Permuting regular fractional factorial designs for screening quantitative factors

Fractional factorial designs are widely used in screening experiments. They are often chosen by the minimum aberration criterion, which regards factor levels as symbols. For designs with quantitative factors, however, permuting the levels for one or more factors could alter their geometrical structures and statistical properties. We provide a justification of the minimum β-aberration criterion for quantitative factors and study level permutations for regular fractional factorial designs in order to improve their efficiency for screening quantitative factors. We show how regular designs can be linearly permuted to reduce contamination of nonnegligible interactions on the estimation of linear effects without increasing the run size. We further show that such linear permutations are unique under the minimum β-aberration criterion and the best level permutations can be determined without an exhaustive search. We establish additional theoretical results for three-level designs and obtain the best level permutations for regular designs with 27 and 81 runs. We illustrate the practical benefits of level permutation with an antiviral drug combination experiment.

[1]  Hongquan Xu,et al.  Algorithmic Construction of Efficient Fractional Factorial Designs With Large Run Sizes , 2007, Technometrics.

[2]  Jesús López Fidalgo,et al.  Moda 8 - Advances in Model-Oriented Design and Analysis , 2007 .

[3]  C. F. Jeff Wu,et al.  Optimal Projective Three-Level Designs for Factor Screening and Interaction Detection , 2004, Technometrics.

[4]  Weng Kee Wong,et al.  Recent developments in nonregular fractional factorial designs , 2008, 0812.3000.

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

[6]  W. G. Hunter,et al.  Minimum Aberration 2 k–p Designs , 1980 .

[7]  Kenny Q. Ye,et al.  Geometric isomorphism and minimum aberration for factorial designs with quantitative factors , 2004, math/0503678.

[8]  Dennis K. J. Lin,et al.  Uniform fractional factorial designs , 2012, 1206.0897.

[9]  Hongquan Xu,et al.  A catalogue of three-level regular fractional factorial designs , 2005 .

[10]  Kenneth Joseph Ryan,et al.  Minimum Aberration Fractional Factorial Designs With Large N , 2010, Technometrics.

[11]  Lih-Yuan Deng,et al.  Orthogonal Arrays: Theory and Applications , 1999, Technometrics.

[12]  Jiahua Chen,et al.  A catalogue of two-level and three-level fractional factorial designs with small runs , 1993 .

[13]  Rahul Mukerjee,et al.  A Modern Theory Of Factorial Designs , 2006 .

[14]  Hongquan Xu,et al.  Minimum aberration blocking schemes for two- and three-level fractional factorial designs , 2006 .

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

[17]  Weng Kee Wong,et al.  Application of fractional factorial designs to study drug combinations , 2013, Statistics in medicine.

[18]  W. G. Hunter,et al.  Minimum Aberration 2k-p Designs , 1980 .

[19]  Changbao Wu,et al.  Fractional Factorial Designs , 2022 .