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Create D-Optimal

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QXL DOE Tab > Create Design > Create D-Optimal Design

D-Optimal Designs can be created by selecting QXL DOE Tab > Create Design > Create D-Optimal Design.

D-Optimal designs are generated by an algorithm such that they maximize the determinate of the information matrix (X'X). This results in a minimization of the generalized variance of the parameter estimates for the resulting model. It should be noted that an "optimal" design is not necessarily a good design. Care should be exercised by the user to ensure the model will meet their objectives.

Select Interactions for the Model

Use the "Add>>" button to select interactions from the "Interactions available" list. If you are interested in all interactions, then using a full factorial is likely preferred to D-Optimal. The run savings resulting from a D-Optimal often comes from asking for fewer interactions.

Choose Number of Runs in D-Optimal Design

Use the drop down box to specify the number of runs you would like to have in the resulting D-Optimal design. You must have at least one run for every term in the model including the constant. For example, if you have the terms A, B, AB, and AA in the model, you would need to have at least 5 runs in the model.

Quantum XL will generate the D-Optimal designs for +/-N runs. For example, if you select 20 runs +/-3 runs, Quantum XL will generate the D-Optimal Designs for 17, 18, 19, 20, 21, 22, and 23 runs.

D-Optimal Design(s)

Quantum XL will display the available designs sorted by the number of runs. The determinate, average VIF, and maximum VIF for that design are displayed in the table. The determinate isn't meaningful to most experimenters unless it is used to compare to algorithms. However, the average and maximum VIF can keep you from choosing a D-Optimal design that suffers from excessive multi-colinearity.

Practical Notes for D-Optimal

  • D-Optimal designs are advanced and should only be used by experimenters with training in the area.

  • D-Optimal designs are not necessarily "good designs". In general, the fewer the runs the worse the properties of the design (although this isn't always true). The VIF for a D-Optimal design can easily be well over 10, resulting in a design that is highly correlated.

  • D-Optimal designs are most helpful when either runs are very expensive or a standard design doesn't exist for the specific situation.

  • Before collecting the data for a D-Optimal design, generate random data to ensure the Variance Inflation Factors (VIFs) are acceptable.

  • Quantum XL uses the K-Exchange algorithm until it can no longer improve the design, and then changes to the Modified Federov algorithm to make final improvements.