• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.141-151
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• 2005

Under the assumption that the three-level factors are quantitative, the linear effects are taken more attention than the quadratic effects of the interaction terms. Webb (1971) presented some small incomplete factorial designs that are mixed two- and three-level designs with 20 or fewer runs. The designs provided the estimating linear-by-linear components of interactions between the three-level factors; moreover, they could also offer estimation of interactions that interest the experiments. Webb used ad hoc methods to find these plans; hence, there was still no unified structure to those experiments. In this paper, we develop the methods to construct the $2^{n}3^3$ and $2^{1}3^3$ designs. The designs constructed by these methods not only supply orthogonal estimates of all the main effects but also permit estimation of all the two-factor interactions not involving the quadratic effects. Furthermore, the designs we find are nearly orthogonal.

• Journal of the military operations research society of Korea
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• v.27 no.1
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• pp.73-88
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• 2001

Designing high quality products and processes at a low cost is central technological and economic challenge to the engineer. The combination of engineering concepts and statistical implementations offered by Taguchi\`s off-line design technique has proven t be invaluable. By examining some deficiencies in designs from the Taguchi\`s highly fractional, orthogonal main effect plan based on orthogonal arrays, alternative method is proposed. The maximum resolution or the minimum aberration criterion is commonly used for selecting 2$^{n-m}$ fractional designs. We present new high resolution (low aberration) linear graphs to simplify the complexity of selecting designs with desirable statistical properties. The new linear graphs approach shows a substantial improvement over Taguchi\`s linear graphs and other related graphical methods for planning experiment. The new set of linear graphs will allow the experimenter to maintain the simple approach suggested by Taguchi while obtaining the best statistical properties of the resulting design such as minimum aberration as a by-product without dependency on complicated computational algorithm or additional statistical training.g.