HW5+Solution

# Factorial fit y versus a b c estimated effects and

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Factorial Fit: y versus A, B, C Estimated Effects and Coefficients for y (coded units) Term Effect Coef Constant 71.250 A 1.500 0.750 B -5.000 -2.500 C 23.000 11.500 A*B -0.000 -0.000 A*C 10.000 5.000 B*C 1.500 0.750 A*B*C 0.500 0.250 S = * PRESS = *

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Problem 4 (20 points) Load the data file p4.xlsx into Minitab, and perform a DOE analysis. Report the effect estimation table and show a normal plot and residual versus fitted plot in your solution. What effects are significant? (use a 0.05 criterion) Factorial Fit: y versus A, B Estimated Effects and Coefficients for y (coded units) Term Effect Coef SE Coef T P Constant 72.7500 5.890 12.35 0.000 A 1.5000 0.7500 5.890 0.13 0.905 B -0.5000 -0.2500 5.890 -0.04 0.968 A*B 0.5000 0.2500 5.890 0.04 0.968 S = 16.6583 PRESS = 4440 R-Sq = 0.49% R-Sq(pred) = 0.00% R-Sq(adj) = 0.00% None of the effects are significant

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Problem 5 (10 points) You want to study 7 factors each with 2 levels in an experiment, but you can only afford 8 runs. What fractional factorial design are you going to use? (write down your choice of k and p) If you can only afford 4 runs, is it feasible to use a fractional factorial design? k=# of factors=7 Now we solve for p , so , thus If there is only 4 runs, then we have an inequality that , where n is the number of runs, and p here stands for the number of effects being estimated. Since at least we need to estimate the main effects, so . But we have , so this design is not feasible.
Problem 6 (20 points) Load the data file p9.xlsx into Minitab, and perform a DOE analysis. Report the effect estimation table and show a normal plot and residual versus fitted plot in your solution . Are all the effects estimable? Which effect is aliased with AD? Factorial Fit: y versus A, B, C, D, E Estimated Effects and Coefficients for y (coded units) Term Effect Coef Constant 24.375 A -0.750 -0.375 B 0.750 0.375 C -7.250 -3.625 D -1.250 -0.625 E 3.250 1.625 A*D -0.750 -0.375 A*E -1.250 -0.625 S = * PRESS = * All of the effects are not estimable because they are aliased with each other AD=BE=ACE=BCD
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• Spring '08
• RoshanV
• effect estimation table

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