Statistics for Six Sigma Green Belts: with Minitab and JMP

Cover......Page 1
Contents......Page 8
Acknowledgments......Page 18
About the Author......Page 20
Preface......Page 22
1 FUNDAMENTALS OF SIX SIGMA......Page 24
  The DMAIC Model......Page 25
  Master Black Belt......Page 26
 1.3 Statistics and Six Sigma......Page 27
 1.4 Learning Statistics for Six Sigma Using This Book......Page 28
 References......Page 29
2 INTRODUCTION TO STATISTICS......Page 30
 2.1 Enumerative and Analytic Studies......Page 31
 2.2 Types of Sampling......Page 32
  Stratified Sample......Page 34
  Cluster Sample......Page 35
 2.3 Types of Variables......Page 36
 Summary......Page 37
 References......Page 38
  Using Minitab Worksheets......Page 39
  Opening and Saving Worksheets and Other Components......Page 40
  Printing Worksheets, Graphs, and Sessions......Page 41
  Selecting a Random Sample......Page 42
  Using JMP Data Tables......Page 43
  Selecting a Random Sample......Page 44
3 PRESENTING DATA IN CHARTS AND TABLES......Page 46
  The Bar Chart......Page 47
  The Pareto Diagram......Page 48
  Histogram......Page 50
  The Run Chart......Page 51
 References......Page 53
  Generating a Bar Chart......Page 54
  Generating a Histogram......Page 55
  Generating a Dot Plot......Page 56
  Generating a Run Chart......Page 57
  Generating a Pareto Diagram......Page 58
  Generating a Run Chart......Page 59
4 DESCRIPTIVE STATISTICS......Page 62
  The Arithmetic Mean......Page 63
  The Median......Page 65
  The Mode......Page 66
  Quartiles......Page 67
  The Range......Page 69
  The Variance and the Standard Deviation......Page 70
  Shape......Page 73
  The Five-Number Summary......Page 75
  The Box-and-Whisker Plot......Page 76
 References......Page 79
  Generating a Box-and-Whisker Plot......Page 80
  Generating Descriptive Statistics and a Box-and-Whisker Plot......Page 81
5 PROBABILITY AND PROBABILITY DISTRIBUTIONS......Page 82
 5.1 What Is Probability?......Page 83
 5.2 Some Rules of Probability......Page 85
 5.3 The Probability Distribution......Page 89
  The Average or Expected Value of a Random Variable......Page 91
  Standard Deviation of a Random Variable (σ)......Page 92
 5.4 The Binomial Distribution......Page 95
  Characteristics of the Binomial Distribution......Page 98
 5.5 The Poisson Distribution......Page 99
 5.6 The Normal Distribution......Page 101
  Characteristics of the Normal Distribution......Page 102
 5.7 The Normal Probability Plot......Page 108
 Summary......Page 109
 References......Page 110
  Computing Poisson Probabilities......Page 111
  Constructing a Normal Probability Plot......Page 112
  Computing Binomial Probabilities......Page 114
  Computing Normal Probabilities......Page 115
  Constructing a Normal Probability Plot......Page 116
6 SAMPLING DISTRIBUTIONS AND CONFIDENCE INTERVALS......Page 118
  Basic Concepts......Page 119
  Sampling Distribution of the Mean......Page 120
 6.2 Basic Concepts of Confidence Intervals......Page 122
 6.3 Confidence Interval Estimate for the Mean (σ Unknown)......Page 125
 6.4 Prediction Interval Estimate for a Future Individual Value......Page 128
 6.5 Confidence Interval Estimate for the Proportion......Page 129
 References......Page 131
  Constructing the Confidence Interval Estimate for the Mean......Page 132
  Constructing the Confidence Interval Estimate for the Proportion......Page 133
  Constructing the Confidence Interval Estimate for the Proportion......Page 134
7 HYPOTHESIS TESTING......Page 136
 7.1 Fundamental Concepts of Hypothesis Testing......Page 137
  The Critical Value of the Test Statistic......Page 139
  Regions of Rejection and Nonrejection......Page 140
  The Confidence Coefficient......Page 141
  The Power of a Test......Page 142
  The p-Value Approach to Hypothesis Testing......Page 144
 7.2 Testing for the Difference Between Two Proportions......Page 145
  Pooled-Variance t Test for the Difference in Two Means......Page 149
 7.4 Testing for the Difference Between Two Variances......Page 154
  The F Test for the Ratio of Two Variances......Page 155
  F Test for Differences in Three or More Means......Page 157
  Multiple Comparisons:The Tukey Procedure......Page 161
  ANOVA Assumptions......Page 163
  Levene’s Test for Homogeneity of Variance......Page 165
 7.6 Wilcoxon Rank Sum Test for the Difference Between Two Medians......Page 166
 7.7 Kruskal-Wallis Rank Test: Nonparametric Analysis for the One-Way ANOVA......Page 168
