Applied Statistics for Engineers and Physical Scientists

Chapter 1: Collection and Analysis of Information 1.1 Introduction 1.1.1 Data Collection 1.1.2 Types of Data 1.1.3 The Study of Variability 1.1.4 Distributions 1.1.5 Importance of Variability (or Lack Thereof) for Quality and Productivity Improvement 1.2 Measurements Collected over Time 1.2.1 Time-Sequence Plots 1.2.2 Control Charts: A Special Case of Time-Sequence Plots 1.3 Data Display and Summary 1.3.1 Summary and Display of Measurement Data 1.3.2 Measures of Location 1.3.3 Measures of Variation 1.3.4 Exploratory Data Analysis: Stem-and-Leaf Displays and Box-and-Whisker Plots 1.3.5 Analysis of Categorical Data 1.4 Comparisons of Samples: The Importance of Stratification 1.4.1 Comparing Two Types of Wires 1.4.2 Comparing Lead Concentrations from Two Different Years 1.4.3 Number of Flaws for Three Different Products 1.4.4 Effects of Wind Direction on the Water Levels of Lake Neusiedl 1.5 Graphical Techniques, Correlation, and an Introduction to Least Squares 1.5.1 The Challenger Disaster 1.5.2 The Sample Correlations Coefficient as a Measure of Association in a Scatter Plot 1.5.3 Introduction to Least Squares 1.6 The Importance of Experimentation 1.6.1 Design of Experiments 1.6.2 Design of Experiments with Several Factors and the Determination of Optimum Conditions 1.7 Available Statistical Computer Software and the Visualization of Data 1.7.1 Computer Software 1.7.2 The Visualization of Data Chapter 2: Probability Models and Discrete Distributions 2.1 Probability 2.1.1 The Laws of Probability 2.2 Conditional Probability and Independence 2.2.1 Conditional Probability 2.2.2 Independence 2.2.3 Bayes' Theorem 2.3 Random Variables and Expectations 2.3.1 Random Variables and Their Distributions 2.3.2 Expectations of Random Variables 2.4 The Binomial and Related Distributions 2.4.1 Bernoulli Trials 2.4.2 The Binomial Distribution 2.4.3 The Negative Binomial Distribution 2.4.4 The Hypergeometric Distribution 2.5 Poisson Distribution and Poisson Process 2.5.1 The Poisson Distribution 2.5.2 The Poisson Process 2.6 Multivariate Distributions 2.6.1 Joint, Marginal, and Conditional Distributions 2.6.2 Independence and Dependence of Random Variables 2.6.3 Expectations of Functions of Several Random Variables 2.6.4 Means and Variances of Linear Combinations of Random Variables 2.7 The Estimation of Parameters from Random Samples 2.7.1 Maximum Likelihood Estimation 2.7.2 Examples 2.7.3 Properties of Estimators Chapter 3: Continuous Probability Models 3.1 Continuous Random Variables 3.1.1 Empirical Distributions 3.1.2 Distributions of Continuous Random Variables 3.2 The Normal Distribution 3.3 Other Useful Distributions 3.3.1 Weibull Distribution 3.3.2 Gompertz Distribution 3.3.3 Extreme Value Distribution 3.3.4 Gamma Distribution 3.3.5 Chi-Square Distribution 3.3.6 Lognormal Distribution 3.4 Simulation: Generating Random Variables 3.4.1 Motivation 3.4.2 Generating Discrete Random Variables 3.4.3 Generating Continuous Random Variables 3.5 Distributions of Two or More Continuous Random Variables 3.5.1 Joint, Marginal, and Conditional Distributions, and Mathematical Expectations 3.5.2 Propagation of Errors 3.6 Fitting and Checking Models 3.6.1 Estimation of Parameters 3.6.2 Checking for Normality 3.6.3 Checking Other Models through Quantile-Quantile Plots 3.7 Introduction to Reliability Chapter 4: Statistical Inference: Sampling Distribution, Confidence Intervals, and Tests of Hypotheses 4.1 Sampling Distributions 4.1.1 Introduction and Motivation 4.1.2 Distribution of the Sample Mean X 4.1.3 The Central Limit Theorem 4.1.4 Normal Approximation of the Binomial Distribution 4.2 Confidence Intervals for Means 4.2.1 Determination of the Sample Size 4.2.2 Confidence Intervals for 1- 2 4.3 Inferences from Small Samples and with Unknown Variances 4.3.1 