Using Folded-Over Nonorthogonal Designs

This article demonstrates advantages of using nonorthogonal resolution IV designs for running small screening experiments when the primary goal is identification of important main effects (MEs) with a secondary goal of entertaining a small number of potentially important second-order interactions. This is accomplished by evaluating the structure and performance of designs obtained by folding over small efficient nonorthogonal resolution III designs and comparing them with more commonly used orthogonal resolution III designs of comparable size, such as fractional factorials and Plackett–Burman designs. The folded-over designs are available for a wider class of run sizes and perform as well as or better than resolution III competitors in selecting the correct model when a few active two-factor interactions are present and significantly outperform resolution III competitors in terms of correctly identifying MEs. A simple two-step procedure is proposed for analyzing data from such designs that separates the goals and is well suited for sorting through likely models quickly.

[1]  T. J. Mitchell,et al.  Two-Level Multifactor Designs for Detecting the Presence of Interactions , 1983 .

[2]  Dennis K. J. Lin,et al.  Projection properties of Plackett and Burman designs , 1992 .

[3]  Steve R. Webb,et al.  Non-Orthogonal Designs of Even Resolution* , 1968 .

[4]  Hugh Chipman,et al.  Bayesian variable selection with related predictors , 1995, bayes-an/9510001.

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

[6]  Damaraju Raghavarao,et al.  Some Optimum Weighing Designs , 1959 .

[7]  K. S. Banerjee,et al.  On a Special Subset Giving an Irregular Fractional Replicate of a 2 N Factorial Experiment , 1967 .

[8]  Peter W. M. John,et al.  Three Quarter Replicates of 2 n Designs , 1962 .

[9]  Some Designs for Maximal (+1, -1)-Determinant of Order n ≡2 (mod 4) , 1966 .

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

[11]  K. Kishen,et al.  On the Design of Experiments for Weighing and Making Other Types of Measurements , 1945 .

[12]  C. F. Jeff Wu,et al.  Experiments: Planning, Analysis, and Parameter Design Optimization , 2000 .

[13]  H. Chipman,et al.  A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing , 1997 .

[14]  N. Diamond,et al.  SOME PROPERTIES OF A FOLDOVER DESIGN , 1995 .

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

[16]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

[17]  C. H. Yang.  On designs of maximal (+1,-1)-matrices of order ≡2(\4). II , 1968 .

[18]  A. Mood.  On Hotelling's Weighing Problem , 1946 .

[19]  Changbao Wu,et al.  Construction of supersaturated designs through partially aliased interactions , 1993 .

[20]  C. H. Yang.  Some designs for maximal (+1,-1)-determinant of order ≡2(4) , 1966 .

[21]  Robert W. Mee,et al.  Better Foldover Fractions for Resolution III 2k-p Designs , 2002, Technometrics.

[22]  THE USE OF A CLASS OF FOLDOVER DESIGNS AS SEARCH DESIGNS , 1991 .

[23]  Kenny Q. Ye,et al.  Some properties of blocked and unblocked foldovers of 2k-p designs , 2003 .

[24]  Sidney Addelman,et al.  trans-Dimethanolbis(1,1,1-trifluoro-5,5-dimethylhexane-2,4-dionato)zinc(II) , 2008, Acta crystallographica. Section E, Structure reports online.

[25]  R. Sitter,et al.  Choosing columns from the 12-run Plackett-Burman design , 2004 .

[26]  H. Hotelling.  Some Improvements in Weighing and Other Experimental Techniques , 1944 .

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

[28]  B. Margolin.  Results on Factorial Designs of Resolution IV for the 2 n and 2 n 3 m Series , 1969 .

[29]  William Li,et al.  Optimal Foldover Plans for Two-Level Fractional Factorial Designs , 2003, Technometrics.