A materials scientist has determined four factors that explain much of the variability in the rate of crystal growth. The scientist designs a central composite response surface experiment to define the optimal conditions for crystal growth. After creating the design, the scientist determines that available resources restrict the number of design points that can be included to 20.
The blocks represent the plan to run the design sequentially, first assessing factorial and center points. Depending on the analysis of the first block, the scientist could choose to run the points in the axial block to add quadratic terms to the model.
The scientist wants to use D-optimality as a criterion for selecting 20 points from the original design that follow the original blocking scheme and allow estimation of the terms the scientist planned to study with the complete central composite design.
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: | 10.2292 |
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D-optimality (determinant of XTX): | 2.73819E+18 |
A-optimality (trace of inv(XTX)): | 2.50391 |
G-optimality (avg leverage/max leverage): | 0.8 |
V-optimality (average leverage): | 0.8 |
Maximum leverage: | 1 |