An Overview of Two-level Supersaturated Designs with Cyclic Structure

An overview is given of the link between the k-circulant method of construction of two-level supersaturated designs and construction methods based on cyclic incomplete block designs. It is shown that this link enables a simple formula for the Es2-efficiency of all such designs to be derived. Generators are given for Es2-optimal and near-optimal designs that extend the range of previously known designs or that have a smaller number of highly correlated column pairs.

[1]  R. Plackett,et al.  THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS , 1946 .

[2]  F. E. Satterthwaite.  Random Balance Experimentation , 1959 .

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

[4]  A. Street,et al.  Combinatorics: room squares, sum-free sets, Hadamard matrices , 1972 .

[5]  Jennifer Seberry,et al.  Orthogonal Designs: Quadratic Forms and Hadamard Matrices , 1979 .

[6]  Irwin Guttman,et al.  Robustness to Spurious Observations of Linearized Hodges-Lehmann Estimators and Anscombe , 1980 .

[7]  R. Daniel Meyer,et al.  An Analysis for Unreplicated Fractional Factorials , 1986 .

[8]  A. Street,et al.  Combinatorics of experimental design , 1987 .

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

[10]  Changbao Wu,et al.  Construction of supersaturated designs through partially aliased interactions , 1993 .

[11]  Dennis K. J. Lin.  Generating Systematic Supersaturated Designs , 1995 .

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

[13]  Ching-Shui Cheng,et al.  E(s 2 )-OPTIMAL SUPERSATURATED DESIGNS , 1997 .

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

[15]  H. Chipman,et al.  A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing , 1997 .

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

[17]  Dennis K. J. Lin,et al.  FORWARD SELECTION ERROR CONTROL IN THE ANALYSIS OF SUPERSATURATED DESIGNS , 1998 .

[18]  R. D. Meyer,et al.  Bayesian variable assessment , 1998 .

[19]  Dennis K. J. Lin,et al.  On the identifiability of a supersaturated design , 1998 .

[20]  H. Chipman,et al.  Some risks in the construction and analysis of supersaturated designs , 1999 .

[21]  K. Vijayan,et al.  Some Risks in the Construction and Analysis of Supersaturated Designs , 1999, Technometrics.

[22]  Joseph O. Voelkel,et al.  Asymptotic-power problems in the analysis of supersaturated designs , 2000 .

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

[24]  Steven G. Gilmour,et al.  A general method of constructing E(s2)‐optimal supersaturated designs , 2001 .

[25]  Dennis K. J. Lin,et al.  A Two-Stage Bayesian Model Selection Strategy for Supersaturated Designs , 2002, Technometrics.

[26]  Dursun A. Bulutoglu,et al.  Construction of E(s^2)-optimal supersaturated designs , 2004 .

[27]  Steven G. Gilmour,et al.  Large supersaturated designs , 2004 .

[28]  Yufeng Liu,et al.  k-Circulant Supersaturated Designs , 2004, Technometrics.

[29]  A. Dean,et al.  Construction and analysis of Es 2 ecien t supersaturated designs , 2005 .

[30]  Dursun A. Bulutoglu,et al.  E(s2)-Optimal supersaturated designs with good minimax properties , 2007 .

[31]  Angela M. Dean,et al.  Construction and analysis of Es2 efficient supersaturated designs , 2007 .

[32]  Aloke Dey,et al.  On E(s2)-optimal supersaturated designs , 2008 .

[33]  S. Georgiou.  On the construction of E(s2)-optimal supersaturated designs , 2008 .

[34]  Frederick Kin Hing Phoa,et al.  Analysis of Supersaturated Designs via Dantzig Selector , 2009 .

[35]  Runze Li,et al.  Analysis Methods for Supersaturated Design: Some Comparisons , 2003, Journal of Data Science.