Selecting an Orthogonal or Nonorthogonal Two-Level Design for Screening

ABSTRACT This article presents a comparison of criteria used to characterize two-level designs for screening purposes. To articulate the relationships among criteria, we focus on 7-factor designs with 16–32 runs and 11-factor designs with 20–48 runs. Screening based on selected designs for each of the run sizes considered is studied with simulation using a forward selection procedure and the Dantzig selector. This article compares Bayesian D-optimal designs, designs created algorithmically to optimize estimation capacity over various model spaces, and orthogonal designs by estimation-based criteria and simulation. In this way, we furnish both general insights regarding various design approaches, as well as a guide to make a choice among a few final candidate designs. Supplementary materials for this article are available online.

[1]  Lih-Yuan Deng,et al.  Moment Aberration Projection for Nonregular Fractional Factorial Designs , 2005, Technometrics.

[2]  Ching-Shui Cheng,et al.  Some Projection Properties of Orthogonal Arrays , 1995 .

[3]  Neil A. Butler,et al.  Minimum aberration construction results for nonregular two‐level fractional factorial designs , 2003 .

[4]  Randy R. Sitter,et al.  Using the Folded-Over 12-Run Plackett—Burman Design to Consider Interactions , 2001, Technometrics.

[5]  Angela M. Dean,et al.  Screening Strategies in the Presence of Interactions , 2014, Technometrics.

[6]  Don X. Sun,et al.  An Algorithm for Sequentially Constructing Non-Isomorphic Orthogonal Designs and its Applications , 2002 .

[7]  Dennis K. J. Lin,et al.  FORWARD SELECTION ERROR CONTROL IN THE ANALYSIS OF SUPERSATURATED DESIGNS , 1998 .

[8]  Boxin Tang,et al.  Minimum G Aberration Design Construction and Design Tables for 24 Runs , 2005 .

[9]  R. Plackett,et al.  THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS , 1946 .

[10]  Pieter T. Eendebak,et al.  Complete enumeration of pure‐level and mixed‐level orthogonal arrays , 2009 .

[11]  Terence Tao,et al.  The Dantzig selector: Statistical estimation when P is much larger than n , 2005, math/0506081.

[12]  Arden Miller,et al.  The Analysis of Unreplicated Factorial Experiments Using All Possible Comparisons , 2005, Technometrics.

[13]  Lih-Yuan Deng,et al.  Minimum $G_2$-aberration for nonregular fractional factorial designs , 1999 .

[14]  Lih-Yuan Deng,et al.  GENERALIZED RESOLUTION AND MINIMUM ABERRATION CRITERIA FOR PLACKETT-BURMAN AND OTHER NONREGULAR FACTORIAL DESIGNS , 1999 .

[15]  Changbao Wu,et al.  Analysis of Designed Experiments with Complex Aliasing , 1992 .

[16]  Chen-Tuo Liao,et al.  Design and Analysis of Two-Level Factorial Experiments With Partial Replication , 2009, Technometrics.

[17]  D. Bulutoglu,et al.  Classification of Orthogonal Arrays by Integer Programming , 2008 .

[18]  Steven G. Gilmour,et al.  A General Criterion for Factorial Designs Under Model Uncertainty , 2010, Technometrics.

[19]  Hugh A. Chipman,et al.  Incorporating Prior Information in Optimal Design for Model Selection , 2007, Technometrics.

[20]  Steven G. Gilmour,et al.  Three-level main-effects designs exploiting prior information about model uncertainty , 2007 .

[21]  Christos Koukouvinos,et al.  Model Discrimination Criteria on Model-Robust Designs , 2014, Commun. Stat. Simul. Comput..

[22]  G. Sivyer,et al.  Letter to the Editor , 2014, Dermatology practical & conceptual.

[23]  Byran J. Smucker,et al.  Model-Robust Two-Level Designs Using Coordinate Exchange Algorithms and a Maximin Criterion , 2012, Technometrics.

[24]  A.Emin Kürekçi,et al.  LETTER TO THE EDITOR: Response , 2005, Spine.

[25]  Robert W. Mee,et al.  SECOND ORDER SATURATED ORTHOGONAL ARRAYS OF STRENGTH THREE , 2008 .

[26]  Lih-Yuan Deng,et al.  Design Selection and Classification for Hadamard Matrices Using Generalized Minimum Aberration Criteria , 2002, Technometrics.

[27]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[28]  William Li,et al.  Model-Robust Factorial Designs , 2000, Technometrics.

[29]  C. R. Rao,et al.  Factorial Experiments Derivable from Combinatorial Arrangements of Arrays , 1947 .

[30]  Eric D. Schoen,et al.  Two‐level designs of strength 3 and up to 48 runs , 2012 .

[31]  Boxin Tang,et al.  GENERALIZED MINIMUM ABERRATION AND DESIGN EFFICIENCY FOR NONREGULAR FRACTIONAL FACTORIAL DESIGNS , 2002 .

[32]  W. DuMouchel,et al.  A simple Bayesian modification of D-optimal designs to reduce dependence on an assumed model , 1994 .

[33]  Jim Euchner.  Design , 2014, Catalysis from A to Z.

[34]  Dennis K. J. Lin,et al.  Generating alias relationships for two-level Plackett and Burman designs , 1993 .

[35]  Kenny Q. Ye,et al.  Model discrimination—another perspective on model-robust designs , 2007 .

[36]  A Miller,et al.  Using Folded-Over Nonorthogonal Designs , 2005, Technometrics.

[37]  Hongquan Xu.  Some Nonregular Designs From the Nordstrom and Robinson Code and Their Statistical Properties , 2005 .

[38]  Randy R. Sitter,et al.  Folded over non-orthogonal designs , 2008 .

[39]  Xiang Li,et al.  Regularities in data from factorial experiments , 2006, Complex..

[40]  Robert W. Mee.  Tips for Analyzing Nonregular Fractional Factorial Experiments , 2013 .

[41]  Lloyd S. Nelson,et al.  Analysis of Two-Level Factorial Experiments , 1982 .

[42]  Randy R. Sitter,et al.  Nonregular Designs With Desirable Projection Properties , 2007, Technometrics.

[43]  Byran J. Smucker,et al.  Approximate Model Spaces for Model-Robust Experiment Design , 2015, Technometrics.