivariate control charts

10.7 Summary

10.7.1 Notation

10.7.2 Summary of main results

10.7.3 MATLAB and R commands

10.8 Exercises

11 Design of experiments with regression analysis

11.1 Introduction

11.2 Factorial designs with factors at two levels

11.2.1 Full factorial designs

11.2.1.1 Setting up a 2k design

11.2.1.2 Analysis of 2k design

11.3 Fractional factorial designs

11.4 Central composite designs

11.5 Evolutionary operation (EVOP)

11.6 Summary

11.6.1 Notation

11.6.2 Summary of main results

11.6.3 MATLAB and R commands

11.7 Exercises

12 Design of experiments and analysis of variance

12.1 Introduction

12.2 Comparison of several means with one-way ANOVA

12.2.1 Defining the model

12.2.2 Limitation of multiple t-tests

12.2.3 One-way ANOVA

12.2.4 Testing HO0

12.2.5 Follow up procedure

12.3 Two factors at multiple levels

12.3.1 Two factors without replication (two-way ANOVA)

12.3.2 Two factors with replication (three-way ANOVA)

12.4 Randomized block design

12.5 Split plot design

12.6 Summary

12.6.1 Notation

12.6.2 Summary of main results

12.6.3 MATLAB and R commands

12.7 Exercises

13 Probability models

13.1 System reliability

13.1.1 Series system

13.1.2 Parallel system

13.1.3 k-out-of-n system

13.1.4 Modules

13.1.5 Duality

13.1.6 Paths and cut sets

13.1.7 Reliability function

13.1.8 Redundancy

13.1.9 Non-repairable systems

13.1.10 Standby systems

13.1.11 Common cause failures

13.1.12 Reliability bounds

13.2 Markov chains

13.2.1 Discrete Markov chain

13.2.2 Equilibrium behavior of irreducible Markov chains

13.2.3 Methods for solving equilibrium equations

13.2.4 Absorbing Markov chains

13.2.5 Markov chains in continuous time

13.3 Simulation of systems

13.3.1 The simulation procedure

13.3.2 Drawing inference from simulation outputs

13.3.3 Variance reduction

13.4 Summary

13.4.1 Notation

13.4.2 Summary of main results

13.5 Exercises

14 Sampling strategies

14.1 Introduction

14.2 Simple random sampling from a finite population

14.2.1 Finite population correction

14.2.2 Randomization theory

14.2.2.1 Defining the simple random sample

14.2.2.2 Mean and variance of sample mean

14.2.2.3 Mean and variance of estimator of population total

14.2.3 Model based analysis

14.2.4 Sample size

14.3 Stratified sampling

14.3.1 Principle of stratified sampling

14.3.2 Estimating the population mean and total

14.3.3 Optimal allocation of the sample over strata

14.4 Multi-stage sampling

14.5 Quota sampling

14.6 Ratio estimators and regression estimators

14.6.1 Introduction

14.6.2 Regression estimators

14.6.3 Ratio estimator

14.7 Calibration of the unit cost data base

14.7.1 Sources of error in an AMP

14.7.2 Calibration factor

14.8 Summary

14.8.1 Notation

14.8.2 Summary of main results

14.9 Exercises

Appendix A – Notation

A.1 General

A.2 Probability

A.3 Statistics

A.4 Probability distributions

Appendix B – Glossary

Appendix C – Getting started in R

C.1 Installing R

C.2 Using R as a calculator

C.3 Setting the path

C.4 R scripts

C.5 Data entry

C.5.1 From keyboard

C.5.2 From a file

C.5.2.1 Single variable

C.5.2.2 Several variables

C.6 R vectors

C.7 User defined functions

C.8 Matrices

C.9 Loops and conditionals

C.10 Basic plotting

C.11 Installing packages

C.12 Creating time series objects

Appendix D – Getting started in MATLAB

D.1 Installing MATLAB

D.2 Using MATLAB as a calculator

D.3 Setting the path

D.4 MATLAB scripts (m-files)

D.5 Data entry

D.5.1 From keyboard

D.5.2 From a file

D.5.2.1 Single variable

D.5.2.2 Several variables

D.6 MATLAB vectors

D.7 User defined functions

D.8 Matrices

D.9 Loops and conditionals

D.10 Basic plotting

D.11 Creating time series objects

Appendix E – Experiments

E.1 How good is your probability assessment?

E.1.1 Objectives

E.1.2 Experiment

E.1.3 Question sets

E.1.4 Discussion

E.1.5 Follow up questions

E.2 Buffon’s needle

E.2.1 Objectives

E.2.2 Experiment

E.2.3 Questions

E.2.4 Computer simulation

E.2.5 Historical note

E.3 Robot rabbit

E.3.1 Objectives

E.3.2 Experiment

E.3.3 Data

E.3.4 Discussion

E.3.5 Follow up question

E.4 Use your braking brains

E.4.1 Objectives

E.4.2 Experiment

E.4.3 Discussion

E.5 Predicting descent time from payload

E.5.1 Objectives

E.5.2 Experiment

E.5.3 Discussion

E.5.4 Follow up question

E.6 Company efficiency, resources and teamwork

E.6.1 Objectives

E.6.2 Experiment

E.6.3 Discussion

E.7 Factorial experiment – reaction times by distraction, dexterity and distinctness

E.7.1 Aim

E.7.2 Experiment

E.7.3 Analysis

E.7.4 Discussion

E.7.5 Follow up questions

E.8 Weibull analysis of cycles to failure

E.8.1 Aim

E.8.2 Experiment

E.8.3 Weibull plot

E.8.4 Discussion

E.9 Control or tamper?

E.10 Where is the summit?

References

Index

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Tags: Andrew Metcalfe, David Green, Tony Greenfield, Mayhayaudin Mansor, Andrew Smith, Jonathan Tuke, With Examples