Details


1 The Role of Statistics in Engineering 
1-1 The Engineering Method and Statistical Thinking 
1-2 Collecting Engineering Data 
1-2.1 Basic Principles 
1-2.2 Retrospective Study 
1-2.3 Observational Study
1-2.4 Designed Experiments 
1-2.5 Observing Processes Over Time 
1-3 Mechanistic and Empirical Models 
1-4 Probability and Probability Models 

2 Probability 
2-1 Sample Spaces and Events 
2-1.1 Random Experiments 
2-1.2 Sample Spaces 
2-1.3 Events 
2-1.4 Counting Techniques 
2-2 Interpretations and Axioms of Probability 
2-3 Addition Rules 
2-4 Conditional Probability 
2-5 Multiplication and Total Probability Rules
2-6 Independence 
2-8 Random Variables 

3 Discrete Random Variables and Probability Distributions
3-1 Discrete Random Variables 
3-2 Probability Distributions and Probability Mass Functions 
3-3 Cumulative Distribution Functions 
3-4 Mean and Variance of a Discrete Random Variable 
3-5 Discrete Uniform Distribution
3-6 Binomial Distribution
3-7 Geometric and Negative Binomial Distributions
3-7.1 Geometric Distribution
3-8 Hypergeometric Distribution
3-9 Poisson Distribution

4 Continuous Random Variables and Probability Distributions 
4-1 Continuous Random Variables 
4-2 Probability Distributions and Probability
Density Functions 108
4-3 Cumulative Distribution Functions 
4-4 Mean and Variance of a Continuous Random Variable 
4-5 Continuous Uniform Distribution 
4-6 Normal Distribution 
4-7 Normal Approximation to the Binomial and Poisson Distributions 
4-8 Exponential Distribution 
4-9 Erlang and Gamma Distributions 
4-10 Weibull Distribution 
4-11 Lognormal Distribution 
4-12 Beta Distribution 

5 Joint Probability Distributions 
5-1 Two or More Random Variables 
5-1.1 Joint Probability Distributions 
5-1.2 Marginal Probability Distributions 
5-1.3 Conditional Probability Distributions 
5-1.4 Independence 
5-1.5 More Than Two Random Variables 
5-2 Covariance and Correlation 
5-3 Common Joint Distributions 
5-3.1 Multinomial Probability Distribution 
5-3.2 Bivariate Normal Distribution 
5-4 Linear Functions of Random Variables 
5-5 General Functions of Random Variables 
5-6 Moment-Generating Functions 

6 Descriptive Statistics 
6-1 Numerical Summaries of Data 
6-2 Stem-and-Leaf Diagrams 
6-3 Frequency Distributions and Histograms 
6-4 Box Plots 
6-5 Time Sequence Plots 
6-6 Scatter Diagrams 
6-7 Probability Plots 

7 Point Estimation of Parameters and Sampling Distributions
7-1 Point Estimation 
7-2 Sampling Distributions and the Central Limit Theorem 
7-3 General Concepts of Point Estimation 
7-3.1 Unbiased Estimators 
7-3.2 Variance of a Point Estimator 
7-3.3 Standard Error: Reporting a Point Estimate 
7.3.4 Bootstrap Standard Error 
7-3.5 Mean Squared Error of an Estimator 
7-4 Methods of Point Estimation 
7-4.1 Method of Moments 
7-4.2 Method of Maximum Likelihood 
7-4.3 Bayesian Estimation of Parameters 

8 Statistical Intervals for a Single Sample 
8-1 Confidence Interval on the Mean of a Normal Distribution, Variance Known 
8-1.1 Development of the Confidence Interval and Its Basic Properties 
8-1.2 Choice of Sample Size 
8-1.3 One-Sided Confidence Bounds
8-1.4 General Method to Derive a Confidence Interval 
8-1.5 Large-Sample Confidence Interval for μ 
8-2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown 
8-2.1 t Distribution 
8-2.2 t Confidence Interval on μ 
8-3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution 
8-4 Large-Sample Confidence Interval
for a Population Proportion 
8-5 Guidelines for Constructing Confidence Intervals 
8.6 Bootstrap Confidence Interval
8-7 Tolerance and Prediction Intervals 
8-7.1 Prediction Interval for a Future Observation 
8-7.2 Tolerance Interval for a Normal Distribution