 Summary......Page 170
 References......Page 172
  Testing for the Difference Between the Means of Two Independent Samples......Page 173
  Generating a One-Way ANOVA with Multiple Comparisons......Page 175
  Testing for Equal Variances in the Analysis of Variance......Page 176
  The Kruskal-Wallis Rank Test......Page 177
  Tests for the Difference Between Two Means, Tests for the Difference Between Two Variances, and the Wilcoxon Rank Sum Test......Page 178
  The One-Way ANOVA, Tukey Multiple Comparisons, Tests for Variances, and the Kruskal-Wallis Rank Test......Page 179
8 DESIGN OF EXPERIMENTS......Page 180
 8.1 Design of Experiments: Background and Rationale......Page 181
 8.2 Two-Factor Factorial Designs......Page 182
 8.3 2[sup(k)] Factorial Designs......Page 194
 8.4 Fractional Factorial Designs......Page 212
  Choosing the Treatment Combinations......Page 213
 References......Page 226
  Interaction Plot......Page 228
  Factorial Design......Page 229
  Fractional Factorial Design......Page 231
  Two-Way ANOVA......Page 232
  Fractional Factorial Design......Page 233
9 SIMPLE LINEAR REGRESSION......Page 234
 9.1 Types of Regression Models......Page 235
  The Y Intercept and the Slope......Page 236
  Least-Squares Method......Page 237
  Regression Model Prediction......Page 241
 9.3 Measures of Variation......Page 244
  The Coefficient of Correlation......Page 247
  Standard Error of the Estimate......Page 248
 9.5 Residual Analysis......Page 249
  Evaluating the Assumptions......Page 250
  t Test for the Slope......Page 252
  F Test for the Slope......Page 253
  Confidence Interval Estimate of the Slope (β[sub(1)])......Page 254
 9.8 Pitfalls in Regression Analysis......Page 255
 References......Page 259
  Simple Linear Regression......Page 260
 A9.2 Using JMP for Simple Linear Regression......Page 262
10 MULTIPLE REGRESSION......Page 264
 10.1 Developing the Multiple Regression Model......Page 265
  Interpreting the Regression Coefficients......Page 266
  Predicting the Dependent Variable Y......Page 268
  Test for the Significance of the Overall Multiple Regression Model......Page 269
 10.3 Residual Analysis for the Multiple Regression Model......Page 270
  Confidence Interval Estimation......Page 272
 10.5 Using Dummy Variables and Interaction Terms in Regression Models......Page 273
 10.6 Collinearity......Page 278
 10.7 Model Building......Page 280
  The Stepwise Regression Approach to Model Building......Page 282
  The Best-Subsets Approach to Model Building......Page 284
 10.8 Logistic Regression......Page 289
 References......Page 295
  Using Minitab for a Three-Dimensional Plot......Page 296
  Using Minitab for Stepwise Regression and Best-Subsets Regression......Page 297
  Using Minitab for Logistic Regression......Page 298
  Generating a Multiple Regression Equation......Page 299
  Using JMP for Interactions......Page 300
  Using JMP for Logistic Regression......Page 301
11 CONTROL CHARTS FOR SIX SIGMA MANAGEMENT......Page 302
 11.1 Basic Concepts of Control Charts......Page 303
 11.2 Control Limits and Patterns......Page 305
 11.3 Rules for Determining Out-of-Control Points......Page 306
 11.4 The p-Chart......Page 308
 11.5 The c-Chart......Page 313
 11.6 The u-Chart......Page 316
 11.7 Control Charts for the Mean and Range......Page 319
 11.8 Control Charts for the Mean and the Standard Deviation......Page 324
 11.9 Individual Value and Moving Range Charts......Page 329
 Summary......Page 333
 References......Page 334
  The p-Chart......Page 335
  The u-Chart......Page 336
  R and X Charts......Page 337
  S and X Charts......Page 338
  Individual Value and Moving Range Charts......Page 339
  The c-Chart......Page 341
  X and R-Charts......Page 342
  Individual Value and Moving Range Charts......Page 343
 Part 1 Fill in the Correct Answer......Page 344
 Part 2 Select the Correct Answer......Page 345
  Symbols......Page 346
  Exponents and Square Roots......Page 348
  Equations......Page 349
  Answers to Quiz......Page 350
B: SUMMATION NOTATION......Page 352
 References......Page 355
C: STATISTICAL TABLES......Page 356
D: DOCUMENTATION OF DATA FILES......Page 370
 B......Page 372
 C......Page 373
 E......Page 374
 I......Page 375
 M......Page 376
 P......Page 377
 R......Page 378
 S......Page 379
 Y......Page 381
 C......Page 382
 E......Page 383
 I......Page 384
 J......Page 385
 M......Page 386
 N......Page 388
 S......Page 389
 U......Page 390
 Z......Page 391