This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Chapter 8(a) Solutions 8.3. Consider the plasma etch experiment described in Example 6.1. Suppose that only a onehalf 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 31 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 61 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 Fvalue of 31.61 implies the model is significant. There is only a 0.30% chance that a "Model FValue" this large could occur due to noise. Std. Dev. 48.44 RSquared 0.9595 Mean 778.88 Adj RSquared 0.9292 C.V. 6.22 Pred RSquared 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 AGap 51.88 1 17.13 99.42 4.33 1.00 BC2F6 Flow 73.13 1 17.13 120.67 25.58 1.00 CPower 140.63 1 17.13 93.08 188.17 1.00 Final Equation in Terms of Coded Factors: 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 52 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...
View
Full
Document
This note was uploaded on 01/16/2011 for the course STAT 430 taught by Professor Stefansteiner during the Fall '03 term at Waterloo.
 Fall '03
 StefanSteiner

Click to edit the document details