9 Tests of Hypotheses for a Single Sample 
9-1 Hypothesis Testing 
9-1.1 statistical hypotheses 
9-1.2 Tests of Statistical Hypotheses 
9-1.3 One-Sided and Two-Sided Hypotheses 
9-1.4 P-Values in Hypothesis Tests 
9-1.5 Connection Between Hypothesis Tests and Confidence Intervals 
9-1.6 General Procedure for Hypothesis Tests 
9-2 Tests on the Mean of a Normal Distribution, Variance Known 
9-2.1 Hypothesis Tests on the Mean 
9-2.2 Type II Error and Choice of Sample Size 
9-2.3 Large-Sample Test 
9-3 Tests on the Mean of a Normal Distribution, Variance Unknown 
9-3.1 Hypothesis Tests on the Mean 
9-3.2 Type II Error and Choice of Sample Size
9-4 Tests on the Variance and Standard Deviation of a Normal Distribution 
9-4.1 Hypothesis Tests on the Variance 
9-4.2 Type II Error and Choice of Sample Size
9-5 Tests on a Population Proportion 
9-5.1 Large-Sample Tests on a Proportion 
9-5.2 Type II Error and Choice of Sample Size 
9-6 Summary Table of Inference Procedures for a Single Sample 
9-7 Testing for Goodness of Fit 
9-8 Contingency Table Tests 
9-9 Nonparametric Procedures 
9-9.1 The Sign Test 
9-9.2 The Wilcoxon Signed-Rank Test 
9-9.3 Comparison to the t-Test 
9-10 Equivalence Testing 
9-11 Combining P-Values 

10 Statistical Inference for Two Samples 
10-1 Inference on the Difference in Means of Two Normal Distributions, Variances Known 
10-1.1 Hypothesis Tests on the Difference in Means, Variances Known 
10-1.2 Type II Error and Choice of Sample Size 
10-1.3 Confidence Interval on the Difference in Means, Variances Known 
10-2 Inference on the Difference in Means of two Normal Distributions, Variances Unknown 
10-2.1 Hypotheses Tests on the Difference in Means, Variances Unknown 
10-2.2 Type II Error and Choice of Sample Size 
10-2.3 Confidence Interval on the Difference in Means, Variances Unknown 
10-3 A Nonparametric Test for the Difference in Two Means 
10-3.1 Description of the Wilcoxon Rank-Sum Test 
10-3.2 Large-Sample Approximation 
10-3.3 Comparison to the t-Test 
10-4 Paired t-Test 
10-5 Inference on the Variances of Two Normal Distributions 
10-5.1 F Distribution 
10-5.2 Hypothesis Tests on the Ratio of Two Variances 
10-5.3 Type II Error and Choice of Sample Size 
10-5.4 Confidence Interval on the Ratio of Two Variances 
10-6 Inference on Two Population Proportions 
10-6.1 Large-Sample Tests on the Difference in Population Proportions 
10-6.2 Type II Error and Choice of Sample Size 
10-6.3 Confidence Interval on the Difference in Population Proportions 
10-7 Summary Table and Road Map for Inference Procedures for Two Samples 

11 Simple Linear Regression and Correlation 
11-1 Empirical Models 
11-2 Simple Linear Regression 
11-3 Properties of the Least Squares Estimators 
11-4 Hypothesis Tests in Simple Linear Regression 
11-4.1 Use of t-Tests 
11-4.2 Analysis of Variance Approach to Test Significance of Regression 
11-5 Confidence Intervals 
11-5.1 Confidence Intervals on the Slope and Intercept 
11-5.2 Confidence Interval on the Mean Response
11-6 Prediction of New Observations 
11-7 Adequacy of the Regression Model 
11-7.1 Residual Analysis 
11-7.2 Coefficient of Determination (R2) 
11-8 Correlation 
11-9 Regression on Transformed Variables 
11-10 Logistic Regression 

