# hw6 - Problem 8-7 a Write out the alias structure for this...

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Problem 8-7. a) Write out the alias structure for this design. What is the resolution of this design? Considering I=A*B*C*D as the design generator, the design has the following alias structure: Alias Structure I + A*B*C*D A + B*C*D B + A*C*D C + A*B*D D + A*B*C E + A*B*C*D*E A*B + C*D A*C + B*D A*D + B*C A*E + B*C*D*E B*E + A*C*D*E C*E + A*B*D*E D*E + A*B*C*E Hence, the resolution of this design is IV b). Analyze the data. What factors influence the mean free height? The Minitab table for the data is given below: StdOrder RunOrder CenterPt Blocks A B C D E Free Height 1 1 1 1 -1 -1 -1 -1 -1 7,78 2 2 1 1 1 -1 -1 1 -1 8,15 3 3 1 1 -1 1 -1 1 -1 7,5 4 4 1 1 1 1 -1 -1 -1 7,59 5 5 1 1 -1 -1 1 1 -1 7,54 6 6 1 1 1 -1 1 -1 -1 7,69 7 7 1 1 -1 1 1 -1 -1 7,56 8 8 1 1 1 1 1 1 -1 7,56 9 9 1 1 -1 -1 -1 -1 1 7,5 10 10 1 1 1 -1 -1 1 1 7,88 11 11 1 1 -1 1 -1 1 1 7,5 12 12 1 1 1 1 -1 -1 1 7,63 13 13 1 1 -1 -1 1 1 1 7,32 14 14 1 1 1 -1 1 -1 1 7,56 15 15 1 1 -1 1 1 -1 1 7,18 16 16 1 1 1 1 1 1 1 7,81 17 17 1 1 -1 -1 -1 -1 -1 7,78 18 18 1 1 1 -1 -1 1 -1 8,18 19 19 1 1 -1 1 -1 1 -1 7,56 20 20 1 1 1 1 -1 -1 -1 7,56 21 21 1 1 -1 -1 1 1 -1 8 22 22 1 1 1 -1 1 -1 -1 8,09 23 23 1 1 -1 1 1 -1 -1 7,52 24 24 1 1 1 1 1 1 -1 7,81

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25 25 1 1 -1 -1 -1 -1 1 7,25 26 26 1 1 1 -1 -1 1 1 7,88 27 27 1 1 -1 1 -1 1 1 7,56 28 28 1 1 1 1 -1 -1 1 7,75 29 29 1 1 -1 -1 1 1 1 7,44 30 30 1 1 1 -1 1 -1 1 7,69 31 31 1 1 -1 1 1 -1 1 7,18 32 32 1 1 1 1 1 1 1 7,5 33 33 1 1 -1 -1 -1 -1 -1 7,81 34 34 1 1 1 -1 -1 1 -1 7,88 35 35 1 1 -1 1 -1 1 -1 7,5 36 36 1 1 1 1 -1 -1 -1 7,75 37 37 1 1 -1 -1 1 1 -1 7,88 38 38 1 1 1 -1 1 -1 -1 8,06 39 39 1 1 -1 1 1 -1 -1 7,44 40 40 1 1 1 1 1 1 -1 7,69 41 41 1 1 -1 -1 -1 -1 1 7,12 42 42 1 1 1 -1 -1 1 1 7,44 43 43 1 1 -1 1 -1 1 1 7,5 44 44 1 1 1 1 -1 -1 1 7,56 45 45 1 1 -1 -1 1 1 1 7,44 46 46 1 1 1 -1 1 -1 1 7,62 47 47 1 1 -1 1 1 -1 1 7,25 48 48 1 1 1 1 1 1 1 7,59 Using this data we get the following table for the factor effects and the analysis of variance: Fractional Factorial Fit Estimated Effects and Coefficients for Free (coded units) Term Effect Coef StDev Coef T P Constant 7,6256 0,02003 380,62 0,000 A 0,2421 0,1210 0,02003 6,04 0,000 B -0,1637 -0,0819 0,02003 -4,09 0,000 C -0,0496 -0,0248 0,02003 -1,24 0,224 D 0,0912 0,0456 0,02003 2,28 0,029 E -0,2387 -0,1194 0,02003 -5,96 0,000 A*B -0,0296 -0,0148 0,02003 -0,74 0,465 A*C 0,0013 0,0006 0,02003 0,03 0,975 A*D -0,0229 -0,0115 0,02003 -0,57 0,571 A*E 0,0637 0,0319 0,02003 1,59 0,121 B*E 0,1529 0,0765 0,02003 3,82 0,001 C*E -0,0329 -0,0165 0,02003 -0,82 0,417 D*E 0,0396 0,0198 0,02003 0,99 0,330 Analysis of Variance for Free (coded units)
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hw6 - Problem 8-7 a Write out the alias structure for this...

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