Some results on blocked regular 2-level fractional factorial designs with clear effects

Abstract Blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation. In this article, the clear effect concept is discussed for the blocked fractional factorial designs. First, some theoretical results on the existence of clear main effects and two-factor interactions (2fi's) in regular 2 m - p : 2 l designs with resolution III, IV - and IV are obtained, where a 2 m - p : 2 l design means a 2 m - p design in 2 l blocks. Then, the blocked designs containing clear 2fi's are mainly considered and the upper and lower bounds on the maximum number of clear 2fi's in 2 m - p : 2 l designs with resolution III and IV - are derived. The lower bounds are achieved by constructing specific designs. Some tables are also given for comparing the bounds with true values, which show that many designs constructed by our methods have the maximum number of clear 2fi's.

[1]  C. F. Jeff Wu,et al.  Choice of Optimal Blocking Schemes in Two-Level and Three-Level Designs , 2002, Technometrics.

[2]  Rahul Mukerjee,et al.  Blocking in regular fractional factorials: a projective geometric approach , 1999 .

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

[4]  Dennis K. J. Lin,et al.  Capacity considerations for two-level fractional factorial designs , 1990 .

[5]  Runchu Zhang,et al.  Choice of optimal initial designs in sequential experiments , 2005 .

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

[7]  Runchu Zhang,et al.  Theory of optimal blocking of nonregular factorial designs , 2004 .

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

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

[10]  K. A. Brownlee,et al.  Fractional Factorial Experiment Designs for Factors at Two Levels. , 1958 .

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

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

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

[14]  Ching-Shui Cheng,et al.  Theory of optimal blocking of $2^{n-m}$ designs , 1999 .

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

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

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

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

[19]  W. S. Connor,et al.  Fractional factorial experiment designs for factors at three levels , 1961 .