Example of creating a central composite design
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Suppose you want to conduct an experiment to maximize crystal growth. You have determined that three variables - time the crystals are exposed to a catalyst, temperature in the exposure chamber, and percentage of the catalyst in the air inside the chamber - explain much of the variability in the rate of crystal growth.

You generate the default central composite design for three factors and two blocks (to represent the two days you conduct the experiment). You assign the factor levels and randomize the design.

1    Choose Stat > DOE > Response Surface > Create Response Surface Design.

2    Under Type of Design, choose Central composite.

3    From Number of factors, choose 3.

4    Click Designs. To create the design with 2 blocks, highlight the second row in the Design box at the top. Click OK.

5    Click Factors. Complete the Name, Low, and High columns of the table as shown below:

Factors

Names

Low

High

A

Time

6

9

B

Temperature

40

60

C

Catalyst

3.5

7.5

6    Click OK.

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

Session window output

Central Composite Design

 

 

Factors:       3     Replicates:     1

Base runs:    20     Total runs:    20

Base blocks:   2     Total blocks:   2

 

Two-level factorial: Full factorial

 

Cube points:             8

Center points in cube:   4

Axial points:            6

Center points in axial:  2

 

α: 1.633

 

 

Design Table (randomized)

 

Run  Blk       A       B       C

  1    1   1.000   1.000   1.000

  2    1  -1.000   1.000   1.000

  3    1   1.000  -1.000  -1.000

  4    1   0.000   0.000   0.000

  5    1   0.000   0.000   0.000

  6    1  -1.000   1.000  -1.000

  7    1   1.000   1.000  -1.000

  8    1   0.000   0.000   0.000

  9    1   0.000   0.000   0.000

 10    1  -1.000  -1.000  -1.000

 11    1   1.000  -1.000   1.000

 12    1  -1.000  -1.000   1.000

 13    2   1.633   0.000   0.000

 14    2   0.000   0.000   0.000

 15    2  -1.633   0.000   0.000

 16    2   0.000   1.633   0.000

 17    2   0.000  -1.633   0.000

 18    2   0.000   0.000   1.633

 19    2   0.000   0.000   0.000

 20    2   0.000   0.000  -1.633

Interpreting the results

You have created a central composite design with three factors that will be run in two blocks. This design is both rotatable and orthogonally blocked - see Central composite designs.

Because you chose to display the summary and design tables, Minitab shows the experimental conditions or settings for each of the factors for the design points. When you perform the experiment, use the order that is shown to determine the conditions for each run. For example, in the first run of your experiment, you would set the time (A) at 9 minutes (1 = high), the temperature (B) at 60° (1 = high), and use 7.5 grams of the catalyst (C) (1 = high).

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