Indicator function and its application in two-level factorial designs

A two-level factorial design can be uniquely represented by a polynomial indicator function. Therefore, properties of factorial designs can be studied through their indicator functions. This paper shows that the indicator function is an effective tool in studying two-level factorial designs. The indicator function is used to generalize the aberration criterion of a regular two-level fractional factorial design to all two-level factorial designs. An important identity of generalized aberration is proved. The connection between a uniformity measure and aberration is also extended to all two-level factorial designs.

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

[2]  H. Wynn,et al.  Algebraic Statistics: Computational Commutative Algebra in Statistics , 2000 .

[3]  Ching-Shui Cheng,et al.  Some hidden projection properties of orthogonal arrays with strength three , 1998 .

[4]  Lih-Yuan Deng,et al.  GENERALIZED RESOLUTION AND MINIMUM ABERRATION CRITERIA FOR PLACKETT-BURMAN AND OTHER NONREGULAR FACTORIAL DESIGNS , 1999 .

[5]  Fred J. Hickernell,et al.  A generalized discrepancy and quadrature error bound , 1998, Math. Comput..

[6]  Boxin Tang,et al.  Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2-aberration , 2001 .

[7]  William Li,et al.  Columnwise-pairwise algorithms with applications to the construction of supersaturated designs , 1997 .

[8]  Dennis K. J. Lin,et al.  Projection properties of Plackett and Burman designs , 1992 .

[9]  Henry P. Wynn,et al.  Generalised confounding with Grobner bases , 1996 .

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

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

[12]  Eva Riccomagno,et al.  Replications with Gröbner bases , 2001 .

[13]  Aloke Dey,et al.  Fractional Factorial Plans , 1999 .

[14]  Kai-Tai Fang,et al.  A connection between uniformity and aberration in regular fractions of two-level factorials , 2000 .

[15]  Giovanni Pistone,et al.  Classification of two-level factorial fractions , 2000 .