12 Multiple Linear Regression 
12-1 Multiple Linear Regression Model 
12-1.1 Introduction 
12-1.2 Least Squares Estimation of the Parameters 
12-1.3 Matrix Approach to Multiple Linear Regression
12-1.4 Properties of the Least Squares Estimators 
12-2 Hypothesis Tests In Multiple Linear Regression
12-2.1 Test for Significance of Regression 
12-2.2 Tests on Individual Regression
Coefficients and Subsets of Coefficients
12-3 Confidence Intervals In Multiple Linear Regression 
12-3.1 Confidence Intervals on Individual Regression Coefficients 
12-3.2 Confidence Interval on the Mean Response 
12-4 Prediction of New Observations 
12-5 Model Adequacy Checking 
12-5.1 Residual Analysis 
12-5.2 Influential Observations 
12-6 Aspects of Multiple Regression Modeling 
12-6.1 Polynomial Regression Models 
12-6.2 Categorical Regressors and Indicator Variables
12-6.3 Selection of Variables and Model Building
12-6.4 Multicollinearity 

13 Design and Analysis of Single-Factor
13-1 Designing Engineering Experiments 
13-2 Completely Randomized Single-Factor Experiment 
13-2.1 Example: Tensile Strength 
13-2.2 Analysis of Variance 
13-2.3 Multiple Comparisons Following the ANOVA 549
13-2.4 Residual Analysis and Model Checking 
13-2.5 Determining Sample Size 
13-3 The Random-Effects Model 
13-3.1 Fixed Versus Random Factors 
13-3.2 ANOVA and Variance Components 
13-4 Randomized Complete Block Design 
13-4.1 Design and Statistical Analysis 
13-4.2 Multiple Comparisons 
13-4.3 Residual Analysis and Model Checking 

14 Design of Experiments with Several Factors 
14-1 Introduction 
14-2 Factorial Experiments 
14-3 Two-Factor Factorial Experiments 
14-3.1 Statistical Analysis of the Fixed-Effects Model 
14-3.2 Model Adequacy Checking 
14-3.3 One Observation per Cell 
14-4 General Factorial Experiments 
14-5 2k Factorial Designs 
14-5.1 22 Design 
14-5.2 2k Design for k≥3 Factors 
14-5.3 Single Replicate of the 2k Design 
14-5.4 Addition of Center Points to a 2k Design
14-6 Blocking and Confounding in the 2k Design 
14-7 Fractional Replication of the 2k Design 
14-7.1 One-Half Fraction of the 2k Design 
14-7.2 Smaller Fractions: The 2k–p Fractional Factorial 
14-8 Response Surface Methods and Designs 

15 Statistical Quality Control 
15-1 Quality Improvement and Statistics 
15-1.1 Statistical Quality Control 
15-1.2 Statistical Process Control 
15-2 Introduction to Control Charts 
15-2.1 Basic Principles 
15-2.2 Design of a Control Chart 
15-2.3 Rational Subgroups 
15-2.4 Analysis of Patterns on Control Charts
15-3 X and R or S Control Charts 
15-4 Control Charts for Individual Measurements 
15-5 Process Capability 
15-6 Attribute Control Charts 
15-6.1 P Chart (Control Chart for Proportions) 
15-6.2 U Chart (Control Chart for Defects per Unit) 
15-7 Control Chart Performance 
15-8 Time-Weighted Charts 
15-8.1 Cumulative Sum Control Chart 
15-8.2 Exponentially Weighted Moving-Average Control Chart
15-9 Other SPC Problem-Solving Tools
15-10 Decision Theory 
15-10.1 Decision Models
15-10.2 Decision Criteria
15-11 Implementing SPC