Statistical Methods for Six Sigma

1. Introduction.
2. Basic Statistics.
2.1 Descriptive Statistics.
2.2 Statistical Distributions.
2.3 Confidence Intervals.
2.4 Sample Size.
2.5 Tolerance Intervals.
2.6 Normality, Independence and Homoscedasticity.
3. Comparative Experiments and Regression Analysis.
3.1 Hypothesis Testing Framework.
3.2 Comparing Single Population.
3.3 Comparing Two Populations.
3.4 Comparing Multiple Populations.
3.5 Correlation.
3.6 Regression Analysis.
4. Control Charts.
4.1 Role of Control Charts.
4.2 Logic of Control Limits.
4.3 Variable Control Charts.
4.4 Attribute Control Charts.
4.5 Interpreting Control Charts.
4.6 Key Success Factors.
5. Process Capability.
5.1 Capability and Performance Indices.
5.2 E stimating Capability and Performance Indices.
5.3 Six-Sigma Goal.
5.4 Planning for Improvement.
6. Other Useful Charts.
6.1 Risk-based Control Ch arts.
6.2 Modified Control Limit Chart.
6.3 Moving Average Control Chart.
6.4 Short Run Control Charts
6.5 Charts for Non-Normal Distributions.
7. Variance Components Analysis.
7.1 Chart (Random Factor).
7.2 One-way Classification (Fixed Factor).
7.3 Structured Studies and Variance Components.
8. Quality Planning with Variance Components.
8.1 Typical Manufacturing Application.
8.2 Economic Loss Functions.
8.3 Planning for Quality Improvement.
8.4 Application to Multi-Lane Manufacturing Process.
8.5 Variance Transmission Analysis.
8.6 Application to a Factorial Design.
8.7 Variance Components and Specifications.
9. Measurement Systems Analysis.
9.1 Statistical Properties of Measurement Systems.
9.2 Acceptance Criteria.
9.3 Calibration Study.
9.4 Stability and Bias Study.
9.5 Repeatability and Reproducibility (R&R) Study.
9.6 Robustness and Intermediate Precision Studies.
9.7 Linearity Study.
9.8 Method Transfer Study.
9.9 Calculating Significant Figures.
10. What Color is Your Belt?
10.1 Test.
10.2 Answers.
Appendix A: Tail Area of Unit Normal Distribution.
Appendix B: Probability Points of the t Distribution withv Degrees of Freedom.
Appendix C: Probability Points of the x²Distribution with v Degrees of Freedom.
Appendix D1.k Values for Two-Sided Normal ToleranceLimits.
Appendix D2.k Values for One-Sided Normal ToleranceLimits.
Appendix E1: Percentage Points of the F Distribution:Upper 5% Points.
Appendix E2: Percentage Points of the F Distribution:Upper 2.5% Points.
Appendix F: Critical Values of Hartley's Maximum F Ratio Testfor Homogeneity of Variances.
Appendix G: Table of Control Chart Constants.
Glossary Of Symbols.
References.
Index.