Creating clear designs: a graph-based algorithm and a catalog of clear compromise plans

A graph-based algorithm is proposed for creating regular fractional factorial designs with two-level factors such that a pre-specified set of two-factor interactions is clear of aliasing with any main effects or two-factor interactions (clear design). The Clear Interactions Graph (CIG) used in the algorithm is unique for each design and different in nature from the well-known Taguchi linear graph. Based on published catalogs of two-level fractional factorials, enhanced by the CIG, a search algorithm finds an appropriate clear design or declares its non-existence. The approach is applied to the creation of a catalog of minimum aberration clear compromise plans, which is also of interest in its own right. [Supplementary materials are available for this article. Go to the publisher’s online edition of IIE Transactions for additional discussions on run times and implementation of the algorithm for larger designs.]

[1]  Yu Ding,et al.  Graph based isomorph-free generation of two-level regular fractional factorial designs , 2010 .

[2]  Weiming Ke,et al.  Selecting 2m−p Designs Using a Minimum Aberration Criterion When Some Two-Factor Interactions Are Important , 2003, Technometrics.

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

[4]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[5]  Changbao Wu,et al.  A graph-aided method for planning two-level experiments when certain interactions are important , 1992 .

[6]  Edward M. Reingold,et al.  Tidier Drawings of Trees , 1981, IEEE Transactions on Software Engineering.

[7]  Changbao Wu,et al.  Clear two-factor interactions and minimum aberration , 2002 .

[8]  Robert W. Mee.  A Comprehensive Guide to Factorial Two-Level Experimentation , 2009 .

[9]  Weiming Ke,et al.  COMPROMISE PLANS WITH CLEAR TWO-FACTOR INTERACTIONS , 2005 .

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

[11]  Mario Vento,et al.  An Improved Algorithm for Matching Large Graphs , 2001 .

[12]  Robert W. Mee,et al.  Resolution IV Designs with 128 Runs , 2005 .

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

[14]  Susan M. Sanchez,et al.  Very large fractional factorial and central composite designs , 2005, TOMC.

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

[16]  S. Addelman.  Symmetrical and Asymmetrical Fractional Factorial Plans , 1962 .

[17]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .