mont4e_sm_ch14_sec07 - Section 14-7 14-35 a) Design 25-1...

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14-42 Section 14-7 14-35 a) Design 2 5-1 Run No. A B C D E resp 1 -1 -1 -1 -1 1 8 2 1 -1 -1 -1 -1 9 3 -1 1 -1 -1 -1 34 4 1 1 -1 -1 1 52 5 -1 -1 1 -1 -1 16 6 1 -1 1 -1 1 22 7 -1 1 1 -1 1 45 8 1 1 1 -1 -1 60 9 -1 -1 -1 1 -1 8 10 1 -1 -1 1 1 10 11 -1 1 -1 1 1 30 12 1 1 -1 1 -1 50 13 -1 -1 1 1 1 15 14 1 -1 1 1 -1 21 15 -1 1 1 1 -1 44 16 1 1 1 1 1 63 b) Design Generators: E = ABCD Alias Structure I + ABCDE A + BCDE B + ACDE C + ABDE D + ABCE E + ABCD AB + CDE AC + BDE AD + BCE AE + BCD BC + ADE BD + ACE BE + ACD CD + ABE CE + ABD DE + ABC
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14-43 c) Term Effect Coef Constant 30.4375 factor_A 10.8750 5.4375 factor_B 33.6250 16.8125 factor_C 10.6250 5.3125 factor_D -0.6250 -0.3125 factor_E 0.3750 0.1875 factor_A*factor_B 7.1250 3.5625 factor_A*factor_C 0.6250 0.3125 factor_A*factor_D 0.8750 0.4375 factor_A*factor_E 1.3750 0.6875 factor_B*factor_C 0.8750 0.4375 factor_B*factor_D -0.3750 -0.1875 factor_B*factor_E 0.1250 0.0625 factor_C*factor_D 0.6250 0.3125 factor_C*factor_E 0.6250 0.3125 factor_D*factor_E -1.6250 -0.8125 d) Factors A, B, and C and interaction AB are significant e) Term Effect Coef StDev Coef T P Constant 30.438 0.4243 71.73 0.000 factor_A 10.875 5.438 0.4243 12.81 0.000 factor_B 33.625 16.812 0.4243 39.62 0.000 factor_C 10.625 5.313 0.4243 12.52 0.000 factor_A*factor_B 7.125 3.562 0.4243 8.40 0.000 14-36 Estimated Effects and Coefficients for resp (coded units) Estimated Effects and Coefficients for yield (coded units) Term Effect Coef Constant 17.875 A 3.750 1.875 B 0.250 0.125 C 2.750 1.375 D 4.250 2.125 A*B -0.750 -0.375 A*C -4.250 -2.125 A*D 4.250 2.125 30 20 10 0 1 0 -1 Effect Normal Score AB C A B Normal Probability Plot of the Effects (response is resp, Alpha = .10) A: A B: B C: C D: D E: E
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14-44 None of the factors appear to be significant in the 2 4-1 design. 14-37 a) The generator is E= -ABCD b) The resolution is resolution V c) Estimated Effects and Coefficients for y (coded units) Term Effect Coef Constant 1.2263 A 0.1450 0.0725 B 0.0875 0.0438 C 0.0375 0.0187 D -0.0375 -0.0187 E -0.4700 -0.2350 A*B 0.0150 0.0075 A*C 0.0950 0.0475 A*D 0.0300 0.0150 A*E -0.1525 -0.0762 B*C -0.0675 -0.0338 B*D 0.1625 0.0813 B*E -0.4050 -0.2025 C*D 0.0725 0.0363 C*E 0.1350 0.0675 D*E -0.3150 -0.1575 Effect Percent 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 99 95 90 80 70 60 50 40 30 20 10 5 1 Factor D EE Name AA BB CC D Effect Type Not Significant Significant BE E Normal Probability Plot of the Effects (response is y, Alpha = .05) Lenth's PSE = 0.13125 From the graph shown above, E, BE, and DE are important effects. From the effect estimation from table above these same effects are computed to be the largest effects (in absolute value). -5 0 5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Effect Normal Score Normal Probability Plot of the Effects (response is resp, Alpha = .10) A: A B: B C: C D: D
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14-45 d) For the model with E, BE, and DE the normality assumption and constant variance seem to be reasonable. DESIGN-EXPERT Plot Response 1 Studentized Residuals Normal % probability Normal plot of residuals -1.89 -1.01 -0.14 0.74 1.61 1 5 10 20 30 50 70 80 90 95 99 DESIGN-EXPERT Plot Response 1 Predicted Studentized Residuals Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 0.63 0.93 1.23 1.52 1.82 For a hierarchical model, the effects o include are B, D, E, BE, and DE. The ANOVA and residual plot follow:
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14-46 Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model1.97 5 0.39 8.94 0.0019 B 0.031 1 0.031 0.69 0.4242 D 5.625E-003 1 5.625E-003 0.13 0.7284 E 0.88 1 0.88 20.03 0.0012
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This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.

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mont4e_sm_ch14_sec07 - Section 14-7 14-35 a) Design 25-1...

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