A Comprehensive Guide to Factorial Two-Level Experimentation (eBook)

Robert Mee (Autor)

eBook Download: PDF

2009 | 2009
XXIII, 545 Seiten
Springer New York (Verlag)
978-0-387-89103-3 (ISBN)

Infos

This book contains the most comprehensive coverage available anywhere for two-level factorial designs.

The re-analysis of 50 published examples serves as a how-to guide for analysis of the many types of full factorial and fractional factorial designs.

By focusing on two-level designs, this book is accessible to a wide audience of practitioners who use planned experiments.

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Factorial designs enable researchers to experiment with many factors. The 50 published examples re-analyzed in this guide attest to the prolific use of two-level factorial designs. As a testimony to this universal applicability, the examples come from diverse fields: Analytical Chemistry, Animal Science, Automotive Manufacturing, Ceramics and Coatings, Chromatography, Electroplating, Food Technology, Injection Molding, Marketing, Microarray Processing, Modeling and Neural Networks, Organic Chemistry, Product Testing, Quality Improvement, Semiconductor Manufacturing, and Transportation.Focusing on factorial experimentation with two-level factors makes this book unique, allowing the only comprehensive coverage of two-level design construction and analysis. Furthermore, since two-level factorial experiments are easily analyzed using multiple regression models, this focus on two-level designs makes the material understandable to a wide audience. This book is accessible to non-statisticians having a grasp of least squares estimation for multiple regression and exposure to analysis of variance. "e;This book contains a wealth of information, including recent results on the design of two-level factorials and various aspects of analysis The examples are particularly clear and insightful."e; (William Notz, Ohio State University)"e;One of the strongest points of this book for an audience of practitioners is the excellent collection of published experiments, some of which didn't 'come out' as expected A statistically literate non-statistician who deals with experimental design will have plenty of motivation to read this book, and the payback for the effort will be substantial."e; (Max Morris, Iowa State University)

