In the Example of selecting a D-optimal response surface design, a materials scientist selects a subset of 20 design points from a candidate set of 30 points.
After the scientist collects the data for the 20 selected design points, the scientist decides they have resources to run five additional design points. Because the scientist already collected the data for the original design, the scientist needs to protect these points in the augmented design so they cannot be excluded during the augmentation/optimization procedure. To protect these points, use negative indicators for the design points that were already selected for the first optimal design.
The scientist decides to run 5 additional design points. Because the scientist has already collected the data for the original design, those points cannot be excluded during the augmentation/optimization procedure. To protect the 20 original design points, the scientist uses negative indicators for the design points that were already selected for the first optimal design. See step #2 for details on how to create a column of indicators.
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 |
---|---|---|---|---|---|---|---|---|
StdOrder | RunOrder | PtType | Blocks | A | B | C | D | OptPoint |
12 | 1 | 1 | 1 | 8.25 | 55 | 0.75 | 6.5 | 1 |
11 | 2 | 1 | 1 | 6.75 | 55 | 0.75 | 6.5 | 0 |
C9 | C10 |
---|---|
OptPoint | Keep runs with −1 |
1 | −1 |
0 | 0 |
In this example, the first design was generated sequentially and the exchange method was used to improve the first design, exchanging one design point at a time.
The design points that are selected depend on the row order of the points in the candidate set. Therefore, Minitab can select a different optimal design from the same set of candidate points if they are in a different order. This can occur because multiple D-optimal designs can exist for a specified candidate set of points.
Condition number: | 8.53018 |
---|---|
D-optimality (determinant of XTX): | 3.73547E+20 |
A-optimality (trace of inv(XTX)): | 1.99479 |
G-optimality (avg leverage/max leverage): | 0.64 |
V-optimality (average leverage): | 0.64 |
Maximum leverage: | 1 |