Mee A Comprehensive Guide to Factorial Two-Level Experimentation

1. Auflage 2009
ISBN: 978-0-387-89103-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 545 Seiten

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.

"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." (William Notz, Ohio State University)

"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." (Max Morris, Iowa State University)

Autoren/Hrsg.

Mee, Robert

Inhaltsverzeichnis

1;Dedication;6
2;Preface;8
3;Contents;12
4;List of Examples Analyzed;16
5;Full Factorial Designs;18
5.1;1 Introduction to Full Factorial Designs with Two- Level Factors;19
5.1.1;1.1 Advantages of Full Factorial Designs;19
5.1.2;1.2 Standard Regression Models for Factorial Designs with Two- Level Factors;25
5.1.3;1.3 Least Squares Estimation of a Regression Model;28
5.1.4;1.4 Presenting a Fitted Model Graphically;35
5.1.5;1.5 Four Steps for Planning a Successful Experiment;39
5.2;2 Analysis of Full Factorial Experiments;43
5.2.1;2.1 Analysis Strategy Overview;43
5.2.2;2.2 Analysis of Numerical Responses with Replication;45
5.2.3;2.3 The Inclusion of Centerpoint Replicates;47
5.2.4;2.4 Analysis of Numerical Responses Without Replication;51
5.2.5;2.5 Normal Plot of Effects and Other Analysis Tools;61
5.2.6;2.6 Diagnostics for a Fitted Model;64
5.2.7;2.7 Transformations of the Response;69
5.2.8;2.8 Analysis of Counts, Variances, and Other Statistics;73
5.2.9;2.9 Unequal Replication and Unequal Variance;83
5.2.10;2.10 The Impact of Missing Treatment Combinations;86
5.3;3 Common Randomization Restrictions;91
5.3.1;3.1 Sources of Variation and a Design’s Unit Structure;91
5.3.2;3.2 Treatment*Unit Interactions;94
5.3.3;3.3 Blocking: Partitioning a Factorial into Smaller Experiments;95
5.3.4;3.4 Analyzing Randomized Block Factorial Designs;102
5.3.5;3.5 Split-Unit Designs;113
5.3.6;3.6 Multiway Blocking;120
5.4;4 More Full Factorial Design Examples;131
5.4.1;4.1 Example 4.1: Replicated 23 With Subsampling Within Runs;131
5.4.2;4.2 Example 4.2: 29 Factorial for Peptide Research;138
5.4.3;4.3 Example 4.3: 25 with Centerpoint Runs for Ceramic Strength;150
6;Fractional Factorial Designs;159
6.1;5 Fractional Factorial Designs: The Basics;160
6.1.1;5.1 Initial Fractional Factorial Example;160
6.1.2;5.2 Introduction to Regular Fractional Factorial Designs;165
6.1.3;5.3 Basic Analysis for Regular Fractional Factorial Designs;176
6.2;6 Fractional Factorial Designs for Estimating Main Effects;187
6.2.1;6.1 Analysis of Regular Resolution III Fractional Factorial Designs;188
6.2.2;6.2 Some Theory Regarding Resolution III Designs;204
6.2.3;6.3 Nonregular Orthogonal Designs of Strength 2;208
6.2.4;6.4 Optimal Nonorthogonal Saturated Main Effect Designs;240
6.2.5;6.5 Supersaturated Designs;245
6.2.6;6.6 Conclusions;258
6.3;7 Designs for Estimating Main Effects and Some Two- Factor Interactions;259
6.3.1;7.1 Five Examples Analyzed;260
6.3.2;7.2 Regular Resolution IV Designs;281
6.3.3;7.3 Strength-3 Orthogonal Arrays;291
6.3.4;7.4 Nonorthogonal Resolution IV Designs;293
6.3.5;7.5 Summary Regarding Choice of a Design;296
6.4;8 Resolution V Fractional Factorial Designs;297
