Home / DOE / Create Designs / Create Optimal Design / Options
Create Optimal Design Options¶
Every control on the seven steps of the Create Optimal Design (D, A, I) wizard.
Every step carries Back, Next and Cancel, except the first, which has no Back, and the last, which offers Finish in place of Next.
Step 1: Candidate source¶
Where do the candidate runs come from?
| Choice | What it uses |
|---|---|
| Use an existing design sheet in this workbook | the runs already on a Quantum XL design sheet |
| Full factorial from defined factors and levels | the full factorial over factors you type |
The second choice can be mixed level, with continuous and categorical factors together.
When the workbook holds no Quantum XL design sheet, the first choice has nothing to read and the second is selected for you, with the reason on screen.
Step 2a: Design sheet¶
Pick the design sheet whose runs are the candidate runs.
Shown only when you chose an existing sheet. It lists the Quantum XL design sheets in the workbook.
Step 2b: Factors and levels¶
Type the factors and their levels. The candidate runs are the full factorial over them.
Shown only when you chose a full factorial. Two grids.
Factors, with three columns:
| Column | What it holds |
|---|---|
| Factor name | the factor's name |
| Categorical | tick when its levels are categories rather than numbers |
| Number of levels | how many levels it has. New rows start at 3 |
Level values, with a Level column, holds the actual value of each level of the selected factor.
Step 3: Model terms¶
Choose the interaction, quadratic and custom terms that go in the model. Main effects are always in the model.
Two trees side by side, Terms available and Terms in model, with Add and Remove between them. Selecting a group header selects the whole group, and Shift or Ctrl click selects several terms that move in one gesture.
Build custom terms opens the Custom Terms Builder:
Type one term per row. Blank rows are ignored.
A running counter sits under the trees:
Degrees of freedom remaining: 7
Main effects cannot be removed. They are always in the model, which is why they are not offered in the available tree.
The model starts with no interaction, quadratic or custom term in it. Every such term begins in Terms available and you move in the ones you want, whatever model the design sheet itself carries. The page opens with something already in Terms in model in two cases only, and both are a choice you made earlier: you have been on this page before in this run of the wizard, or the sheet carries the settings from a previous optimal design run on it.
Step 4: Run range and criterion¶
Choose how many runs the design has and the criterion the search optimizes.
Run range¶
| Control | What it sets |
|---|---|
| Number of runs in optimal design | the run size at the centre of the search |
| Plus/minus runs | how many sizes either side of it are also searched |
A sentence under the boxes says what Next will do, naming the criterion and every run size the range asks for.
The smallest run count accepted is the number of model columns. Choosing more terms in step 3 therefore raises the floor on the design size.
Optimality criterion¶
Three buttons, in this order. A-optimal is the one the wizard opens on. Each carries a one-line description, quoted here as the product words it.
A-optimal
Minimizes the trace of (X'X) inverse, the sum of the variances of the regression coefficients. It controls those variances one at a time rather than jointly.
I-optimal
Minimizes the average prediction variance, integrated over the design region rather than evaluated at the design points. It is the prediction-oriented criterion, and the usual choice for second-order designs fitted to find an optimum.
D-optimal
Maximizes the determinant of X'X, which minimizes the volume of the joint confidence region for the regression coefficients. It is the estimation-oriented criterion, and the usual choice for first-order and screening designs.
Step 5: Search¶
One optimal design is searched for, for each run size in the range.
Progress only. There is nothing to set.
Step 6: Results¶
Pick the design to write to the worksheet.
One row per run size. The columns and the four detail sections are described on the index page. Select the row you want and go on.
The power assumptions¶
Three boxes sit inside a row's detail, directly above the Variance inflation and power, by model column section, so it is clear what they belong to. They are one set of values for the whole page, not per row: every design's power is computed from the same three numbers, and editing one recomputes every row.
| Box | Default | What it must be |
|---|---|---|
| Anticipated coefficient | 1 |
a number other than zero |
| Standard deviation | 1 |
a number greater than zero |
| Significance level | 0.05 |
a number between 0 and 1, excluding both |
The sentence above them says what they mean:
The power columns are the chance of detecting a term whose coefficient is the anticipated coefficient, tested at the significance level, when the response's standard deviation is this value.
A value outside its range is refused with a message naming that box, for example The standard deviation must be a number greater than zero.
Only the power columns move. The design itself, the leverage table, the correlations and the alias matrix are all built without these three values, so an edit leaves every one of them exactly as the search produced it. An open row detail keeps its place while the power numbers under it change.
The coefficient and the standard deviation act as a ratio, not separately. Power depends on the anticipated coefficient measured against the standard deviation, so a coefficient of 2 with a standard deviation of 2 gives the same power as a coefficient of 1 with a standard deviation of 1. Doubling both changes nothing; what matters is how large a coefficient is relative to the noise you expect.
Step 7: Replicates and outputs¶
Choose the number of replicates, name each output and its type and choose the sheet layout.
Number of replicates, a whole number from 1 to 10,000. Replicates are applied after the design is chosen, by repeating it, so they multiply the rows and do not change which runs were selected.
Number of replicates must be a whole number between 1 and 10000.
A design is written at least once, so the replicate count is at least 1.
Number of replicates must be 10000 or less.
The outputs, each with a name and a type. New ones are named Output 1, Output 2 and so on.
At least one is required:
A design needs at least one output.
The sheet layout, either Table format or Stacked format.
Finish writes the design sheet.