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Designed Experimentation
Solutions for HW5
111
111
A chemical plant produces oxygen by liquefying air and separating it into its component gases by
fractional distillation.
The purity of the oxygen is a function of the main condenser temperature and the
pressure ratio between the upper and lower columns.
Current operating conditions are temperature
=
)
(
1
ξ
220°C and pressure ratio
=
)
(
2
1.2.
Using the following data find the path of steepest ascent.
Temperature (
x
1
)
Pressure Ratio (
x
2
)
Purity
225
1.1
82.8
225
1.3
83.5
215
1.1
84.7
215
1.3
85.0
220
1.2
84.1
220
1.2
84.5
220
1.2
83.9
220
1.2
84.3
First we create a 2
2
+ 4 center points model in Minitab.
After entering the data and performing the analysis,
we get the following results…
Factorial Fit: Purity versus Temperature, Pressure
Estimated Effects and Coefficients for Purity (coded units)
Term
Effect
Coef
SE Coef
T
P
Constant
84.0000
0.1291
650.66
0.000
Temperature
1.7000
0.8500
0.1291
6.58
0.007
Pressure
0.5000
0.2500
0.1291
1.94
0.148
Temperature*Pressure
0.2000
0.1000
0.1291
0.77
0.495
Ct Pt
0.2000
0.1826
1.10
0.353
S = 0.258199
RSq = 94.22%
RSq(adj) = 86.51%
From the review of the P values, we find that Temperature is a highly significant variable, and Pressure and
the T*P interaction is not significant.
From a review of the actual ANOVA:
Analysis of Variance for Purity (coded units)
Source
DF
Seq SS
Adj SS
Adj MS
F
P
Main Effects
2
3.14000
3.14000
1.57000
23.55
0.015
2Way Interactions
1
0.04000
0.04000
0.04000
0.60
0.495
Curvature
1
0.08000
0.08000
0.08000
1.20
0.353
Residual Error
3
0.20000
0.20000
0.06667
Pure Error
3
0.20000
0.20000
0.06667
Total
7
3.46000
We find that main effects are highly significant and the 2way interaction and curvature are not significant.
We can decide to do several things at this point:
1.
Since the interaction and curvature are not significant, we will leave them out of the final steepest
path equation.
We see that the Main Effect term is highly significant, so we now will either…
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Create a path of steep ascent that only includes factor Temp, and go in a straight horizontal path.
There is a strong argument for this in that it is a much stronger term than Pressure.
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 Spring '08
 Staff

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