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| Introduction | |
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| Tool Selection Guide | |
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| Minitab Commands | |
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| Excel Statistical Functions | |
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| Probability Distributions | |
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| What Is a Probability Distribution? | |
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| Application of Probability Distributions in Six Sigma | |
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| Discrete Probability Distributions | |
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| Binomial Distributions | |
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| Poisson Distribution | |
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| Continuous Probability Distributions | |
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| Normal Distribution | |
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| Exponential Distribution | |
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| Weibull Distribution | |
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| Probability Plots | |
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| Transforming Non-Normal Data to Normal | |
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| Box-Cox Transformation | |
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| How to Use Probability Distributions | |
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| Sampling | |
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| Why Use Sampling? | |
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| Application of Sampling in Six Sigma | |
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| Sample Types | |
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| Sampling Terminology | |
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| Types of Population Data | |
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| What Affects Sample Size? | |
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| Confidence | |
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| Sampling Techniques | |
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| Simple Random Sample | |
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| Stratified Random Sample | |
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| Systematic Sampling | |
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| Formulas Used for Determining Sample Size | |
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| Allocating Samples for Stratified Random Sampling | |
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| Risk-Based Allocation Approach | |
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| Neyman Allocation Method | |
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| Determining Sample Sizes for Hypothesis Tests | |
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| How to Estimate Sample Size | |
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| Confidence Intervals | |
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| What Is a Confidence Interval? | |
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| Application of Confidence Intervals in Six Sigma | |
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| Confidence Interval for the Mean | |
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| Mean Estimation--Standard Deviation ([sigma]) Is Known | |
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| Mean Estimation--Standard Deviation ([sigma]) Unknown | |
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| Confidence Interval for Proportions | |
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| Confidence Interval for the Variance of a Normal Distribution | |
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| How to Determine Confidence Intervals | |
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| Hypothesis Testing | |
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| What Is Hypothesis Testing? | |
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| Application of Hypothesis Testing in Six Sigma | |
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| Types of Hypothesis Tests | |
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| Two-Tailed Hypothesis Tests | |
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| One-Tailed Hypothesis Tests | |
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| Decision Errors and Hypothesis Testing | |
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| Type I Error | |
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| Type II Error | |
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| Significance Level and the Power of the Hypothesis Test | |
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| Decision Rules | |
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| Converting Alpha Risk to Z-Values | |
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| P-Values | |
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| Hypothesis Tests of the Mean | |
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| Z-Test | |
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| Two-Sample Z-Test | |
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| Paired Z-Test | |
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| t-Test | |
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| Two-Sample t-Test | |
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| Paired t-Test | |
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| Hypothesis Tests of Proportions | |
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| Single Proportion Test | |
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| Two-Sample Proportion Test | |
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| Hypothesis Tests of Variance | |
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| X[superscript 2] Test | |
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| F-Test | |
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| How to Perform Hypothesis Testing | |
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| Control Charts | |
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| What Are Control Charts? | |
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| Application of Control Charts to Six Sigma | |
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| How to Use Control Charts | |
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| Control Charts for Discrete (Attribute) Data | |
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| p Chart | |
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| np Chart | |
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| c Chart | |
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| u Chart | |
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| Control Charts for Continuous Data | |
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| Individuals Chart | |
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| Moving Range (MR) Chart | |
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| Range (R) Chart | |
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| x Chart | |
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| EWMA Chart | |
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| How to Create and Use Control Charts | |
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| Correlation Analysis | |
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| What Is Correlation Analysis | |
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| Application of Correlation Analysis in Six Sigma | |
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| Scatter Plots | |
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| Correlation Matrix | |
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| Significance of the Correlation Analysis | |
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| How to Perform Correlation Analysis | |
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| Regression Analysis | |
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| What Is Regression Analysis? | |
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| Application of Regression Analysis in Six Sigma | |
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| Simple Linear Regression | |
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| How to Interpret Regression Analysis Results | |
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| Confidence and Prediction Intervals | |
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| How Do We Know That Our Regression Model Is Good Enough to Use? | |
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| P-Value (X-Variable Coefficient) | |
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| r[superscript 2]--Coefficient of Determination | |
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| Using Residual and Normal Probability Plots to Validate Regression Models | |
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| Interpreting Residual Plots | |
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| Multiple Regression | |
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| Multicollinearity | |
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| Variance Inflation Factor (VIF) | |
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| Systematic Procedure for VIF [greater than sign] 10 | |
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| Regression ANOVA | |
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| Model Validation | |
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| Interpreting the Regression Output | |
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| Interpreting the Regression Output of the Reduced Model (Weight, Volume, and Distance) | |
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| Interpreting the Regression Output of the Reduced Model (Volume and Distance) | |
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| Multiple Regression Analysis Using Qualitative Input Variables | |
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| Interpreting Regression Output When Using Qualitative Variables | |
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| Curvilinear Regression | |
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| How to Perform Regression Analysis | |
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| Design of Experiments | |
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| What Is Design of Experiments? | |
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| Application of Design of Experiments in Six Sigma | |
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| Factorial Experiments | |
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| Design Terminology | |
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| Design Fundamentals | |
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| Full Factorial Design | |
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| How Do I Know Which Process Factors Are Significant? | |
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| Pareto Chart of Standardized Effects | |
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| How Can We Determine the Value of the Significant Effects? | |
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| Predicting Process Output Using the Results of Our Factorial Experiment | |
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| Randomization and Blocking | |
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| Randomization | |
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| Randomized Block Design (Blocking) | |
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| Fractional Factorial Designs | |
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| Confounding and Design Resolution | |
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| Design Resolution | |
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| Design Notation | |
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| How to Perform a DOE | |
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| Analysis of Variance (ANOVA) | |
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| What Is Analysiss of Variance? | |
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| Application of ANOVA in Six Sigma | |
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| One-Way ANOVA | |
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| How to Read a One-Way ANOVA Table | |
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| Two-Way ANOVA | |
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| Two-Way ANOVA with Replication--Interaction Effects | |
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| How to Read a Two-Way ANOVA Table | |
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| Nested ANOVA | |
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| Variance Components | |
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| Analysis of Means | |
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| Main Effects Plots | |
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| Interaction Plots | |
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| Interval Plots | |
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| Balanced ANOVA and General Linear Models (GLM) | |
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| How to Perform Analysis of Variance (ANOVA) | |
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| References | |
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| Glossary of Terms | |