Fast Flexible Filling Designs

Note: If you have Categorical factors or factor constraints, then Fast Flexible Filling is the only Method available.

The algorithms for Fast Flexible Filling designs begin by generating a large number of random points within the specified design region. These points are then clustered using a Fast Ward algorithm into a number of clusters that equals the Number of Runs that you specified.

The final design points can be obtained by using the default MaxPro (maximum projection) optimality criterion or by selecting the Centroid criterion. You can find these options under FFF Optimality Criterion in the report’s red triangle menu.

MaxPro

For p factors and n equal to the specified Number of Runs, the MaxPro criterion strives to find points in the clusters that minimize the following criterion:

The MaxPro criterion maximizes the product of the distances between potential design points in a way that involves all factors. This supports the goal of providing good space-filling properties on projections of factors. See Joseph et al. (2014, forthcoming). The Max Pro option is the default.

Centroid

This method places a design point at the centroid of each cluster. It has the property that the average distance from an arbitrary point in the design space to its closest neighboring design point is smaller than for other designs.

Note: You can set a preference to always use a given optimality criterion. Select File > Preferences > Platforms > DOE. Check FFF Optimality Criterion and select your preferred criterion.

Set Average Cluster Size

The Set Average Cluster Size option is found under Advanced Options in the Space Filling Design red triangle menu. This option enables you to specify the average number of randomly- generated points used to define each cluster or, equivalently, each design point.

By default, if the Number of Runs is set to 200 or less, a total of 10,000 randomly generated points are used as the basis for the clustering algorithm. When the number of Runs exceeds 200, a default value of 50 is used. Increasing this value can be particularly useful in designs with a large number of factors or where disallowed combinations restrict the distribution of points used in the clustering algorithm.

Note: Depending on the number of factors and the specified value for Number of Runs, you might want to increase the average number of initial points per design point by selecting Advanced Options > Set Average Cluster Size.

Constraints

Once you complete the Factors outline, click Continue. The Define Factor Constraints outline appears. Use this outline to restrict the design region. For details about the outline, see Define Factor Constraints.

You can use the Use Disallowed Combinations Filter and Use Disallowed Combinations Script options to specify disallowed factor level combinations. Or, you can use the Specify Linear Constraints option to specify bounds in terms of linear inequalities. However, the design is generated differently for these two methods.

Use Disallowed Combinations Filter and Use Disallowed Combinations Script

When disallowed combinations are specified, the random points that form the basis for the clustering algorithm are randomly distributed within the unconstrained design region. Then disallowed points are removed and clustering proceeds with the remaining points.

Note: Depending on the nature of the constraints and the specified Number of Runs, the default coverage of the unconstrained design space by the initial randomly generated points might not be sufficient to produce the required Number of Runs. In this case, you might obtain a JMP Alert indicating that the algorithm “Could not find sufficient number of points.” To increase the initial number of points that form the basis for the clustering algorithm, specify a larger average number of initial points per design point by selecting Advanced Options > Set Average Cluster Size. (See Set Average Cluster Size).

Specify Linear Constraints

When you use the Specify Linear Constraints option, the random points that form the basis for the clustering algorithm are randomly distributed within the constrained design region. The clustering algorithm uses these points.

Creating and Viewing a Constrained Fast Flexible Filling Design

Constructing the Design

1.	Select DOE > Space Filling Design.

2.	Enter Values of 0 and 1 for both X1 and X2.

3.	Click Continue.

4.	In the Define Linear Constraints outline, select Specify Linear Constraints.

Notice that Fast Flexible Filling is the only available Space Filling Design Method.

5.	Select Add.

6.	Enter the following coefficients and bound:

7.	Type 200 next to Number of Runs.

8.	Select Fast Flexible Filling.

JMP creates a design that satisfies the constraints. Open the Design outline to view the design.

9.	Select Make Table to construct the data table.

Constructing the Plot

1.	With the data table active, select Graph > Graph Builder.

2.	Drag X1 to the drop zone labeled X.

3.	Drag X2 to the drop zone labeled Y.

4.	Remove the Smoother by clicking the smoother icon.

5.	In the Graph Builder red triangle menu, click Show Control Panel to deselect it.

You should see a graph similar to the one in Fast Flexible Filling Design with One Linear Constraint. Note that the points satisfy the linear constraint

Fast Flexible Filling Design with One Linear Constraint