Example for Create Mixture Design (Simplex Centroid)

Researchers want to study how the proportions of three ingredients in an herbal blend household deodorizer affect the acceptance of the product based on scent. The three components are neroli oil, rose oil, and tangerine oil.

Choose Stat > DOE > Mixture > Create Mixture Design.
Under Type of Design, select Simplex centroid.
From Number of components, select 3.
Click Designs, and then click OK.
Click Components. Under Name, for components A through C, type Neroli, Rose, and Tangerine, respectively. Click OK.
Click Results. Select Detailed description and design table.
Click OK in each dialog box.

Interpret the results

The design summary table includes the total number of components, process variables, design points, design degree, and mixture total.

The number of boundaries for each dimension indicates the complexity of the design space. That is, how many vertices, edges, planes, etc., confine the design space. Design points are often placed at a "corner" (vertex) or in the middle (edge or plane) of a boundary. The sample output shows that the design space has seven boundaries: 3 zero-dimensional vertices, 3 one-dimensional edges, and 1 two-dimensional plane.

Tip

To graphically display the design space and design points after you create a mixture design, create a Simplex Design Plot.

Minitab displays the number of design points for each point type. The interpretation of the point type value depends on whether the design is constrained or unconstrained. This is an unconstrained design because the proportions of all the components can range from 0 to 1. For unconstrained designs, the point type value usually indicates how many components are in the blend. However, there are two exceptions:

Type 0 is the center point. The center point corresponds to the blend in which all components are included in equal proportions. This design has one center point.
Type - 1 is an axial point. An axial point is special complete blend that lies exactly halfway between the center point and a vertex. This design has three axial points.

In some mixture experimentation, it is necessary to set a lower bound and/or an upper bound on some or all of the components. For this design, the bounds of mixture components table indicates that none of the components have bounds because the proportions can range from 0 to 1.

The design table displays the component values for each experimental run using coded component names and uncoded values. For example, in the first run, component A and B have proportions of 0 and component C has a proportion of 1. With 3 components, the design has 10 runs. In the worksheet, Minitab displays the names of the components and the levels.

Note

Minitab randomizes the design by default, so when you create this design, the run order will not match the order in the example output.

Design Summary

Components:	3	Design points:	10
Process variables:	0	Design degree:	3

Mixture total: 1.00000

Number of Boundaries for Each Dimension

Point Type	1	2	0
Dimension	0	1	2
Number	3	3	1

Number of Design Points for Each Type

Point Type	1	2	3	0	-1
Distinct	3	3	0	1	3
Replicates	1	1	0	1	1
Total number	3	3	0	1	3

Bounds of Mixture Components

	Amount		Proportion		Pseudocomponent
Comp	Lower	Upper	Lower	Upper	Lower	Upper
A	0.0000	1.0000	0.0000	1.0000	0.0000	1.0000
B	0.0000	1.0000	0.0000	1.0000	0.0000	1.0000
C	0.0000	1.0000	0.0000	1.0000	0.0000	1.0000

Design Table (randomized)

Run	Type	A	B	C
1	1	0.0000	0.0000	1.0000
2	2	0.0000	0.5000	0.5000
3	0	0.3333	0.3333	0.3333
4	2	0.5000	0.0000	0.5000
5	1	1.0000	0.0000	0.0000
6	2	0.5000	0.5000	0.0000
7	-1	0.1667	0.1667	0.6667
8	-1	0.1667	0.6667	0.1667
9	-1	0.6667	0.1667	0.1667
10	1	0.0000	1.0000	0.0000