The Simplex Centroid Design

A simplex centroid design of degree k with n factors consists of mixture runs with the following characteristics:

•	all one factor

•	all combinations of two factors at equal levels

•	all combinations of three factors at equal levels

•	and so on, up to k factors at a time combined at k equal levels.

1.	Select DOE > Mixture Design.

2.	Enter factors and responses. The steps for entering responses are outlined in Responses in Custom Designs.

3.	After you enter responses and factors, click Continue.

4.	Enter the number of ingredients in the box under K. JMP creates runs for each ingredient without mixing. JMP also creates runs that mix equal proportions of K ingredients at a time to the specified limit.

5.	Click the Simplex Centroid button.

6.	View factor settings and Output Options, as illustrated in Example of Factor Settings and Output Options.

7.	Specify Run Order, which is the order in which the runs that appear in the data table that you will create. Run order choices are:

Keep the Same: The rows (runs) in the output table appear as they do in the Factor Settings panel.

Sort Left to Right: The rows (runs) in the output table appear sorted from left to right.

Randomize: The rows (runs) in the output table appear in a random order.

Sort Right to Left: The rows (runs) in the output table appear sorted from right to left.

Randomize within Blocks: The rows (runs) in the output table appear in random order within the blocks that you set up.

8.	Specify Number of Replicates. The number of replicates is the number of times to replicate the entire design, including center points. Enter the number of times you want to replicate the design in the associated text box. One replicate doubles the number of runs.

9.	Click Make Table.

The table of runs for a design of degree 1 with three factors (left in Three-Factor Simplex Centroid Designs of Degrees 1 and 2) shows runs for each single ingredient followed by the center point. The table of runs to the right is for three factors of degree 2. The first three runs are for each single ingredient, the second set shows each combination of two ingredients in equal parts, and the last run is the center point.

1.	Choose DOE > Mixture Design.

2.	Enter three mixture factors.

3.	Click Continue.

4.	Enter 1 in the K box, and click Simplex Centroid to see the design on the left in Create Simplex Centroid Designs of Degrees 1 and 2.

5.	Click the Back button, click Continue, and then enter 2 in the K box. Then click Simplex Centroid to see the design on the right in Create Simplex Centroid Designs of Degrees 1 and 2.

1.	Choose DOE > Mixture Design.

2.	Enter five factors and click Continue.

3.	Use the default value, 4, in the K box.

4.	Click Simplex Centroid.

5.	Click Make Table.

Partial Listing of Factor Settings for Five-Factor Simplex Centroid Design shows part of the 31-run design. Note that your table might look different because the design was created with Run Order set to Randomize.