Classification of three-level strength-3 arrays

Generalized aberration (GA) is one of the most frequently used criteria to quantify the suitability of an orthogonal array (OA) to be used as an experimental design. The two main motivations for GA are that it quantifies bias in a main-effects only model and that it is a good surrogate for estimation efficiencies of models with all the main effects and some two-factor interaction components. We demonstrate that these motivations are not appropriate for three-level OAs of strength 3 and we propose a direct classification with other criteria instead. To illustrate, we classified complete series of three-level strength-3 OAs with 27, 54 and 81 runs using the GA criterion, the rank of the matrix with two-factor interaction contrasts, the estimation efficiency of two-factor interactions, the projection estimation capacity, and a new model robustness criterion. For all of the series, we provide a list of admissible designs according to these criteria. © 2011 Elsevier B.V.

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

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

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

[4]  Don X. Sun,et al.  Optimal blocking schemes for 2 n and 2 n−p designs , 1997 .

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

[6]  A. S. Hedayat,et al.  On the maximal number of factors and the enumeration of 3-symbol orthogonal arrays of strength 3 and index 2 , 1997 .

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

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

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

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

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

[12]  Mingyao Ai,et al.  Optimal criteria and equivalence for nonregular fractional factorial designs , 2005 .

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

[14]  David M. Steinberg,et al.  Minimum aberration and model robustness for two‐level fractional factorial designs , 1999 .

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

[16]  Kai-Tai Fang,et al.  A note on generalized aberration in factorial designs , 2001 .

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

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

[19]  Don X. Sun,et al.  Optimal Blocking Schemes for 2n and 2n—p Designs , 1997 .

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