Benefits and Fast Construction of Efficient Two-Level Foldover Designs

Recent work in two-level screening experiments has demonstrated the advantages of using small foldover designs, even when such designs are not orthogonal for the estimation of main effects (MEs). In this article, we provide further support for this argument and develop a fast algorithm for constructing efficient two-level foldover (EFD) designs. We show that these designs have equal or greater efficiency for estimating the ME model versus competitive designs in the literature and that our algorithmic approach allows the fast construction of designs with many more factors and/or runs. Our compromise algorithm allows the practitioner to choose among many designs making a trade-off between efficiency of the main effect estimates and correlation of the two-factor interactions (2FIs). Using our compromise approach, practitioners can decide just how much efficiency they are willing to sacrifice to avoid confounded 2FIs as well as lowering an omnibus measure of correlation among the 2FIs.

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

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

[3]  Bradley. Jones.  Comment: Enhancing the Search for Compromise Designs , 2013, Technometrics.

[4]  R. K. Meyer,et al.  The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs , 1995 .

[5]  Christopher J. Nachtsheim,et al.  Definitive Screening Designs with Added Two-Level Categorical Factors* , 2013 .

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

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

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

[9]  C. F. Jeff Wu,et al.  Experiments , 2021, Wiley Series in Probability and Statistics.

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

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

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

[13]  Christopher J. Nachtsheim,et al.  Blocking Schemes for Definitive Screening Designs , 2016, Technometrics.

[14]  Christopher J. Nachtsheim,et al.  A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects , 2011 .

[15]  Kenny Q. Ye,et al.  Algorithmic construction of catalogs of non-isomorphic two-level orthogonal designs for economic run sizes , 2008 .