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Assignment_Solution_Chp_8a

# Assignment_Solution_Chp_8a - Chapter 8(a Solutions 8.3...

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1 Chapter 8(a) – Solutions 8.3. Consider the plasma etch experiment described in Example 6.1. Suppose that only a one-half fraction of the design could be run. Set up the design and analyze the data. Because Example 6.1 is a replicated 2 3 factorial experiment, a half fraction of this design is a 2 3-1 with four runs. The experiment is replicates to assure an adequate estimate of the MS E . Etch Rate Factor Levels A B C=AB (A/min) Low (-) High (+) - - + 1037 A (Gap, cm) 0.80 1.20 - - + 1052 B (C 2 F 6 flow, SCCM) 125 200 + - - 669 C (Power, W) 275 325 + - - 650 - + - 633 - + - 601 + + + 729 + + + 860 The analysis shown below identifies all three main effects as significant. Because this is a resolution III design, the main effects are aliased with two factor interactions. The original analysis from Example 6-1 identifies factors A , C , and the AC interaction as significant. In our replicated half fraction experiment, factor B is aliased with the AC interaction. This problem points out the concerns of running small resolution III designs. Design Expert Output Response: Etch Rate ANOVA for Selected Factorial Model Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model 2.225E+005 3 74169.79 31.61 0.0030 significant A 21528.13 1 21528.13 9.18 0.0388 B 42778.13 1 42778.13 18.23 0.0130 C 1.582E+005 1 1.582E+005 67.42 0.0012 Pure Error 9385.50 4 2346.37 Cor Total 2.319E+005 7 The Model F-value of 31.61 implies the model is significant. There is only a 0.30% chance that a "Model F-Value" this large could occur due to noise. Std. Dev. 48.44 R-Squared 0.9595 Mean 778.88 Adj R-Squared 0.9292 C.V. 6.22 Pred R-Squared 0.8381 PRESS 37542.00 Adeq Precision 12.481 Coefficient Standard 95% CI 95% CI Factor Estimate DF Error Low High VIF Intercept 778.88 1 17.13 731.33 826.42 A-Gap -51.88 1 17.13 -99.42 -4.33 1.00 B-C2F6 Flow -73.13 1 17.13 -120.67 -25.58 1.00 C-Power 140.63 1 17.13 93.08 188.17 1.00 Final Equation in Terms of Coded Factors:

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2 Etch Rate = +778.88 -51.88 * A -73.13 * B +140.63 * C Final Equation in Terms of Actual Factors: Etch Rate = -332.37500 -259.37500 * Gap -1.95000 * C2F6 Flow +5.62500 * Power 8.4. Problem 6.24 describes a process improvement study in the manufacturing process of an integrated circuit. Suppose that only eight runs could be made in this process. Set up an appropriate 2 5-2 design and find the alias structure. Use the appropriate observations from Problem 6.21 as the observations in this design and estimate the factor effects. What conclusions can you draw? I = ABD = ACE = BCDE A (ABD) =BD A (ACE) =CE A (BCDE) =ABCDE A=BD=CE=ABCDE B (ABD) =AD B (ACE) =ABCE B (BCDE) =CDE B=AD=ABCE=CDE C (ABD) =ABCD C (ACE) =AE C (BCDE) =BDE C=ABCD=AE=BDE D (ABD) =AB D (ACE) =ACDE D (BCDE) =BCE D=AB=ACDE=BCE E (ABD) =ABDE E (ACE) =AC E (BCDE) =BCD E=ABDE=AC=BCD BC (ABD) =ACD BC (ACE) =ABE BC (BCDE) =DE BC=ACD=ABE=DE BE (ABD) =ADE BE (ACE) =ABC BE (BCDE) =CD BE=ADE=ABC=CD A B C D=AB E=AC - - - + + de 6 + - - - - a 9 - + - - + be 35 + + - + - abd 50 - - + + - cd 18 + - + - + ace 22 - + + - - bc 40 + + + + + abcde 63 Design Expert Output Term Effect SumSqr % Contribtn Model Intercept Model A 11.25 253.125 8.91953 Model B 33.25 2211.13 77.9148 Model C 10.75 231.125 8.1443 Model D 7.75 120.125 4.23292 Error E 2.25 10.125 0.356781 Error BC -1.75 6.125 0.215831 Error BE 1.75 6.125 0.215831 Lenth's ME 28.232 Lenth's SME 67.5646
3 Half Normal plot Half Norm al % probability Effect 0.00 8.31 16.63 24.94 33.25 0 20 40 60 70 80 85 90 95 97 99 A B C D The main A , B , C , and D are large. However, recall that we are really estimating A+BD+CE , B+AD , C+DE and D+AD . There are other possible interpretations of the experiment because of the aliasing.

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Assignment_Solution_Chp_8a - Chapter 8(a Solutions 8.3...

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