Business Process Improvement - Engineering Statistics Handbook

handbook/pri......Page 0
5. Process Improvement......Page 1
5. Process Improvement......Page 3
5.1. Introduction......Page 9
5.1.1. What is experimental design?......Page 10
5.1.2. What are the uses of DOE?......Page 13
5.1.3. What are the steps of DOE?......Page 19
5.2. Assumptions......Page 21
5.2.1. Is the measurement system capable?......Page 22
5.2.2. Is the process stable?......Page 23
5.2.3. Is there a simple model?......Page 24
5.2.4. Are the model residuals well-behaved?......Page 25
5.3. Choosing an experimental design......Page 35
5.3.1. What are the objectives?......Page 37
5.3.2. How do you select and scale the process variables?......Page 39
5.3.3. How do you select an experimental design?......Page 42
5.3.3.1. Completely randomized designs......Page 45
5.3.3.2. Randomized block designs......Page 48
5.3.3.2.1. Latin square and related designs......Page 52
5.3.3.2.2. Graeco-Latin square designs......Page 58
5.3.3.2.3. Hyper-Graeco-Latin square designs......Page 62
5.3.3.3. Full factorial designs......Page 65
5.3.3.3.1. Two-level full factorial designs......Page 66
5.3.3.3.2. Full factorial example......Page 69
5.3.3.3.3. Blocking of full factorial designs......Page 75
5.3.3.4. Fractional factorial designs......Page 79
5.3.3.4.1. A 23-1 design (half of a 23)......Page 81
5.3.3.4.2. Constructing the 23-1 half-fraction design......Page 85
5.3.3.4.3. Confounding (also called aliasing)......Page 88
5.3.3.4.4. Fractional factorial design specifications and design resolution......Page 91
5.3.3.4.5. Use of fractional factorial designs......Page 98
5.3.3.4.6. Screening designs......Page 100
5.3.3.4.7. Summary tables of useful fractional factorial designs......Page 102
5.3.3.5. Plackett-Burman designs......Page 105
5.3.3.6. Response surface designs......Page 108
5.3.3.6.1. Central Composite Designs (CCD)......Page 114
5.3.3.6.2. Box-Behnken designs......Page 119
5.3.3.6.3. Comparisons of response surface designs......Page 121
5.3.3.6.4. Blocking a response surface design......Page 126
5.3.3.7. Adding centerpoints......Page 131
5.3.3.8. Improving fractional factorial design resolution......Page 135
5.3.3.8.1. Mirror-Image foldover designs......Page 136
5.3.3.8.2. Alternative foldover designs......Page 141
5.3.3.9. Three-level full factorial designs......Page 144
5.3.3.10. Three-level, mixed-level and fractional factorial designs......Page 148
5.4. Analysis of DOE data......Page 153
5.4.1. What are the steps in a DOE analysis?......Page 154
5.4.2. How to "look" at DOE data......Page 156
5.4.3. How to model DOE data......Page 159
5.4.4. How to test and revise DOE models......Page 161
5.4.5. How to interpret DOE results......Page 163
5.4.6. How to confirm DOE results (confirmatory runs)......Page 164
5.4.7. Examples of DOE's......Page 166
5.4.7.1. Full factorial example......Page 167
5.4.7.2. Fractional factorial example......Page 182
5.4.7.3. Response surface model example......Page 200
5.5. Advanced topics......Page 216
5.5.1. What if classical designs don't work?......Page 218
5.5.2. What is a computer-aided design?......Page 220
5.5.2.1. D-Optimal designs......Page 222
5.5.2.2. Repairing a design......Page 227
5.5.3. How do you optimize a process?......Page 228
5.5.3.1. Single response case......Page 230
5.5.3.1.1. Single response: Path of steepest ascent......Page 231
5.5.3.1.2. Single response: Confidence region for search path......Page 237
5.5.3.1.3. Single response: Choosing the step length......Page 241
5.5.3.1.4. Single response: Optimization when there is adequate quadratic fit......Page 245
5.5.3.1.5. Single response: Effect of sampling error on optimal solution......Page 254
5.5.3.1.6. Single response: Optimization subject to experimental region constraints......Page 255
5.5.3.2. Multiple response case......Page 257
5.5.3.2.1. Multiple response: Path of steepest ascent......Page 258
5.5.3.2.2. Multiple response: The desirability approach......Page 261
5.5.3.2.3. Multiple response: The mathematical programming approach......Page 267
