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R-sq(adj) =Ӥt{?1Regression Information2222223 (Term)Effect) Coefficient)Standard Error)Low CI)High CI)T Value*P Value+ Intercept,~,P>@,"u?,d]F=@,#?@,kwR@-v<+A:Aperture Setting,@&@,@@,"u?,uq `@,r@,C+@-k7[>+B:Exposure Time,@@,0@,"u?,d]F80@,#1@,6>W[)E@-!E=+C:Develop Time,%@,@,"u?,uq @,r@,_,+@-]@@a> .AB/@/ @/"u?/6@/r@/vq -!@0ύ!>>dd  =8X1Tahoma1Tahoma1Tahoma1Tahoma1Tahoma"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)5*0_("$"* #,##0_);\("$"* #,##0\);_("$"* "-"_);_(@_),)'_(* #,##0_);\(* #,##0\);_(* "-"_);_(@_)=,8_("$"* #,##0.00_);\("$"* #,##0.00\);_("$"* "-"??_);_(@_)4+/_(* #,##0.00_);\(* #,##0.00\);_(* "-"??_);_(@_)                + ) , *  H Sheet1   dMbP?_*+%&A Page &P&?'?(?)?"d??@}& F>dd&   $@F@.@ ??   ! GFII@$@X@?dEffect Probability)User Name Company 8/5/2008 10:15:27 AM#ReliaSoft DOE++ - www.ReliaSoft.com Alpha = 0.1!Normal Probability Plot of EffectStandardized Effect (T Value) ProbabilityColorColor = Size = X = Y =  Starts at:  Ends at:  Duration: ???*****#ReliaSoft DOE++ - www.ReliaSoft.comZ @@@@v@v@TahomaDBTahomaDB o_?_Fj?{Gz?c]Kȵ?gj+?ͪժ?y):?#G?333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahoma|Z rqYieldSignificant EffectsYield(Effect Points)Significant Effects Yield Y' = Yd?YieldDistribution LineYield(Distribution Line)Distribution Line Yield Y' = Yd?  YieldSignificant EffectsYield(Effect Points)Significant Effects Yield Y' = Yd?ABAB g-!@)@C:Develop TimeC:Develop Timen ,+@B@A:Aperture SettingA:Aperture SettingC+@@O@B:Exposure TimeB:Exposure TimeɎZ)E@U@YieldDistribution LineYield(Distribution Line)Distribution Line Yield Y' = Yd?5JIHGFEDCBA@><:86420,($ 1=swz>)i?@3@I@@KenX@@ (@Y@@@Y@A@Y@B@Y@C@Y@D@Y@E@Y@F@Y@G@Y@H@Y@I@Y@J@Y@   ????{Gz?{Gz?{Gz??333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomatTahoma|Z  @@@@v@v@TahomaDBTahomaDB        dƚK  ,  '' & MDCR-O. &MDCR-{  --'' &MDCR-T1;0;-1; &MDCR-F \"Tahoma ww 0w f-!#ReliaSoft DOE++ - www.ReliaSoft.com2 &MDCR-T3;0;0; &MDCR-F &MDCR-S-' &MDCR-T2;0;0; &MDCR-F "Tahoma ww 0w f-!!Normal Probability Plot of Effectw &MDCR-T3;0;0; &MDCR-F &MDCR-S  \"Tahoma ww 0w f- ! Alpha = 0.1F&2 &MDCR-T3;0;0; &MDCR-F &MDCR-S-R&R&' &MDCR-T2;0;0; &MDCR-F >"Tahoma ww 0w f-!Standardized Effect (T Value)f%n &MDCR-T3;0;0; &MDCR-F &MDCR-S>"Tahoma ww 0w f- ! Probability} &MDCR-T3;0;0; &MDCR-F &MDCR-S# &MDCR-T4;0;0; &MDCR-F\"Tahoma ww 0w f- !