Mee A Comprehensive Guide to Factorial Two-Level Experimentation

1. Auflage 2009
ISBN: 978-0-387-89103-3
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 545 Seiten

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.

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