| Preface | p. ix |
| Acknowledgments | p. x |
| Introduction | p. 1 |
| Six Sigma Methodology | p. 2 |
| Define the organization | p. 2 |
| Measure the organization | p. 6 |
| Analyze the organization | p. 11 |
| Improve the organization | p. 13 |
| Statistics, Quality Control, and Six Sigma | p. 14 |
| Poor quality defined as a deviation from engineered standards | p. 15 |
| Sampling and quality control | p. 16 |
| Statistical Definition of Six Sigma | p. 16 |
| Variability: the source of defects | p. 17 |
| Evaluation of the process performance | p. 18 |
| Normal distribution and process capability | p. IS |
| An Overview of Minitab and Microsoft Excel | p. 23 |
| Starting with Minitab | p. 23 |
| Minitab's menus | p. 25 |
| An Overview of Data Analysis with Excel | p. 33 |
| Graphical display of data | p. 35 |
| Data Analysis add-in | p. 37 |
| Basic Tools for Data Collection, Organization and Description | p. 41 |
| The Measures of Central Tendency Give a First Perception of Your Data | p. 42 |
| Arithmetic mean | p. 42 |
| Geometric mean | p. 47 |
| Mode | p. 49 |
| Median | p. 49 |
| Measures of Dispersion | p. 49 |
| Range | p. 50 |
| Mean deviation | p. 50 |
| Variance | p. 52 |
| Standard deviation | p. 54 |
| Chebycheff's theorem | p. 55 |
| Coefficient of variation | p. 55 |
| The Measures of Association Quantify the Level of Relatedness between Factors | p. 56 |
| Covariance | p. 56 |
| Correlation coefficient | p. 58 |
| Coefficient of determination | p. 62 |
| Graphical Representation of Data | p. 62 |
| Histograms | p. 62 |
| Stem-and-leaf graphs | p. 64 |
| Box plots | p. 66 |
| Descriptive Statistics-Minitab and Excel Summaries | p. 68 |
| Introduction to Basic Probability | p. 73 |
| Discrete Probability Distributions | p. 74 |
| Binomial distribution | p. 74 |
| Poisson distribution | p. 79 |
| Poisson distribution, rolled throughput yield, and DPMO | p. 80 |
| Geometric distribution | p. 84 |
| Hypergeometric distribution | p. 85 |
| Continuous Distributions | p. 88 |
| Exponential distribution | p. 88 |
| Normal distribution | p. 90 |
| The log-normal distribution | p. 97 |
| How to Determine, Analyze, and Interpret Your Samples | p. 99 |
| How to Collect a Sample | p. 100 |
| Stratified sampling | p. 100 |
| Cluster sampling | p. 100 |
| Systematic sampling | p. 100 |
| Sampling Distribution of Means | p. 100 |
| Sampling Error | p. 101 |
| Central Limit Theorem | p. 102 |
| Sampling from a Finite Population | p. 106 |
| Sampling Distribution of p | p. 106 |
| Estimating the Population Mean with Large Sample Sizes | p. 108 |
| Estimating the Population Mean with Small Sample Sizes and [sigma] Unknown: t-Distribution | p. 113 |
| Chi Square (x[superscript 2]) Distribution | p. 114 |
| Estimating Sample Sizes | p. 117 |
| Sample size when estimating the mean | p. 117 |
| Sample size when estimating the population proportion | p. 118 |
| Hypothesis Testing | p. 121 |
| How to Conduct a Hypothesis Testing | p. 122 |
| Null hypothesis | p. 122 |
| Alternate hypothesis | p. 122 |
| Test statistic | p. 123 |
| Level of significance or level of risk | p. 123 |
| Decision rule determination | p. 123 |
| Decision making | p. 124 |
| Testing for a Population Mean | p. 124 |
| Large sample with known [sigma] | p. 124 |
| What is the p-value and how is it interpreted? | p. 126 |
| Small samples with unknown [sigma] | p. 128 |
| Hypothesis Testing about Proportions | p. 130 |
| Hypothesis Testing about the Variance | p. 131 |
| Statistical Inference about Two Populations | p. 132 |
| Inference about the difference between two means | p. 133 |
| Small independent samples with equal variances | p. 134 |
| Testing the hypothesis about two variances | p. 140 |
| Testing for Normality of Data | p. 142 |
| Statistical Process Control | p. 145 |
| How to Build a Control Chart | p. 147 |