Inhalt

Dedication 6
Preface 8
Contents 12
List of Examples Analyzed 16
Full Factorial Designs 18
1 Introduction to Full Factorial Designs with Two- Level Factors 19
1.1 Advantages of Full Factorial Designs 19
1.2 Standard Regression Models for Factorial Designs with Two- Level Factors 25
1.3 Least Squares Estimation of a Regression Model 28
1.4 Presenting a Fitted Model Graphically 35
1.5 Four Steps for Planning a Successful Experiment 39
2 Analysis of Full Factorial Experiments 43
2.1 Analysis Strategy Overview 43
2.2 Analysis of Numerical Responses with Replication 45
2.3 The Inclusion of Centerpoint Replicates 47
2.4 Analysis of Numerical Responses Without Replication 51
2.5 Normal Plot of Effects and Other Analysis Tools 61
2.6 Diagnostics for a Fitted Model 64
2.7 Transformations of the Response 69
2.8 Analysis of Counts, Variances, and Other Statistics 73
2.9 Unequal Replication and Unequal Variance 83
2.10 The Impact of Missing Treatment Combinations 86
3 Common Randomization Restrictions 91
3.1 Sources of Variation and a Design’s Unit Structure 91
3.2 Treatment*Unit Interactions 94
3.3 Blocking: Partitioning a Factorial into Smaller Experiments 95
3.4 Analyzing Randomized Block Factorial Designs 102
3.5 Split-Unit Designs 113
3.6 Multiway Blocking 120
4 More Full Factorial Design Examples 131
4.1 Example 4.1: Replicated 23 With Subsampling Within Runs 131
4.2 Example 4.2: 29 Factorial for Peptide Research 138
4.3 Example 4.3: 25 with Centerpoint Runs for Ceramic Strength 150
Fractional Factorial Designs 159
5 Fractional Factorial Designs: The Basics 160
5.1 Initial Fractional Factorial Example 160
5.2 Introduction to Regular Fractional Factorial Designs 165
5.3 Basic Analysis for Regular Fractional Factorial Designs 176
6 Fractional Factorial Designs for Estimating Main Effects 187
6.1 Analysis of Regular Resolution III Fractional Factorial Designs 188
6.2 Some Theory Regarding Resolution III Designs 204
6.3 Nonregular Orthogonal Designs of Strength 2 208
6.4 Optimal Nonorthogonal Saturated Main Effect Designs 240
6.5 Supersaturated Designs 245
6.6 Conclusions 258
7 Designs for Estimating Main Effects and Some Two- Factor Interactions 259
7.1 Five Examples Analyzed 260
7.2 Regular Resolution IV Designs 281
7.3 Strength-3 Orthogonal Arrays 291
7.4 Nonorthogonal Resolution IV Designs 293
7.5 Summary Regarding Choice of a Design 296
8 Resolution V Fractional Factorial Designs 297
8.1 Regular Resolution V 2k f Fractional FactorialDesigns 297
8.2 Strength-4 Orthogonal Arrays 299
8.3 Three-Quarter Fraction of Regular Resolution V Designs 302
8.4 Smaller Nonorthogonal Resolution V Designs 307
8.5 Recommendations Regarding Design Choice 312
8.6 Analysis of Resolution V Experiments 313
9 Augmenting Fractional Factorial Designs 331
9.1 Follow-up Experimentation Choices 331
9.2 Confirmation Runs 333
9.3 Steepest Ascent Search 335
9.4 Foldover After a Resolution III Fraction 342
9.5 Foldover and Semifolding After a Resolution IV Fraction 346
9.6 Optimal Design Augmentation 352
9.7 Adding and Dropping Factors 356
10 Fractional Factorial Designs with Randomization Restrictions 357
10.1 Randomized Block Designs for Fractional Factorials 357
10.2 Split-Unit Designs for Fractional Factorials 364
10.3 Analysis of Fractional Factorials with Randomization Restrictions 368
10.4 Sequences of Fractional Factorial Designs 385
11 More Fractional Factorial Design Examples 389
11.1 A Mirror-Image Foldover with Unexpected Results 389
11.2 Steepest Ascent with Constraints 396
11.3 A Group Screening Experiment 399
11.4 Nonorthogonal Blocking for a Fractional Factorial 403
Additional Topics 409
12 Response Surface Methods and Second-Order Designs 410
12.1 The Response Surface Methodology Strategy 410
12.2 Central Composite Designs 412
12.3 Other Composite Designs 416
12.4 Box–Behnken Designs 420
12.5 Analysis/Interpretation of the Fitted Second-Order Model 422
13 Special Topics Regarding the Design 428
13.1 Power and the Choice of Sample Size 428
13.2 Choice of Factor Levels 433
13.3 Tips for Studying Variation 435
13.4 Accommodating Factors with More Levels 437
13.5 Special Requirements for Run Order and Treatment Combinations 441
14 Special Topics Regarding the Analysis 449
14.1 Minimal Replication and Lenth’s Method 449
14.2 Alternatives to Lenth t-Tests for UnreplicatedDesigns 452
14.3 Analyzing the Variation in Structured Samples 461
14.4 Generalized Least Squares Analysis When Variances Are Unequal 466
14.5 Mixed-Model Analysis 469
14.6 Highly Multivariate Response Data 473
14.7 Four Analysis Blunders to Avoid 478
Appendices and Tables 481
A Upper Percentiles of t Distributions, ta 482
B Upper Percentiles of F Distributions, Fa 483
C Upper Percentiles for Lenth t Statistics, cIERa and cEER 486
D Computing Upper Percentiles for Maximum Studentized Residual 489
E Orthogonal Blocking for Full 2k Factorial Designs 491
F Column Labels of Generators for Regular Fractional Factorial Designs 493
G Tables of Minimum Aberration Regular Fractional Factorial Designs 495
H Minimum Aberration Blocking Schemes for Fractional Factorial Designs 504
I Alias Matrix Derivation 518
J Distinguishing Among Fractional Factorial Designs 520
References 524
Abbreviations and Symbols 546
Index 550

Produkt-Details

• Erscheint lt. Verlag: 23.6.2009
• Zusatzinfo: XXIII, 545 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Marketing / Vertrieb
• Schlagworte: Analysis of Variance • Chemistry • Data Analysis • Design • Design of Experiments • Distribution • Excel • Experiment • Fractional factorial design • Marketing • Modeling • Multifactor experiment • Neural networks • Process Improvement • Processing • quality • search engine marketing (SEM) • Statistics • Transport • Variance
• ISBN-10: 0-387-89103-X / 038789103X
• ISBN-13: 978-0-387-89103-3 / 9780387891033