Nonregular Designs With Desirable Projection Properties

In many industrial applications, the experimenter is interested in estimating some of the main effects and two-factor interactions. In this article we rank two-level orthogonal designs based on the number of estimable models containing a subset of main effects and their associated two-factor interactions. By ranking designs in this way, the experimenter can directly assess the usefulness of the experimental plan for the purpose in mind. We apply the new ranking criterion to the class of all non isomorphic two-level orthogonal designs with 16 and 20 runs and introduce a computationally efficient algorithm, based on two theoretical results, which will aid in finding designs with larger run sizes. Catalogs of useful designs with 16, 20, 24, and 28 runs are presented.

[1]  Kenny Q. Ye,et al.  Model discrimination—another perspective on model-robust designs , 2007 .

[2]  William Li,et al.  Screening designs for model selection , 2006 .

[3]  A Miller,et al.  Using Folded-Over Nonorthogonal Designs , 2005, Technometrics.

[4]  Lih-Yuan Deng,et al.  Design catalog based on minimum G-aberration , 2004 .

[5]  C. F. Jeff Wu,et al.  Optimal Projective Three-Level Designs for Factor Screening and Interaction Detection , 2004, Technometrics.

[6]  R. Sitter,et al.  Choosing columns from the 12-run Plackett-Burman design , 2004 .

[7]  A. Moreira,et al.  Application of Plackett‐Burman design and response surface methodology to achieve exponential growth for aggregated shipworm bacterium , 2004, Biotechnology and bioengineering.

[8]  Ching-Shui Cheng,et al.  Hidden projection properties of some nonregular fractional factorial designs and their applications. , 2003 .

[9]  H. Carlsson,et al.  Enhanced detection of nitroaromatic explosive vapors combining solid-phase extraction-air sampling, supercritical fluid extraction, and large-volume injection-GC. , 2003, Analytical chemistry.

[10]  Miguel del Nogal Sánchez,et al.  Calibration transfer for solving the signal instability in quantitative headspace-mass spectrometry. , 2003, Analytical chemistry.

[11]  Ashok Pandey,et al.  Production of Phytase by Mucorracemosus in Solid‐State Fermentation , 2003, Biotechnology progress.

[12]  O. Devos,et al.  Use of a Plackett-Burman design with multivariate calibration for the analysis of polycyclic aromatic hydrocarbons in micellar media by synchronous fluorescence. , 2002, Analytical chemistry.

[13]  Don X. Sun,et al.  An Algorithm for Sequentially Constructing Non-Isomorphic Orthogonal Designs and its Applications , 2002 .

[14]  Z. Wen,et al.  Application of statistically-based experimental designs for the optimization of eicosapentaenoic acid production by the diatom Nitzschia laevis. , 2001, Biotechnology and bioengineering.

[15]  Henry W. Altland.  Experiments: Planning, Analysis, and Parameter Design Optimization , 2001, Technometrics.

[16]  Randy R. Sitter,et al.  Using the Folded-Over 12-Run Plackett—Burman Design to Consider Interactions , 2001, Technometrics.

[17]  Changbao Wu,et al.  FACTOR SCREENING AND RESPONSE SURFACE EXPLORATION , 2001 .

[18]  William Li,et al.  Model-Robust Factorial Designs , 2000, Technometrics.

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

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

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

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

[23]  D. W. Bacon,et al.  A study of polyethylene‐gr‐2‐tert‐butyl amino methacrylate‐supported TiCl4 catalyst for ethylene polymerization , 1996 .

[24]  N. Diamond,et al.  SOME PROPERTIES OF A FOLDOVER DESIGN , 1995 .

[25]  Ching-Shui Cheng,et al.  Some Projection Properties of Orthogonal Arrays , 1995 .

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

[27]  G. Box.  George's Column: What Can You Find Out From Sixteen Experimental Runs? , 1992 .

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

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