Definitive Screening Design for Eight Continuous Factors shows an example of a definitive design with eight continuous factors. Notice that each pair of rows is a foldover pair; each even-numbered row is -1 times the previous row. The foldover aspect of the design removes the confounding of two-factor interactions and main effects. Each factor is set at its center value for three runs; this, together with the design’s construction, makes all quadratic effects estimable. Adding the center run in the last row enables you to fit a model that includes an intercept and all main and quadratic effects. This structure is typical of definitive screening designs for continuous factors.
Definitive Screening Design for Eight Continuous Factors
Definitive screening designs in JMP are constructed using conference matrices (Xiao et al., 2012). A conference matrix is an m x m matrix C where m is even. The matrix C has 0s on the diagonal, off-diagonal entries equal to 1 or –1, and satisfies .
Suppose that the number of factors, k, is five or larger. For the case of k ≤ 4 factors, see Definitive Screening Designs for Four or Fewer Factors.
Consider the case of continuous factors. When k is even, the k x k conference matrix is used to define k runs of the design. Its negative, –C, defines the foldover runs. A center point is added to ensure that a model containing an intercept, main effects, and quadratic effects is estimable. So, for k even, the number of runs is 2k + 1. When k is odd, a (k+1) x (k+1) conference matrix is used, with its last column deleted. Thus, for k odd, the number of runs is 2k + 3.
For certain even values of m, a conference matrix might not exist. In such a case, a definitive screening design can be constructed using the next largest conference matrix. As a result, the required number of runs might exceed 2k + 3, in the continuous case, and 2k + 4, in the categorical case.
Definitive screening designs for four or fewer factors are constructed using the five-factor definitive screening design as a base. This is because designs for k ≤ 4 factors constructed strictly according to the conference matrix approach have undesirable properties. In particular, it is difficult to separate second-order effects.
If you specify k ≤ 4 factors, a definitive screening design for five factors is constructed and unnecessary columns are dropped. For this reason, the number of runs for an unblocked design with k ≤ 4 factors is 13 if all factors are continuous or 14 if some factors are categorical.
Color Map on Correlations for Full Quadratic Model shows a Color Map on Correlations for the design with eight continuous factors shown in Definitive Screening Design for Eight Continuous Factors. The color map is for a full quadratic design. The eight pure quadratic effects are listed to the far right. You can construct this plot by using DOE > Evaluate Design and entering the appropriate terms into the Alias Terms list. See Alias Terms in Evaluate Designs for details.
Color Map on Correlations for Full Quadratic Model