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Create Optimal Design¶
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QXL DOE New > Create Design > Special > Create Optimal Design (D, A, I)
An optimal design is chosen rather than tabulated. You give the model you want to fit, the runs you can afford, and the criterion to optimize, and Quantum XL selects the set of runs that scores best on that criterion.
What this design gives you¶
The standard designs come in fixed sizes. An optimal design does not. If 20 runs is what the budget allows and no standard design has 20 runs, this is the command that fills the gap. It is also the way to build a design for a model no standard design can hold, and the way to choose from a candidate list of runs that are actually achievable.
Three criteria are offered, and they answer different questions. See Options for what each one optimizes, and Math Details for the definitions.
The seven steps¶
The wizard is titled Create Optimal Design (D, A, I) and walks seven steps. One of the two candidate-source steps is skipped, whichever you did not choose, so the count is seven rather than eight.
| Step | Page | What it asks |
|---|---|---|
| 1 | Candidate source | Choose where the candidate runs come from. |
| 2 | Design sheet or Factors and levels | which runs to choose from |
| 3 | Model terms | Choose the interaction, quadratic and custom terms that go in the model. Main effects are always in the model. |
| 4 | Run range and criterion | Choose how many runs the design has and the criterion the search optimizes. |
| 5 | Search | One optimal design is searched for, for each run size in the range. |
| 6 | Results | Pick the design to write to the worksheet. |
| 7 | Replicates and outputs | Choose the number of replicates, name each output and its type and choose the sheet layout. |
Where the candidate runs come from¶
Step 1 decides which step 2 you see.
Use an existing design sheet in this workbook.
Any design Quantum XL created can be the source of the candidate runs, for example a full factorial, a custom design, or a Box Behnken design.
Full factorial from defined factors and levels.
Quantum XL builds the full factorial over the factors and levels you type and uses its rows as the candidate runs. It can be mixed level, with continuous and categorical factors.
When the workbook holds no Quantum XL design sheet the first choice has nothing to read, and the wizard says so and selects the second:
This workbook holds no Quantum XL design sheet, so the first choice has nothing to read. The second choice is selected.
The model comes before the runs¶
Model terms matters more here than anywhere else, because the design is built to estimate exactly the model you specify. Main effects are always in the model; you choose the interaction, quadratic and custom terms that join them.
The page keeps a running count as you go:
Degrees of freedom remaining: 7
Several run sizes at once¶
Run range and criterion asks for a run count and a plus/minus number, so the search covers a range of sizes rather than one. One optimal design is searched for, for each run size in the range, and the Results page puts them side by side so they can be compared before you pick one.
The Results page¶
One row per run size, with these columns:
| Column | What it reports |
|---|---|
| Runs | the run size this row is for |
| D-efficiency (%) | how this design scores on the D criterion, as a percentage. Higher is better |
| A-efficiency (%) | how it scores on the A criterion, as a percentage. Higher is better |
| G-efficiency (%) | how it scores on the G criterion, which is about the worst prediction variance in the region. Higher is better |
| I (average prediction variance) | the I criterion's own value, not a percentage. Lower is better |
| Max VIF | the largest variance inflation factor over the model columns |
| Status | whether this size produced a design |
All four measures are reported for every design, whichever criterion you optimized, so a design chosen for one criterion can be read against the others. The definitions are on the Math Details page.
The condition number is deliberately not reported. The published bands for it belong to a version computed after each column is scaled to unit length, which is not what was being computed here, so the column was removed rather than ship a number whose bands may not apply to it. The Max VIF column already reports term-by-term overlap.
A row opens to show more. The detail under a row holds four sections: Variance inflation and power, by model column, Leverage, by run, Correlations among the model columns, and the Alias matrix.
Power is computed from three values you type, in boxes that sit above the first of those sections: Anticipated coefficient, Standard deviation and Significance level. They are one set for the whole page rather than per row, so an edit recomputes the power columns of every design. The Options page gives their defaults and what each will accept.
Each of those says so plainly when it cannot be shown, rather than appearing empty. For example:
The alias matrix is not available because this design is singular, so the aliasing cannot be worked out.
Power is not reported for this design. The engine reports no power for a singular design.
Related¶
- Options, for every control on every step.
- Math Details, for what each criterion optimizes and how the reported efficiencies are defined.
- Create Custom Design, which takes the runs you supply rather than selecting them.