Example of augmenting a D-optimal design
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In the Example of selecting a D-optimal response surface design, you selected a subset of 20 design points from a candidate set of 30 points. After you collected the data for the 20 selected design points, you found out that you could run five additional design points. Because you already collected the data for the original design, you need to protect these points in the augmented design so they can not be excluded during the augmentation/optimization procedure. To protect these points, you need to have negative indicators for the design points that were already selected for the first optimal design.

1    Open the worksheet OPTDES2.MTW. (The design and indicator columns have been saved for you.)

2    Choose Stat > DOE > Response Surface > Select Optimal Design.

3    Choose Augment/improve design, then enter OptPoint in the box.

4    In Number of points in optimal design, type 25.

5    Click Terms. Click OK in each dialog box.

Session window output

Optimal Design: Blocks, A, B, C, D

 

 

Response surface design augmented according to D-optimality

 

Number of candidate design points: 30

Number of design points to augment/improve: 20

Number of design points in optimal design: 25

 

Model terms: Block, A, B, C, D, AA, BB, CC, DD, AB, AC, AD, BC, BD, CD

 

Initial design augmented by Sequential method

Initial design improved by Exchange method

Number of design points exchanged is 1

 

 

Optimal Design

 

Row number of selected design points: 1, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 22, 23, 24, 25,

                                      26, 27, 28, 30, 2, 5, 14, 18, 20, 21

 

Condition number:                              9.11934

D-optimality (determinant of XTX):         3.73547E+20

A-optimality (trace of inv(XTX)):              2.01042

G-optimality (avg leverage/max leverage):         0.64

V-optimality (average leverage):                  0.64

Maximum leverage:                                    1

Interpreting the results

The Session window output contains the following five parts:

·    A summary of the D-optimal design. This design was obtained by augmenting a design with containing 20 points by adding 5 more design points. The candidate set contains 30 design points.

·    The model terms. D-optimal designs depend on the specified model. In this example, the terms include:

Block A B C D AA BB CC DD AB AC AD BC BD CD

These full quadratic model terms are the default in the Terms subdialog box. Remember, a design that is D-optimal for one model will most likely not be D-optimal for another model.

·    The method by which the initial design was augmented and whether or not an improvement of the initial design was requested. In this example, two design points were added sequentially and the exchange method (using one design point) was used to improve the initial design.

·    The selected design points in the order they were chosen. The numbers shown identify the row of the design points in the worksheet.

Note

The design points that are selected depend on the row order of the points in the candidate set. Therefore, Minitab may select a different optimal design from the same set of candidate points if they are in a different order. This can occur because there may be more than one D-optimal design for a given candidate set of points.

·    Minitab displays some variance-minimizing optimality measures. You can use this information to compare designs. For example, if you compare the optimality of the original 20-point design from the example of selecting a D-optimal response surface design with this 25-point design, you will notice that the D-optimality increased from  2.73819E+18 to 3.73547E+20. Larger D-optimality values indicate a more optimal design.