Example of creating a Box-Behnken design
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Suppose you have a process for pressure treating utility poles with creosote. In the treating step of the process, you place air-dried poles inside a treatment chamber. The pressure in the chamber is increased and the chamber is flooded with hot creosote. The poles are left in the chamber until they have absorbed 12 pounds of creosote per cubic foot. You would like to experiment with different settings for the pressure, temperature of the creosote, and time in the chamber. Your goal is to get the creosote absorption as close to 12 pounds per cubic foot as possible, with minimal variation. Previous investigation suggests that the response surface for absorption exhibits curvature.

The chamber will withstand internal pressures up to 220 psi, although the strain on equipment is pronounced at over 200 psi. The current operating value is at 175 psi, so you feel comfortable with a range of values between 150 and 200. Current operating values for temperature and time are 210 degrees F and 5 hours, respectively. You feel that temperature cannot vary by more than 10° from the current value. Time can be varied from 4 to 6 hours.

A Box-Behnken design is a practical choice when you cannot run all of the factors at their high (or low) levels at the same time. Here, the high level for pressure is already at the limit of what the chamber can handle. If temperature were also at its high level, this increases the effective pressure, and running at these settings for a long period of time is not recommended. The Box-Behnken design will assure that no runs require all factors to be at their high settings simultaneously.

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

2    Under Type of Design, choose Box-Behnken.

3    From Number of factors, choose 3.

4    Click Designs. Click OK.

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

 

Factors

Names

Low

High

 

A

Pressure

150

200

 

B

Temperature

200

220

 

C

Time

4

6

6    Click OK.

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

Session window output

Box-Behnken Design

 

 

Factors:       3     Replicates:     1

Base runs:    15     Total runs:    15

Base blocks:   1     Total blocks:   1

 

Center points: 3

 

 

Design Table (randomized)

 

Run  Blk   A   B   C

  1    1   0   0   0

  2    1  -1   1   0

  3    1   1  -1   0

  4    1  -1  -1   0

  5    1   0   0   0

  6    1   0   1  -1

  7    1   1   0  -1

  8    1  -1   0  -1

  9    1  -1   0   1

 10    1   1   1   0

 11    1   1   0   1

 12    1   0  -1   1

 13    1   0  -1  -1

 14    1   0   0   0

 15    1   0   1   1

Interpreting the results

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 pressure at 175 psi (0 = center), the temperature at 210°F (0 = center), and treat the utility poles for 5 hours (0 = center).

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