Six Sigma Case Studies with Minitab®

147Mixture Designs to Optimize Pollution Level and Temperature of Fuels

“Components” and the dialog box shown in Figure9.30 opens. Enter “100”

for “Single total”. Also, name the three components in the “Name” column,

enter “20” for “Lower”, and enter “100” for “Upper”, for each of the three

components. Click on “OK” and it takes you back to the dialog box shown

in Figure9.28. Click on “Options” and the dialog box shown in Figure9.31

opens. Uncheck the “Randomize runs” box so that it is easier for you to rep-

licate the results in this case study. Click on “OK” and it takes you back to

the dialog box shown in Figure 9.28. Click on “OK” and the partial mix-

ture design shown in Figure9.32 is the result. In order to see the simplex

FIGURE 9.18

Removal of QR and PR terms.

Analysis of Variance for Sulfation (component proportions)

Source DF Seq SS Adj SS Adj MS F P

Regression 3 360.40 360.40 120.134 2.42 0.102

Linear 2 344.53 358.76 179.379 3.61 0.049

Quadratic 1 15.87 15.87 15.874 0.32 0.579

P*Q 1 15.87 15.87 15.874 0.32 0.579

Residual Error 17 843.81 843.81 49.636

Lack-of-Fit 3 11.85 11.85 3.950 0.07 0.977

Pure Error 14 831.96 831.96 59.426

Total 20 1204.21

FIGURE 9.19

Revised ANOVA output after removal of QR and PR terms.

148 Six Sigma Case Studies with Minitab

®

design plot, select “Simplex Design Plot” as was shown in Figure9.8. Doing

so opens the dialog box shown in Figure9.33. Click on “OK” and the simplex

design plot shown in Figure9.34 is the result. As shown in Figure9.35, label

an empty column as “Temperature” and enter the data. (For example, in the

rst run, the temperature is found to be “398” when P = 60%, Y = 20%, and

Z = 20%.) Open the CHAPTER_9_ZEO.MTW worksheet for the data shown

in Figure9.35 (the worksheet is available at the publisher’s website; the data

from the worksheet are also provided in the Appendix).

To analyze the design created for fuel Zeo, select “Analyze Mixture Design”

as shown in Figure9.36. Doing so opens the dialog box shown in Figure9.37.

FIGURE 9.20

Removal of PQ term.

Analysis of Variance for Sulfation (component proportions)

Source DF Seq SS Adj SS Adj MS F P

Regression 2 344.53 344.53 172.264 3.61 0.048

Linear 2 344.53 344.53 172.264 3.61 0.048

Residual Error 18 859.68 859.68 47.760

Lack-of-Fit 4 27.72 27.72 6.931 0.12 0.974

Pure Error 14 831.96 831.96 59.426

Total 20 1204.21

FIGURE 9.21

Revised ANOVA output after removal of PQ term.

149Mixture Designs to Optimize Pollution Level and Temperature of Fuels

FIGURE 9.22

Selection of “Response Optimizer” for fuel Neo.

FIGURE 9.23

Available response variable for optimization for fuel Neo.

150 Six Sigma Case Studies with Minitab

®

FIGURE 9.24

Selection of response variable for optimization for fuel Neo.

FIGURE 9.25

Entry of upper bound for sulfation.

151Mixture Designs to Optimize Pollution Level and Temperature of Fuels

High

Cur

Low

D

1.0000

Optimal

Sulfation

Minimum

y = 3.7213

d = 1.0000

Composite

Desirability

1.0000

[ ]:Q

100.0

[0.0]

0.0

[ ]:R

100.0

[100.0]

0.0

[ ]:P

100.0

[0.0]

0.0

FIGURE 9.26

Optimal amounts of fuel Neo components.

FIGURE 9.27

Selection of “Create Mixture Design” for fuel Zeo.