This is because definitive screening designs with four or fewer factors are created based on the definitive screening design with five factors.
Creating designs from conference matrices of order four or less can result in undesirable design properties, particularly difficulty distinguishing between quadratic effects.
Definitive Screening Design Structure (All Continuous Factors)
A definitive screening design (DSD) is an experimental design constructed on an even-dimensional m × m conference matrix.
In DSD, a design is created by adding a foldover matrix −C with the opposite sign to the experimental conditions corresponding to matrix C, and then adding one row for the center points.
The minimum number of experiments required varies depending on whether the number of factors k is even or odd.
When the number of factors k is even
To create a minimal run design, first create a k×k conference matrix.
If we fold this matrix (adding the negated matrix −C) and add a row for the center point, the number of experiments becomes 2×k+1.
When the number of factors k is odd
The conference matrix must have even dimensions, so if the number of factors k is odd, a (k+1)×(k+1) conference matrix is used to create a DSD with the minimum number of experiments.
If we fold over this matrix and add a center point, the number of experiments becomes 2×(k+1)+1=2×k+3.
*In this case, delete the last column that is no longer needed.
Using this concept, we explain the minimum number of experiments for DSD with four or fewer factors when all factors are continuous.
*For details about the structure of DSD, including when two-level categorical factors are present, please see the online help here .
DSD with 4 or fewer factors (all continuous scale factors)
Number of factors 4
When k=4, according to the above "When the number of factors k is even", the minimum number of experiments is 2×4+1 = 9.
However, the conference matrix used in practice is one with five factors.
In this case, k is replaced with 5, so 2×5+3=13, so the minimum number of experiments is 13 (unnecessary columns in an actual design are removed).
* Number of additional experiments: 0
Number of factors 3
When k=3, according to the above "When the number of factors k is odd", the minimum number of experiments is 2×3+3 = 9.
However, the conference matrix used in practice is one with five factors.
In this case, k is replaced with 5, so 2×5+3=13, so the minimum number of experiments is 13 (unnecessary columns in an actual design are removed).
* Number of additional experiments: 0
