Three‐level and mixed‐level orthogonal arrays for lean designs

Orthogonal arrays (OA's) are widely used in design of experiments. Each OA has a specific number of rows that is fixed by the number of factors in the OA and the number of levels in each factor. In a practical application of an industrial experiment, however, because of various operational constraints it could happen that the number of runs of the experiment cannot be set exactly equal to the number of rows of an OA. In this case, a lean design can be used. A lean design is obtained by removing some specific rows and columns from the extended design matrix formed from an OA, so that the resulting sub‐matrix still allows efficient estimation of the effects of some of the factors. Tables for 2‐level lean designs are already available in the literature. In this paper, the authors will investigate 3‐level lean designs and mixed‐level lean designs, and construct tables for such designs for convenient use. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  S. Mohan,et al.  Assessment of aerosol (PM10) and trace elemental interactions by Taguchi experimental design approach. , 2008, Ecotoxicology and environmental safety.

[2]  Murat Kulahci,et al.  Partial confounding and projective properties of Plackett–Burman designs , 2007, Qual. Reliab. Eng. Int..

[3]  Peter Krajnik,et al.  Robust design of flank milling parameters based on grey-Taguchi method , 2007 .

[4]  Optimal additions to and deletions from two‐level orthogonal arrays , 2007 .

[5]  Leslie M. Moore,et al.  Combined array experiment design , 2006, Reliab. Eng. Syst. Saf..

[6]  T. Yih-fong.  Parameter design optimisation of computerised numerical control turning tool steels for high dimensional precision and accuracy , 2006 .

[7]  Warren F. Kuhfeld,et al.  Large Factorial Designs for Product Engineering and Marketing Research Applications , 2005, Technometrics.

[8]  Robert W. Mee.  Efficient Two-Level Designs for Estimating All Main Effects and Two-Factor Interactions , 2004 .

[9]  Thong Ngee Goh,et al.  Orthogonal Arrays for Experiments with Lean Designs , 2003 .

[10]  Karen A. F. Copeland.  Experiments: Planning, Analysis, and Parameter Design Optimization , 2002 .

[11]  Ling-Yau Chan,et al.  A characterization for orthogonal arrays of strength two via a regression model , 2001 .

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

[13]  K. Fang,et al.  Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points , 1997 .

[14]  R. H. Myers,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[15]  Thong Ngee Goh.  Economical experimentation via ‘lean design’ , 1996 .

[16]  C. Radhakrishna Rao.  Some Combinatorial Problems of Arrays and Applications to Design of Experiments††Paper read at the International Symposium on Combinatorial Mathematics and its Applications, Fort Collins, Colorado, September 1971. , 1973 .

[17]  E. S. Pearson.  Biometrika tables for statisticians , 1967 .

[18]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[19]  C. R. Rao,et al.  Factorial Experiments Derivable from Combinatorial Arrangements of Arrays , 1947 .