Example of an Extreme Vertices Design
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Suppose you need to determine the proportions of flour, milk, baking powder, eggs, and oil in a pancake mix that would produce an optimal product based on taste. Because previous experimentation suggests that a mix that does not contain all of the ingredients or has too much baking powder will not meet the taste requirements, you decide to constrain the design by setting lower bounds and upper bounds.

You decide that quadratic model will sufficiently model the response surface, so you decide to create a second-degree design.

1    Choose Stat > DOE > Mixture > Create Mixture Design.

2    Under Type of Design, choose Extreme vertices.

3    From Number of components, choose 5.

4    Click Designs. From Degree of design, choose 2.

5    Make sure Augment the design with center point and Augment the design with axial points are checked. Click OK.

6    Click Components. Complete the Name, Lower, and Upper columns of the table as shown below, then click OK.

Component

Name

Lower

Upper

A

Flour

.425

1

B

Milk

.30

1

C

Baking powder

.025

.05

D

Eggs

.10

1

E

Oil

.10

1

7    Click Results. Choose Detailed description and design table. Click OK in each dialog box.

Session window output

Extreme Vertices Design

 

 

Components:         5  Design points:  33

Process variables:  0  Design degree:   2

 

Mixture total: 1.00000

 

 

Number of Boundaries for Each Dimension

 

Point Type  1   2   3  4  0

Dimension   0   1   2  3  4

Number      8  16  14  6  1

 

 

Number of Design Points for Each Type

 

Point Type    1   2  3  4  5  0  -1

Distinct      8  16  0  0  0  1   8

Replicates    1   1  0  0  0  1   1

Total number  8  16  0  0  0  1   8

 

 

Bounds of Mixture Components

 

            Amount            Proportion        Pseudocomponent

Comp     Lower     Upper     Lower     Upper     Lower     Upper

A     0.425000  0.475000  0.425000  0.475000  0.000000  1.000000

B     0.300000  0.350000  0.300000  0.350000  0.000000  1.000000

C     0.025000  0.050000  0.025000  0.050000  0.000000  0.500000

D     0.100000  0.150000  0.100000  0.150000  0.000000  1.000000

E     0.100000  0.150000  0.100000  0.150000  0.000000  1.000000

 

* NOTE * Bounds were adjusted to accommodate specified constraints.

 

 

Design Table (randomized)

 

Run  Type         A         B         C         D         E

  1     1  0.425000  0.300000  0.050000  0.100000  0.125000

  2     2  0.437500  0.300000  0.050000  0.112500  0.100000

  3    -1  0.429687  0.329687  0.031250  0.104688  0.104688

  4     2  0.450000  0.300000  0.025000  0.125000  0.100000

  5     2  0.425000  0.300000  0.025000  0.125000  0.125000

  6     2  0.425000  0.325000  0.025000  0.125000  0.100000

  7     2  0.462500  0.300000  0.037500  0.100000  0.100000

  8     1  0.425000  0.300000  0.025000  0.150000  0.100000

  9     2  0.425000  0.312500  0.050000  0.100000  0.112500

 10     2  0.425000  0.337500  0.037500  0.100000  0.100000

 11    -1  0.429687  0.304688  0.043750  0.117188  0.104688

 12     2  0.425000  0.300000  0.050000  0.112500  0.112500

 13    -1  0.429687  0.304688  0.031250  0.104688  0.129688

 14     2  0.450000  0.325000  0.025000  0.100000  0.100000

 15     2  0.425000  0.312500  0.050000  0.112500  0.100000

 16     2  0.437500  0.312500  0.050000  0.100000  0.100000

 17    -1  0.429687  0.304688  0.031250  0.129688  0.104688

 18     0  0.434375  0.309375  0.037500  0.109375  0.109375

 19    -1  0.454687  0.304688  0.031250  0.104688  0.104688

 20     1  0.425000  0.325000  0.050000  0.100000  0.100000

 21     2  0.437500  0.300000  0.050000  0.100000  0.112500

 22     1  0.425000  0.300000  0.050000  0.125000  0.100000

 23     2  0.425000  0.300000  0.037500  0.137500  0.100000

 24     2  0.425000  0.300000  0.037500  0.100000  0.137500

 25     1  0.425000  0.300000  0.025000  0.100000  0.150000

 26    -1  0.429687  0.304688  0.043750  0.104688  0.117188

 27     2  0.425000  0.325000  0.025000  0.100000  0.125000

 28    -1  0.442187  0.304688  0.043750  0.104688  0.104688

 29    -1  0.429687  0.317188  0.043750  0.104688  0.104688

 30     1  0.475000  0.300000  0.025000  0.100000  0.100000

 31     1  0.450000  0.300000  0.050000  0.100000  0.100000

 32     1  0.425000  0.350000  0.025000  0.100000  0.100000

 33     2  0.450000  0.300000  0.025000  0.100000  0.125000

Interpreting the results

Minitab creates an augmented five-component extreme vertices design. The base design provides 24 design points; augmentation adds 9 design points for a total of 33 runs. Augmenting this design adds 8 axial points and 1 center point to the design.

Because you chose to display the summary and data tables, Minitab shows the component proportions you will use to create 33 blends of your mixture. When you perform the experiment, use the blends in the run order that is shown. (Because you did not change the mixture total from the default of one, Minitab expresses each component in proportions.)

Minitab randomizes the design by default, so if you try to replicate this example, your run order may not match the order shown.