137
9
Mixture Designs to Optimize Pollution
Level and Temperature of Fuels
This case study is about a laboratory using Six Sigmas dene-measure-
analyze-design-verify (DMADV) approach to design the compositions of
two fuel mixtures: Neo and Zeo.
Sections 9.1 and 9.2 give brief descriptions of the dene phase and the
measure phase, respectively. Section 9.3 illustrates the analyze phase with
detailed instructions for using Minitab
®
. The design and verify phases are
briey explained in Section 9.4.
9.1 Define Phase
The laboratory wishes to decide the components and their proportions for
two fuel mixtures: Neo and Zeo.
9.2 Measure Phase
The objective for Neo is to minimize the pollution level, and the objective for
Zeo is to optimize the temperature generated by the fuel.
9.3 Analyze Phase
The laboratory is considering three components for fuel Neo: P, Q, and R.
The total percentage of the proportions of these three components must be
100, and each component may range between 0% and 100%. To design the
fuel mixture, select “Create Mixture Design” as shown in Figure9.1. Doing
so opens the dialog box shown in Figure9.2. Select “Simplex centroid” for
“Type of Design” and “3” for “Number of components. Click on “Designs”
138 Six Sigma Case Studies with Minitab
®
FIGURE 9.2
Selection of “Simplex centroid”.
FIGURE 9.1
Selection of “Create Mixture Design” for fuel Neo.
139Mixture Designs to Optimize Pollution Level and Temperature of Fuels
and the dialog box shown in Figure9.3 opens. Select “3” for “Number of
replicates for the whole design” and click on “OK. This takes you back to
the dialog box shown in Figure9.2. Click on “Components” and the dialog
box shown in Figure9.4 opens. Enter “100” for “Single total”. Also, name the
three components in the “Name” column, enter “0” 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9.2. Click on “Options”
and the dialog box shown in Figure 9.5 opens. Uncheck the “Randomize
runs” box so that it is easier for you to replicate the results in this case study.
Click on “OK” and it takes you back to the dialog box shown in Figure9.2.
Click on “Results” and the dialog box shown in Figure9.6 opens. Ensure
that “Detailed description” is selected, and click on “OK. This takes you
back to the dialog box shown in Figure9.2. Click on “OK” and the partial
mixture design shown in Figure9.7 is the result. In order to see the simplex
design plot, select “Simplex Design Plot” as shown in Figure9.8. Doing so
opens the dialog box shown in Figure9.9. Click on “OK” and the simplex
design plot shown in Figure9.10 is the result. As shown in Figure9.11, label
an empty column as “Sulfation” (a measure of pollution level). The data from
the experiment are shown in Figure9.11. (For example, in the rst run, the
sulfation level is found to be “3” when P = 100%, Q = 0%, and R = 0%.) Open
the CHAPTER_9_NEO.MTW worksheet to analyze the data (the worksheet
FIGURE 9.3
Entry of replicates.
140 Six Sigma Case Studies with Minitab
®
FIGURE 9.5
Unchecking “Randomize runs” box for fuel Neo.
FIGURE 9.6
Selection of “Detailed description” for fuel Neo.
FIGURE 9.4
Entry of lower and upper bounds for components of fuel Neo.
141Mixture Designs to Optimize Pollution Level and Temperature of Fuels
FIGURE 9.7
Partial mixture design for fuel Neo.
FIGURE 9.8
Selection of “Simplex Design Plot” for fuel Neo.

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