Factor Assignment for Three-Level Supersaturated Design
Supersaturated design can be used to screen a number of potentially relevant factors with a smaller number of runs; thus, the resulting matrix has a greater number of columns than rows. Three-level supersaturated design is useful when second-order effects also need to be determined. However, experimenters may actually miss factor main effects because the nature of the three-level supersaturated design does not imply that all of its columns are orthogonal to each other. This paper shows how to assign factors to three-level supersaturated design that considers low-order interactions. Specifically, factor assignment for an existing 27x61 supersaturated design matrix is presented to avoid confounding all main effects with all lxl interactions, but not with other decomposed two-way interactions. Assignment columns are determined by the following steps. First, two arbitrary columns that are mutually orthogonal are selected after the orthogonality of all combinations of pairs of columns is evaluated by using the chi-square statistic. Second, if the l X l interaction column of the selected pair of columns demonstrates orthogonality with the previously chosen columns, the selected pair is taken as possible assignment columns. Finally, the above steps are repeated until all columns are examined. On applying this method to the existing design matrix, none columns were found as possible assignment columns. The usefulness of these assignment columns is shown by comparing with the existing factor assignment method in terms of the level of nonorthogonality. Moreover, this paper also presents a linear graph to estimate all main effects and several lX l interaction effects.
design of experiments inner product interaction columns linear graph
Hironobu Kawamura Kohei Takada Tomomichi Suzuki
Department of Industrial Administration, Tokyo University of Science, Japan
国际会议
The Institute Industrial Engineera Asian Conference 2011(2011年国际工业工程师协会亚洲会议)
上海
英文
507-513
2011-06-10（万方平台首次上网日期，不代表论文的发表时间）