Solution HW5 - Designed Experimentation Solutions for HW5...

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Designed Experimentation Solutions for HW5 11-1 11-1 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 ξ 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 R-Sq = 94.22% R-Sq(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 2-Way 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 2-way 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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2. 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. This gives a coded equation of Purity = 84.0 + 0.85A. Or we can… 3. Create a path of steepest ascent with both the Main Effects terms. The argument for this case is
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