Tolerance Limits 4.3.2 Confidence Intervals for 1- 2 4.4 Other Confidence Intervals 4.4.1 Confidence Intervals for Variances 4.4.2 Confidence Intervals for Proportions 4.5 Tests of Characteristics of a Single Distribution 4.5.1 Introduction 4.5.2 Possible Errors and Operating Characteristic Curves 4.5.3 Tests of Hypotheses When the Sample Size Can Be Selected 4.5.4 Tests of Hypotheses When the Sample Size Is Fixed 4.6 Tests of Characteristics of Two Distributions 4.6.1 Comparing Two Independent Samples 4.6.2 Paired-Sample t-Test 4.6.3 Test of p1= p2 4.6.4 Test of s2/1 = s2/2 4.7 Certain Chi-Square Tests 4.7.1 Testing Hypotheses about Parameters in a Multinomial Distribution 4.7.2 Contingency Tables and Tests of Independence 4.7.3 Goodness-of-Fit Tests Chapter 5: Statistical Process Control 5.1 Shewhart Control Charts 5.1.1 X-Charts and R-charts 5.1.2 p-Charts and c-Charts 5.1.3 Other Control Charts 5.2 Process Capability Indices 5.2.1 Introduction 5.2.2 Process Capability Indices 5.2.3 Discussion of Process Capability Indices 5.3 Acceptance Sampling 5.4 Problem Solving 5.4.1 Introduction 5.4.2 Pareto Diagram 5.4.3 Diagnosis of Causes and Defects 5.4.4 Six Sigma Initiatives Chapter 6: Experiments with One Factor 6.1 Completely Randomized One-Factor Experiments 6.1.1 Analysis-of-Variance Table 6.1.2 F-Test for Treatment Effects 6.1.3 Graphical Comparison of k Samples 6.2 Other Inferences in One-Factor Experiments 6.2.1 Reference Distribution for Treatment Averages 6.2.2 Confidence Intervals for a Particular Difference 6.2.3 Tukey's Multiple-Comparison Procedure 6.2.4 Model Checking 6.2.5 The Random-Effects Model 6.2.6 Computer Software 6.3 Randomized Complete Block Designs 6.3.1 Estimation of Parameters and ANOVA 6.3.2 Expected Mean Squares and Tests of Hypotheses 6.3.3 Increased Efficiency by Blocking 6.3.4 Follow-Up Tests 6.3.5 Diagnostic Checking 6.3.6 Computer Software 6.4 Designs with Two Blocking Variables: Latin Squares 6.4.1 Construction and Randomization of Latin Squares 6.4.2 Analysis of Data from a Latin Square Chapter 7: Experiments with Two or More Factors 7.1 Two-Factor Factorial Designs 7.1.1 Graphics in the Analysis of Two-Factor Experiments 7.1.2 Special Case n = 1 7.1.3 Random Effects 7.1.4 Computer Software 7.2 Nested Factors and Hierarchical Designs 7.3 General Factorial and 2K Factorial Experiments 7.3.1 2 K Factorial Experiments 7.3.2 Significance of Estimated Effects 7.4 2'-K Fractional Factorial Experiments 7.4.1 Half Fractions of 2K Factorial Experiments 7.4.2 Higher Fractions of 2K Factorial Experiments 7.4.3 Computer Software Chapter 8: Regression Analysis 8.1 The Simple Linear Regression Model 8.1.1 Estimation of Parameters 8.1.2 Residuals and Fitted Values 8.1.3 Sampling Distributions of ss0 and ss1 8.2 Inferences in the Regression Model 8.2.1 Coefficient of Determination 8.2.2 Analysis-of-Variance Table and F-Test 8.2.3 Confidence Intervals and Tests of Hypotheses for Regression Coefficients 8.3 The Adequacy of the Fitted Model 8.3.1 Residual Checks 8.3.2 Output from Computer Programs 8.3.3 The Importance of Scatter Plots in Regression 8.4 The Multiple Linear Regression Model 8.4.1 Estimation of the Regression Coefficients 8.4.2 Residuals, Fitted Values, and the Sum-of-Squares Decomposition 8.4.3 Inference in the Multiple Linear Regression Model 8.4.4 A Further Example: Formaldehyde Concentrations 8.5 More on Multiple Regression 8.5.1 Multicollinearity among the Explanatory Variables 8.5.2 Another Example of Multiple Regression 8.5.3 A Note on Computer Software 8.5.4 Nonlinear Regression 8.6 Response Surface Methods 8.6.1 The "Change One Variable at a Time" Approach 8.6.2 Method of Steepest Ascent 8.6.3 Designs for Fitting Second-Order Modes: The 3K Factorial and the Central Composite Design 8.6.4 Interpretation of the Second-Order Model 8.6.5 An Illustration