6.4.1;8.1 Regular Resolution V 2k f Fractional FactorialDesigns;297
6.4.2;8.2 Strength-4 Orthogonal Arrays;299
6.4.3;8.3 Three-Quarter Fraction of Regular Resolution V Designs;302
6.4.4;8.4 Smaller Nonorthogonal Resolution V Designs;307
6.4.5;8.5 Recommendations Regarding Design Choice;312
6.4.6;8.6 Analysis of Resolution V Experiments;313
6.5;9 Augmenting Fractional Factorial Designs;331
6.5.1;9.1 Follow-up Experimentation Choices;331
6.5.2;9.2 Confirmation Runs;333
6.5.3;9.3 Steepest Ascent Search;335
6.5.4;9.4 Foldover After a Resolution III Fraction;342
6.5.5;9.5 Foldover and Semifolding After a Resolution IV Fraction;346
6.5.6;9.6 Optimal Design Augmentation;352
6.5.7;9.7 Adding and Dropping Factors;356
6.6;10 Fractional Factorial Designs with Randomization Restrictions;357
6.6.1;10.1 Randomized Block Designs for Fractional Factorials;357
6.6.2;10.2 Split-Unit Designs for Fractional Factorials;364
6.6.3;10.3 Analysis of Fractional Factorials with Randomization Restrictions;368
6.6.4;10.4 Sequences of Fractional Factorial Designs;385
6.7;11 More Fractional Factorial Design Examples;389
6.7.1;11.1 A Mirror-Image Foldover with Unexpected Results;389
6.7.2;11.2 Steepest Ascent with Constraints;396
6.7.3;11.3 A Group Screening Experiment;399
6.7.4;11.4 Nonorthogonal Blocking for a Fractional Factorial;403
7;Additional Topics;409
7.1;12 Response Surface Methods and Second-Order Designs;410
7.1.1;12.1 The Response Surface Methodology Strategy;410
7.1.2;12.2 Central Composite Designs;412
7.1.3;12.3 Other Composite Designs;416
7.1.4;12.4 Box–Behnken Designs;420
7.1.5;12.5 Analysis/Interpretation of the Fitted Second-Order Model;422
7.2;13 Special Topics Regarding the Design;428
7.2.1;13.1 Power and the Choice of Sample Size;428
7.2.2;13.2 Choice of Factor Levels;433
7.2.3;13.3 Tips for Studying Variation;435
7.2.4;13.4 Accommodating Factors with More Levels;437
7.2.5;13.5 Special Requirements for Run Order and Treatment Combinations;441
7.3;14 Special Topics Regarding the Analysis;449
7.3.1;14.1 Minimal Replication and Lenth’s Method;449
7.3.2;14.2 Alternatives to Lenth t-Tests for UnreplicatedDesigns;452
7.3.3;14.3 Analyzing the Variation in Structured Samples;461
7.3.4;14.4 Generalized Least Squares Analysis When Variances Are Unequal;466
7.3.5;14.5 Mixed-Model Analysis;469
7.3.6;14.6 Highly Multivariate Response Data;473
7.3.7;14.7 Four Analysis Blunders to Avoid;478
8;Appendices and Tables;481
8.1;A Upper Percentiles of t Distributions, ta;482
8.2;B Upper Percentiles of F Distributions, Fa;483
8.3;C Upper Percentiles for Lenth t Statistics, cIERa and cEER;486
8.4;D Computing Upper Percentiles for Maximum Studentized Residual;489
8.5;E Orthogonal Blocking for Full 2k Factorial Designs;491
8.6;F Column Labels of Generators for Regular Fractional Factorial Designs;493
8.7;G Tables of Minimum Aberration Regular Fractional Factorial Designs;495
8.8;H Minimum Aberration Blocking Schemes for Fractional Factorial Designs;504
8.9;I Alias Matrix Derivation;518
8.10;J Distinguishing Among Fractional Factorial Designs;520
8.11;References;524
8.12;Abbreviations and Symbols;546
8.13;Index;550