On general minimum lower order confounding criterion for s-level regular designs

This paper shows that the existing optimality criteria for s-level designs can be expressed by the aliased component-number pattern, which is the core of the general minimum lower order confounding criterion for s-level designs.

[1]  Boxin Tang,et al.  A general theory of minimum aberration and its applications , 2005 .

[2]  C. F. J. Wu,et al.  MINIMUM ABERRATION DESIGNS FOR MIXED FACTORIALS IN TERMS OF COMPLEMENTARY SETS , 2001 .

[3]  Runchu Zhang,et al.  2 ( n 1 + n 2 ) - ( k 1 + k 2 ) Fractional factorial split-plot designs containing clear effects , 2006 .

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

[5]  Min-Qian Liu,et al.  Weak minimum aberration and maximum number of clear two-factor interactions in $$2_{IV}^{m - p} $$ designs , 2005 .

[6]  Mingyao Ai,et al.  sn−m Designs containing clear main effects or clear two-factor interactions , 2004 .

[7]  Runchu Zhang,et al.  Multistratum fractional factorial split-plot designs with minimum aberration and maximum estimation capacity , 2004 .

[8]  Hongquan Xu,et al.  Blocked Regular Fractional Factorial Designs With Minimum Aberration , 2005, math/0702702.

[9]  Min-Qian Liu,et al.  A note on minimum aberration and clear criteria , 2006 .

[10]  Neil A. Butler,et al.  Some theory for constructing minimum aberration fractional factorial designs , 2003 .

[11]  Runchu Zhang,et al.  Optimal blocking of two-level fractional factorial designs , 2000 .

[12]  Ching-Shui Cheng,et al.  Doubling and projection: A method of constructing two-level designs of resolution IV , 2006, math/0605616.

[13]  Jiahua Chen,et al.  Some Results on $2^{n - k}$ Fractional Factorial Designs and Search for Minimum Aberration Designs , 1992 .

[14]  R. Mukerjee,et al.  Characterization of general minimum lower order confounding via complementary sets , 2009 .

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

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

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

[18]  Min-Qian Liu,et al.  Some results on blocked regular 2-level fractional factorial designs with clear effects , 2006 .

[19]  R. Zhang,et al.  Some results on two-level regular designs with general minimum lower-order confounding , 2011 .

[20]  C. F. J. Wu,et al.  Some identities on $q\sp {n-m}$ designs with application to minimum aberration designs , 1997 .

[21]  Min-Qian Liu,et al.  SOME THEORY FOR CONSTRUCTING GENERAL MINIMUM LOWER ORDER CONFOUNDING DESIGNS , 2011 .

[22]  Runchu Zhang,et al.  MINIMUM ABERRATION (S 2 )S n−k DESIGNS , 2001 .

[23]  Yi Cheng,et al.  On construction of general minimum lower order confounding 2 n- m designs with N / 4 + 1 = n = 9 N / , 2010 .

[24]  M. F. Franklin Constructing Tables of Minimum Aberration pn-m Designs , 1984 .

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

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

[27]  A. S. Hedayat,et al.  2n-m designs with resolution III or IV containing clear two-factor interactions , 1998 .

[28]  Jiahua Chen,et al.  Some Results on $s^{n-k}$ Fractional Factorial Designs with Minimum Aberration or Optimal Moments , 1991 .

[29]  J. S. Hunter,et al.  The 2 k—p Fractional Factorial Designs Part I , 2000, Technometrics.

[30]  Ching-Shui Cheng,et al.  Regular fractional factorial designs with minimum aberration and maximum estimation capacity , 1998 .

[31]  J. S. Hunter,et al.  The 2 k — p Fractional Factorial Designs , 1961 .

[32]  Shengli Zhao,et al.  A theory on constructing 2n-m designs with general minimum lower order confounding , 2011 .

[33]  Mingyao Ai,et al.  Theory of minimum aberration blocked regular mixed factorial designs , 2004 .

[34]  A. S. Hedayat,et al.  2n-l designs with weak minimum aberration , 1996 .

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

[36]  Boxin Tang,et al.  Bounds on the maximum number of clear two‐factor interactions for 2m‐p designs of resolution III and IV , 2002 .

[37]  Zhiming Li,et al.  Three‐level regular designs with general minimum lower‐order confounding , 2013 .

[38]  Yu Zhu,et al.  ON THE COSET PATTERN MATRICES AND MINIMUM M-ABERRATION OF 2 n p DESIGNS , 2005 .

[39]  Runchu Zhang,et al.  General minimum lower order confounding designs: An overview and a construction theory , 2010 .

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

[41]  Boxin Tang,et al.  Characterization of minimum aberration $2\sp {n-k}$ designs in terms of their complementary designs , 1996 .