Example of evaluating a response surface optimal design

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.

In this example, the materials scientist wants to determine how reducing the model changes the optimality.

Note

Remember that a model that is D-optimal for a given model only.

Open the sample data, CrystalGrowth_optimal_design.MTW.
Choose Stat > DOE > Response Surface > Select Optimal Design.
Choose Evaluate design, then enter OptPoint in the box.
Click Terms.
From the Include the following terms drop-down list, select Linear.
Click OK in each dialog box.

Interpret the results

The output contains several components, as follows:

Number of experimental runs

This design has 20 experimental runs.

Model terms

D-optimal designs depend on the specified model. In these results, the terms include the linear terms that you chose in the Terms sub-dialog box. The terms are as follows:

Block A B C D

Remember, a design that is D-optimal for one set of terms is not necessarily D-optimal for a different set of terms.

Experimental runs in the order that they were chosen

The numbers shown identify the row of the experimental run in the original worksheet.

Statistics

You can use optimality metrics to compare designs, but remember that the optimality of a given D-optimal design is model dependent. That is, optimality is defined for a fixed design size and for a particular model. For instance, when comparing designs, larger D-optimality are better, but smaller A-optimality values better.

Evaluation of Specified Response Surface Design

Number of design points in optimal design: 20

Model terms: Block, A, B, C, D

Specified Design

Row number of selected design points: 1, 3, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 22, 23, 24,
25, 26, 27, 28, 30

Condition number:	1.43109
D-optimality (determinant of XTX):	47267840
A-optimality (trace of inv(XTX)):	0.320581
G-optimality (avg leverage/max leverage):	0.871492
V-optimality (average leverage):	0.3
Maximum leverage:	0.344237