Using Discrepancy to Evaluate Fractional Factorial Designs

Fractional factorial design is arguably the most widely used design in experimental investigation, and uniformity has gained popularity in experimental designs in recent years. In this present paper, a suitable measure of uniformity, i.e. a discrete discrepancy, is defined by the reproducing kernel Hilbert space, and is used to evaluate the uniformity of fractional factorial designs. Some relations between orthogonality and uniformity in fractional factorial designs are obtained. The results show that orthogonality and uniformity are strongly related to each other and the discrepancy plays an important role in evaluating such experimental designs.

[1]  Boxin Tang,et al.  A method for constructing supersaturated designs and its Es2 optimality , 1997 .

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

[3]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[4]  G. Wahba.  Spline models for observational data , 1990 .

[5]  Fred J. Hickernell,et al.  Goodness-of-fit statistics, discrepancies and robust designs , 1999 .

[6]  K. H. Booth,et al.  Some Systematic Supersaturated Designs , 1962 .

[7]  H. Keng,et al.  Applications of number theory to numerical analysis , 1981 .

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

[9]  Saburou Saitoh,et al.  Theory of Reproducing Kernels and Its Applications , 1988 .

[10]  Eva Riccomagno,et al.  Experimental Design and Observation for Large Systems , 1996, Journal of the Royal Statistical Society: Series B (Methodological).

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

[12]  Kai-Tai Fang,et al.  Uniformity in Fractional Factorials , 2002 .

[13]  F. J. Hickernell.  Lattice rules: how well do they measure up? in random and quasi-random point sets , 1998 .

[14]  Dennis K. J. Lin,et al.  A new class of supersaturated designs , 1993 .

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

[16]  Min-Qian Liu,et al.  Construction of E(s2) optimal supersaturated designs using cyclic BIBDs , 2000 .

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

[18]  F. J. Hickernell,et al.  Uniform designs limit aliasing , 2002 .

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

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

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

[22]  N. Draper.  Small Composite Designs , 1985 .

[23]  Kai-Tai Fang,et al.  Relationships Between Uniformity, Aberration and Correlation in Regular Fractions 3s-1 , 2002 .

[24]  K. Fang,et al.  Number-theoretic methods in statistics , 1993 .

[25]  Nam-Ky Nguyen.  An algorithmic approach to constructing supersaturated designs , 1996 .