Mixture-Process Factors Design

The Mixture-Process Factors Design enables users to design experiments that include both mixture and process factors.

Note

In JMP 17 and up, you can construct a space-filling design that includes both mixture and process factors using DOE > Special Purpose > Space Filling Design, using the Fast Flexible Filling design method. This utility is intended for use in older JMP versions.

This document will go through an example to illustrate the utility's use.

Example

First, construct both a Components table and a Constraints table. In this example the experiment is designed to optimize Hydrophobicity.

• There are three mixture components: Softener, Repellent A, and Repellent B.
• At least 10% of the mixture must consist of Softener.
• There are two process variables:
• Mixture Amount added to the resin, which can vary between 5 and 20
• Resin Type added to the fabric; there are three possible types, A, B, and C

This is a Mixture-Process Factor experiment with three mixture components and two process factors.

The Components table contains a column for each mixture component and two rows giving the lower and upper bounds for each mixture component. In our example, the components can vary between 9% and 100% of the total mixture. For example:

The Constraints table is optional. It should contain a column for each constraint. If $c$ is the number of components then the table must contain $c + 1$ rows.

Each constraint must be expressed as a linear function of all components set less than or equal to a numerical bound. In our example, Softener must be at least 10% of the mixture. The constraint is expressed as:

$-1 \cdot Softener + 0 \cdot Repellent A + 0 \cdot Repellent B ≤ -0.10$

The corresponding Constraints table is shown, as follows:

In our example, there is a single constraint, so the table consists of a single column. The first three rows contain the coefficients for the constraint, and the last row contains the bound, where the constraint is expressed in terms of a less-than-or-equal-to (≤) inequality.

To run the Mixture-Process Factors design utility:

1. Select it from the Predictum > Self-Validating Ensemble Modeling > Utilities menu.

   

2. Click Open Components Table and navigate to your saved Components table.

3. Depending on whether you have constraints or not, follow one of the following steps:

   • If you have no constraints, click Run.

   • If you have constraints, click Open Constraints Table and navigate to your saved Constraints table. Then, click Run.

   The Space Filling Design dialog opens with your mixture components inserted into the Factors outline box.

   

4. Add your response or responses to the Responses outline box.

5. Add your process variables and their bounds to the Factors outline box, as shown in the following example:

   

6. Click Continue.

   Your constraints will appear in the Define Factor Constraints outline box. The first two constraints shown and the constraints that ensure that the mixture components sum to one.

7. Enter your desired number of runs in the Space Filling Design Methods panel box.

8. Click Fast Flexible Filling Mixture.

   The design table appears.

   

   Note that the component settings have been rounded to two decimal places. The components and process variables have been assigned appropriate column properties.