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)
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)
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.

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