| The Western Electric (WECO) Rules | p. 150 |
| Types of Control Charts | p. 151 |
| Attribute control charts | p. 151 |
| Variable control charts | p. 159 |
| Process Capability Analysis | p. 171 |
| Process Capability with Normal Data | p. 174 |
| Potential capabilities vs. actual capabilities | p. 176 |
| Actual process capability indices | p. 178 |
| Taguchi's Capability Indices C[subscript PM] and P[subscript PM] | p. 183 |
| Process Capability and PPM | p. 185 |
| Capability Sixpack for Normally Distributed Data | p. 193 |
| Process Capability Analysis with Non-Normal Data | p. 194 |
| Normality assumption and Box-Cox transformation | p. 195 |
| Process capability using Box-Cox transformation | p. 196 |
| Process capability using a non-normal distribution | p. 200 |
| Analysis of Variance | p. 203 |
| ANOVA and Hypothesis Testing | p. 203 |
| Completely Randomized Experimental Design (One-Way ANOVA) | p. 204 |
| Degrees of freedom | p. 206 |
| Multiple comparison tests | p. 218 |
| Randomized Block Design | p. 222 |
| Analysis of Means (ANOM) | p. 226 |
| Regression Analysis | p. 231 |
| Building a Model with Only Two Variables: Simple Linear Regression | p. 232 |
| Plotting the combination of x and y to visualize the relationship: scatter plot | p. 233 |
| The regression equation | p. 240 |
| Least squares method | p. 241 |
| How far are the results of our analysis from the true values: residual analysis | p. 248 |
| Standard error of estimate | p. 250 |
| How strong is the relationship between x and y: correlation coefficient | p. 250 |
| Coefficient of determination, or what proportion in the variation of y is explained by the changes in x | p. 255 |
| Testing the validity of the regression line: hypothesis testing for the slope of the regression model | p. 255 |
| Using the confidence interval to estimate the mean | p. 257 |
| Fitted line plot | p. 258 |
| Building a Model with More than Two Variables: Multiple Regression Analysis | p. 261 |
| Hypothesis testing for the coefficients | p. 263 |
| Stepwise regression | p. 266 |
| Design of Experiment | p. 275 |
| The Factorial Design with Two Factors | p. 276 |
| How does ANOVA determine if the null hypothesis should be rejected or not? | p. 277 |
| A mathematical approach | p. 279 |
| Factorial Design with More than Two Factors (2[superscript k]) | p. 285 |
| The Taguchi Method | p. 289 |
| Assessing the Cost of Quality | p. 289 |
| Cost of conformance | p. 290 |
| Cost of nonconformance | p. 290 |
| Taguchi's Loss Function | p. 293 |
| Variability Reduction | p. 295 |
| Concept design | p. 297 |
| Parameter design | p. 298 |
| Tolerance design | p. 300 |
| Measurement Systems Analysis-MSA: Is Your Measurement Process Lying to You? | p. 303 |
| Variation Due to Precision: Assessing the Spread of the Measurement | p. 304 |
| Gage repeatability & reproducibility crossed | p. 305 |
| Gage R&R nested | p. 314 |
| Gage Run Chart | p. 318 |
| Variations Due to Accuracy | p. 320 |
| Gage bias | p. 320 |
| Gage linearity | p. 322 |
| Nonparametric Statistics | p. 329 |
| The Mann-Whitney U test | p. 330 |
| The Mann-Whitney U test for small samples | p. 330 |
| The Mann-Whitney U test for large samples | p. 333 |
| The Chi-Square Tests | p. 336 |
| The chi-square goodness-of-fit test | p. 336 |
| Contingency analysis: chi-square test of independence | p. 342 |
| Pinpointing the Vital Few Root Causes | p. 347 |
| Pareto Analysis | p. 347 |
| Cause and Effect Analysis | p. 350 |
| Binominal Table P(x) = [subscript n]C[subscript x]p[superscript x]q[superscript n-x] | p. 354 |
| Poisson Table P(x) = [lambda superscript x]e[superscript -lambda]/x | p. 357 |
| Normal Z Table | p. 364 |
| Student's t Table | p. 365 |
| Chi-Square Table | p. 366 |
| F Table [alpha] = 0.05 | p. 367 |
| Index | p. 369 |
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