Three-level design

Box GEP, Behnken DW (1960) Some new three level designs for the study of quantitative variables. Technometrics 2 445... 

Factorial designs are usually discussed in terms of coded factor spaces. Table 14.1 shows some of the common coding systems for two- and three-level designs. Our emphasis in this chapter will be on the two-level designs. 

Box, G.E.P., and Behnken, D.W. (1960b), Some New Three Level Designs for the Study of Quantitave Variables, Technometrics, 2, 455. 

It might be supposed that a smaller design that permitted the estimation of the coefficients of interest could be constructed by taking a fraction of the full factorial. However, the aliasing of three-level designs is very complex and so fractionating a three-level design will not be pursued. The interested reader may refer to Kempthome [18]. 

Therefore, unless the number of factors is small, three-level designs are not usually feasible for response surface studies. 

In order to avoid the kind of problem illustrated in Figure 5.4 it is recommended that a three level design be carried out,... 

Xu, H., Cheng, S. W., and Wu, C. F. J. (2004). Optimal projective three-level designs for factor screening and interaction detection. Technometrics, 46, 280-292. 

Three-Level Designs Response Surface Designs... 

Full-factorial three-level designs are sometimes used for investigating few factors (two or three) although their statistical properties with respect to symmetry or confounding of parameter estimates are less favorable than those known for the two-level designs. In the case of many factors, the same problem as with... 

Figure 4.11 Full-factorial three-level design for two factors, 3 design.

Apart from good statistical properties of the central composite design, there is one experimental disadvantage. Because the star points are outside the hypercube, the number of levels that have to be adjusted for every factor is actually five instead of the three in a conventional three-level design. If the adjustment of levels is difficult to achieve, an alternative response surface design would be the design introduced by Box and Behnken. 

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