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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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