| Introduction | x |
| Chapter 1. | Tool Selection Guide | 1 |
| Minitab Commands | 3 |
| Excel Statistical Functions | 7 |
| Chapter 2. | Probability Distributions | 9 |
| What Is a Probability Distribution? | 9 |
| Application of Probability Distributions in Six Sigma | 9 |
| Discrete Probability Distributions | 9 |
| Binomial Distributions | 10 |
| Poisson Distribution | 12 |
| Continuous Probability Distributions | 14 |
| Normal Distribution | 14 |
| Exponential Distribution | 18 |
| Weibull Distribution | 20 |
| Probability Plots | 22 |
| Transforming Non-Normal Data to Normal | 26 |
| Box-Cox Transformation | 29 |
| How to Use Probability Distributions | 34 |
| Chapter 3. | Sampling | 37 |
| Why Use Sampling? | 37 |
| Application of Sampling in Six Sigma | 37 |
| Sample Types | 37 |
| Sampling Terminology | 38 |
| Types of Population Data | 39 |
| What Affects Sample Size? | 39 |
| Confidence | 40 |
| Sampling Techniques | 41 |
| Simple Random Sample | 41 |
| Stratified Random Sample | 41 |
| Systematic Sampling | 41 |
| Formulas Used for Determining Sample Size | 42 |
| Allocating Samples for Stratified Random Sampling | 44 |
| Risk-Based Allocation Approach | 44 |
| Neyman Allocation Method | 45 |
| Determining Sample Sizes for Hypothesis Tests | 46 |
| How to Estimate Sample Size | 47 |
| Chapter 4. | Confidence Intervals | 49 |
| What Is a Confidence Interval? | 49 |
| Application of Confidence Intervals in Six Sigma | 49 |
| Confidence Interval for the Mean | 49 |
| Mean Estimation--Standard Deviation ([sigma]) Is Known | 50 |
| Mean Estimation--Standard Deviation ([sigma]) Unknown | 51 |
| Confidence Interval for Proportions | 52 |
| Confidence Interval for the Variance of a Normal Distribution | 53 |
| How to Determine Confidence Intervals | 54 |
| Chapter 5. | Hypothesis Testing | 55 |
| What Is Hypothesis Testing? | 55 |
| Application of Hypothesis Testing in Six Sigma | 55 |
| Types of Hypothesis Tests | 55 |
| Two-Tailed Hypothesis Tests | 56 |
| One-Tailed Hypothesis Tests | 56 |
| Decision Errors and Hypothesis Testing | 57 |
| Type I Error | 57 |
| Type II Error | 57 |
| Significance Level and the Power of the Hypothesis Test | 58 |
| Decision Rules | 59 |
| Converting Alpha Risk to Z-Values | 61 |
| P-Values | 61 |
| Hypothesis Tests of the Mean | 63 |
| Z-Test | 63 |
| Two-Sample Z-Test | 65 |
| Paired Z-Test | 66 |
| t-Test | 68 |
| Two-Sample t-Test | 72 |
| Paired t-Test | 75 |
| Hypothesis Tests of Proportions | 78 |
| Single Proportion Test | 78 |
| Two-Sample Proportion Test | 80 |
| Hypothesis Tests of Variance | 82 |
| X[superscript 2] Test | 82 |
| F-Test | 83 |
| How to Perform Hypothesis Testing | 88 |
| Chapter 6. | Control Charts | 89 |
| What Are Control Charts? | 89 |
| Application of Control Charts to Six Sigma | 90 |
| How to Use Control Charts | 90 |
| Control Charts for Discrete (Attribute) Data | 95 |
| p Chart | 95 |
| np Chart | 98 |
| c Chart | 99 |
| u Chart | 102 |
| Control Charts for Continuous Data | 105 |
| Individuals Chart | 105 |
| Moving Range (MR) Chart | 106 |
| Range (R) Chart | 107 |
| x Chart | 109 |
| EWMA Chart | 111 |
| How to Create and Use Control Charts | 114 |
| Chapter 7. | Correlation Analysis | 117 |
| What Is Correlation Analysis | 117 |
| Application of Correlation Analysis in Six Sigma | 117 |
| Scatter Plots | 117 |
| Correlation Matrix | 117 |
| Significance of the Correlation Analysis | 121 |
| How to Perform Correlation Analysis | 123 |
| Chapter 8. | Regression Analysis | 125 |
| What Is Regression Analysis? | 125 |
| Application of Regression Analysis in Six Sigma | 125 |
| Simple Linear Regression | 126 |
| How to Interpret Regression Analysis Results | 131 |
| Confidence and Prediction Intervals | 133 |
| How Do We Know That Our Regression Model Is Good Enough to Use? | 134 |
| P-Value (X-Variable Coefficient) | 134 |
| r[superscript 2]--Coefficient of Determination | 134 |
| Using Residual and Normal Probability Plots to Validate Regression Models | 135 |
| Interpreting Residual Plots | 138 |
| Multiple Regression | 138 |
| Multicollinearity | 140 |
| Variance Inflation Factor (VIF) | 140 |
| Systematic Procedure for VIF [greater than sign] 10 | 140 |
| Regression ANOVA | 141 |
| Model Validation | 142 |
| Interpreting the Regression Output | 144 |
| Interpreting the Regression Output of the Reduced Model (Weight, Volume, and Distance) | 146 |
| Interpreting the Regression Output of the Reduced Model (Volume and Distance) | 148 |
| Multiple Regression Analysis Using Qualitative Input Variables | 148 |
| Interpreting Regression Output When Using Qualitative Variables | 151 |
| Curvilinear Regression | 153 |
| How to Perform Regression Analysis | 156 |
| Chapter 9. | Design of Experiments | 159 |
| What Is Design of Experiments? | 159 |
| Application of Design of Experiments in Six Sigma | 160 |
| Factorial Experiments | 160 |
| Design Terminology | 160 |
| Design Fundamentals | 161 |
| Full Factorial Design | 162 |
| How Do I Know Which Process Factors Are Significant? | 165 |
| Pareto Chart of Standardized Effects | 166 |
| How Can We Determine the Value of the Significant Effects? | 168 |
| Predicting Process Output Using the Results of Our Factorial Experiment | 169 |
| Randomization and Blocking | 174 |
| Randomization | 174 |
| Randomized Block Design (Blocking) | 175 |
| Fractional Factorial Designs | 178 |
| Confounding and Design Resolution | 179 |
| Design Resolution | 180 |
| Design Notation | 180 |
| How to Perform a DOE | 190 |
| Chapter 10. | Analysis of Variance (ANOVA) | 192 |
| What Is Analysiss of Variance? | 192 |
| Application of ANOVA in Six Sigma | 192 |
| One-Way ANOVA | 192 |
| How to Read a One-Way ANOVA Table | 194 |
| Two-Way ANOVA | 195 |
| Two-Way ANOVA with Replication--Interaction Effects | 196 |
| How to Read a Two-Way ANOVA Table | 199 |
| Nested ANOVA | 200 |
| Variance Components | 202 |
| Analysis of Means | 203 |
| Main Effects Plots | 205 |
| Interaction Plots | 207 |
| Interval Plots | 209 |
| Balanced ANOVA and General Linear Models (GLM) | 210 |
| How to Perform Analysis of Variance (ANOVA) | 217 |
| Appendix A. | References | 219 |
| Appendix B. | Glossary of Terms | 220 |