5.5.4. What is a mixture design?......Page 270
5.5.4.1. Mixture screening designs......Page 272
5.5.4.2. Simplex-lattice designs......Page 273
5.5.4.3. Simplex-centroid designs......Page 280
5.5.4.4. Constrained mixture designs......Page 281
5.5.4.5. Treating mixture and process variables together......Page 285
5.5.5. How can I account for nested variation (restricted randomization)?......Page 288
5.5.6. What are Taguchi designs?......Page 299
5.5.7. What are John's 3/4 fractional factorial designs?......Page 305
5.5.8. What are small composite designs?......Page 310
5.5.9. An EDA approach to experimental design......Page 313
5.5.9.1. Ordered data plot......Page 316
5.5.9.2. Dex scatter plot......Page 319
5.5.9.3. Dex mean plot......Page 323
5.5.9.4. Interaction effects matrix plot......Page 327
5.5.9.5. Block plot......Page 336
5.5.9.6. Dex Youden plot......Page 341
5.5.9.7. |Effects| plot......Page 344
5.5.9.7.1. Statistical significance......Page 348
5.5.9.7.2. Engineering significance......Page 351
5.5.9.7.3. Numerical significance......Page 353
5.5.9.7.4. Pattern significance......Page 354
5.5.9.8. Half-normal probability plot......Page 355
5.5.9.9. Cumulative residual standard deviation plot......Page 360
5.5.9.9.1. Motivation: What is a Model?......Page 366
5.5.9.9.2. Motivation: How do we Construct a Goodness-of-fit Metric for a Model?......Page 367
5.5.9.9.3. Motivation: How do we Construct a Good Model?......Page 369
5.5.9.9.4. Motivation: How do we Know When to Stop Adding Terms?......Page 372
5.5.9.9.5. Motivation: What is the Form of the Model?......Page 374
5.5.9.9.6. Motivation: Why is the 1/2 in the Model?......Page 376
5.5.9.9.7. Motivation: What are the Advantages of the Linear Combinatoric Model?......Page 380
5.5.9.9.8. Motivation: How do we use the Model to Generate Predicted Values?......Page 382
5.5.9.9.9. Motivation: How do we Use the Model Beyond the Data Domain?......Page 385
5.5.9.9.10. Motivation: What is the Best Confirmation Point for Interpolation?......Page 387
5.5.9.9.11. Motivation: How do we Use the Model for Interpolation?......Page 389
5.5.9.9.12. Motivation: How do we Use the Model for Extrapolation?......Page 392
5.5.9.10. DEX contour plot......Page 394
5.5.9.10.1. How to Interpret: Axes......Page 398
5.5.9.10.2. How to Interpret: Contour Curves......Page 401
5.5.9.10.3. How to Interpret: Optimal Response Value......Page 403
5.5.9.10.4. How to Interpret: Best Corner......Page 404
5.5.9.10.5. How to Interpret: Steepest Ascent/Descent......Page 406
5.5.9.10.6. How to Interpret: Optimal Curve......Page 407
5.5.9.10.7. How to Interpret: Optimal Setting......Page 408
5.6. Case Studies......Page 413
5.6.1. Eddy Current Probe Sensitivity Case Study......Page 414
5.6.1.1. Background and Data......Page 415
5.6.1.2. Initial Plots/Main Effects......Page 417
5.6.1.3. Interaction Effects......Page 421
5.6.1.4. Main and Interaction Effects: Block Plots......Page 423
5.6.1.5. Estimate Main and Interaction Effects......Page 425
5.6.1.6. Modeling and Prediction Equations......Page 428
5.6.1.7. Intermediate Conclusions......Page 430
5.6.1.8. Important Factors and Parsimonious Prediction......Page 432
5.6.1.9. Validate the Fitted Model......Page 436
5.6.1.10. Using the Fitted Model......Page 439
5.6.1.11. Conclusions and Next Step......Page 441
5.6.1.12. Work This Example Yourself......Page 443
5.6.2. Sonoluminescent Light Intensity Case Study......Page 446
5.6.2.1. Background and Data......Page 447
5.6.2.2. Initial Plots/Main Effects......Page 450
5.6.2.3. Interaction Effects......Page 454
5.6.2.4. Main and Interaction Effects: Block Plots......Page 456
5.6.2.5. Important Factors: Youden Plot......Page 458
5.6.2.6. Important Factors: |Effects| Plot......Page 460
5.6.2.7. Important Factors: Half-Normal Probability Plot......Page 462
5.6.2.8. Cumulative Residual Standard Deviation Plot......Page 464
5.6.2.9. Next Step: Dex Contour Plot......Page 466
5.6.2.10. Summary of Conclusions......Page 468
5.6.2.11. Work This Example Yourself......Page 470
5.7. A Glossary of DOE Terminology......Page 473
5.8. References......Page 478