# Select optimal runs, augment, or improve a response surface design

Stat > DOE > Response Surface > Select Optimal Design

## Criterion

Minitab provides two optimality criteria for the selection of design points, as follows:
• D-optimality: D-optimality minimizes the determinant of the variance-covariance matrix of the estimated regression coefficients. You specify the model, then Minitab selects design points that satisfy the D-optimal criterion from a set of candidate design points.
• Distance-based optimality: Distance-based optimality spreads the design points uniformly over the design space. Use this method when it is not possible or desirable to select a model before you begin.

## Select a D-optimal design

Complete the following steps to select a D-optimal design from candidate runs in a response surface design.

1. From Criterion, select D-optimality.
2. Under Task, choose Select optimal design.
3. In Number of points in optimal design, enter the number of experimental runs to select from the candidate set.
4. Click Terms. D-optimality depends on the terms. After you specify the terms, Minitab selects the experimental runs.

## Select a distance-based optimal design

Complete the following steps to select a distance-based optimal design from candidate runs in a response surface design.

1. From Criterion, select Distance-based optimality.
2. In Specify design columns, specify which factors to use in the calculation of the distances. Settings for other factors are still in the worksheet if you select the option to store the optimal design. Usually, you omit factors you plan not to include in the optimal design.
3. Under Task, choose Select optimal design.
4. In Number of points in optimal design, enter the number of runs to select from the candidate set.
###### Note

The number of points that you enter must not be greater than the number of unique experimental runs in the candidate set.

## Augment/improve design

Complete the following steps to add experimental runs or change experimental runs in a D-optimal way.
###### Note

The experimental runs can be the only runs in the worksheet, or you can use a column in the worksheet to identify which runs are part of the design.

1. From Criterion, select D-optimality.
2. From Task, select Augment/improve design (you may optionally provide an indicator column that you created).
3. In Number of points in optimal design, enter the number of experimental runs for the improved design. To keep the same number of runs, enter 0 for the number of points.
4. (Optional) Enter a column that identifies the initial experimental runs to augment and identifies any experimental runs that must be in the optimal design.
• The number in the column is the number of replicates of that experimental run in the initial design. A 0 identifies a point that is not in the initial design, but is part of the candidate set of experimental runs.
• The sign in the column specifies whether the experimental run must be in the optimal design.
• A positive value identifies a point that can leave the design.
• A negative value identifies a point that must remain in the optimal design.
5. Click Terms. D-optimality depends on the terms. After you specify the terms, Minitab augments or improves the optimal design.
In this worksheet, the columns C1 to C8 contain a response surface design. The Initial Design column shows which points are in the initial design to augment or improve:
• −2 indicates that the optimal design will have at least 2 replicates of the experimental run.
• 0 indicates that the initial design does not include the experimental run. The improved design can include or not include this experimental run.
• −1 indicates that the optimal design will have at least 1 replicate of the experimental run.
• 1 indicates that the initial design has 1 replicate of the experimental run. The improved design can include or not include this experimental run.
• 3 indicates that the initial design has 3 replicates of the experimental run. The improved design can include or not include this experimental run.
C1 C2 C3 C4 C5 C6 C7 C8 C9
StdOrder RunOrder PtType Blocks A B C D Initial Design
12 1 1 1 8.25 55 0.75 6.5 −2
11 2 1 1 6.75 55 0.75 6.5 0
20 3 0 1 7.50 50 1.00 5.5 −1
15 4 1 1 6.75 55 1.25 6.5 1
8 5 1 1 8.25 55 1.25 4.5 3

## Augment a distance-based optimal design

Complete the following steps to search for a more optimal distance-based design by adding experimental runs.
###### Note

The experimental runs can be the only runs in the worksheet, or you can use a column in the worksheet to identify which runs are part of the design.

1. From Criterion, select Distance-based optimality.
2. In Specify design columns, specify which factors to use in the calculation of the distances. Settings for other factors are still in the worksheet if you select the option to store the optimal design. Usually, you omit factors you plan not to include in the optimal design.
3. From Task, select Augment/improve design (you may optionally provide an indicator column that you created).
4. (Optional) Enter a column that identifies the initial experimental runs to augment and identifies any experimental runs that must be in the optimal design.
• The number in the column is the number of replicates of that experimental run in the initial design. A 0 identifies a point that is not in the initial design, but is part of the candidate set of experimental runs.
• The sign in the column specifies whether the experimental run must be in the optimal design.
• A positive value identifies a point that can leave the design.
• A negative value identifies a point that must remain in the optimal design.
5. In Number of points in optimal design, enter a number larger than the number of runs in the initial optimal design.
###### Note

To augment a distance-based optimal design, the worksheet must contain runs that are not in the initial optimal design.

## Evaluate D-optimal design

Complete the following steps to calculate optimality measures for a design. You can use this information to compare designs.
###### Note

The experimental runs can be the only runs in the worksheet, or you can use a column in the worksheet to identify which runs are part of the design.

1. From Criterion, select D-optimality.
2. From Task, select Evaluate design (you may optionally provide an evaluate column that you created).
3. (Optional) Enter a column that identifies which experimental runs to evaluate. Positive integers specify the number of replicates of that experimental run in the design to evaluate. A 0 value identifies a point that is not in the design. If you do not enter a column, then Minitab evaluates all of the experimental runs in the worksheet.
4. Click Terms. D-optimality depends on the terms. After you specify the terms, Minitab evaluates the experimental runs.
In this worksheet, the columns C1 to C8 contain a response surface design. The Evaluate Design column shows which points are in the optimal design to evaluate:
• 0 indicates that the design does not include the experimental run.
• 1 indicates that the optimal design has 1 replicate of the experimental run.
• 3 indicates that the optimal design has 3 replicates of the experimental run.
C1 C2 C3 C4 C5 C6 C7 C8 C9
StdOrder RunOrder PtType Blocks A B C D Evaluate Design
12 1 1 1 8.25 55 0.75 6.5 0
11 2 1 1 6.75 55 0.75 6.5 0
20 3 0 1 7.50 50 1.00 5.5 0
15 4 1 1 6.75 55 1.25 6.5 1
8 5 1 1 8.25 55 1.25 4.5 3
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