-50.000F# &MDCR-T5;0;0; &MDCR-F &MDCR-S#  &MDCR-T4;0;0; &MDCR-F !50.000# &MDCR-T5;0;0; &MDCR-F &MDCR-S-# &MDCR-T4;0;0; &MDCR-F#   &MDCR-T4;0;0; &MDCR-F#77 &MDCR-T4;0;0; &MDCR-F#`` &MDCR-T4;0;0; &MDCR-F-#  &MDCR-T4;0;0; &MDCR-F !-30.000F# &MDCR-T5;0;0; &MDCR-F &MDCR-S-#  &MDCR-T4;0;0; &MDCR-F#  &MDCR-T4;0;0; &MDCR-F#  &MDCR-T4;0;0; &MDCR-F#00 &MDCR-T4;0;0; &MDCR-F-#ZZ &MDCR-T4;0;0; &MDCR-F !-10.000F#v &MDCR-T5;0;0; &MDCR-F &MDCR-S-# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F-#** &MDCR-T4;0;0; &MDCR-F !10.000#^ &MDCR-T5;0;0; &MDCR-F &MDCR-S-#SS &MDCR-T4;0;0; &MDCR-F#}} &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F-# &MDCR-T4;0;0; &MDCR-F !30.000#. &MDCR-T5;0;0; &MDCR-F &MDCR-S-### &MDCR-T4;0;0; &MDCR-F#MM &MDCR-T4;0;0; &MDCR-F#ww &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F !10.000X# &MDCR-T5;0;0; &MDCR-F &MDCR-S-## &MDCR-T4;0;0; &MDCR-F- &MDCR-T4;0;0; &MDCR-F &MDCR-T4;0;0; &MDCR-FLL &MDCR-T4;0;0; &MDCR-F !50.000 &MDCR-T5;0;0; &MDCR-F &MDCR-S &MDCR-T4;0;0; &MDCR-F &MDCR-T4;0;0; &MDCR-F(( &MDCR-T4;0;0; &MDCR-F>> &MDCR-T4;0;0; &MDCR-F4 4 &MDCR-T4;0;0; &MDCR-F !99.0007 &MDCR-T5;0;0; &MDCR-F &MDCR-S- &MDCR-T4;0;0; &MDCR-F-"W"$&=MDCR-T58;1;1;Yield(Effect Points) AB X = 8.590 Y = 12.500 &MDCR-F!AB!% &MDCR-T9;1;1; &MDCR-F &MDCR-Sg*&JMDCR-TB8;1;2;Yield(Effect Points) C:Develop Time X = 13.587 Y = 37.500 &MDCR-F !C:Develop Time &MDCR-T9;1;2; &MDCR-F &MDCR-S>~,&NMDCR-TF8;1;3;Yield(Effect Points) A:Aperture Setting X = 13.899 Y = 62.500 &MDCR-F!A:Aperture SettingB &MDCR-T9;1;3; &MDCR-F &MDCR-S 6 ]+&KMDCR-TC8;1;4;Yield(Effect Points) B:Exposure Time X = 42.323 Y = 87.500@ &MDCR-F!B:Exposure Time;h h &MDCR-T9;1;4; &MDCR-F &MDCR-S- %#A&&MDCR-T8;3;0;Yield(Distribution Line) &MDCR-F!Effect Probability! &MDCR-T6;0;0; &MDCR-F &MDCR-S-!& &MDCR-T6;0;0; &MDCR-Fv!v& &MDCR-T6;0;0; &MDCR-F  !YieldRK! &MDCR-T7;1;0; &MDCR-F &MDCR-S !Y' = Y! &MDCR-T7;1;0; &MDCR-F &MDCR-S E("! &MDCR-T7;1;0; &MDCR-F!Significant Effects" &MDCR-T7;1;0; &MDCR-F &MDCR-S-!Z" &MDCR-T7;3;0; &MDCR-F!Distribution Line`" &MDCR-T7;3;0; &MDCR-F &MDCR-S ! 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Pure Error @2@@!Total".@"p@"""#$ %S =&"u?%R-sq ='i?% R-sq(adj) ='Ӥt{?(Regression Information))))))* +Term ,Effect , Coefficient ,Standard Error ,Low CI ,High CI ,T Value -P Value!. Intercept!/~!/P>@!/"u?!/d]F=@!/#?@!/kwR@!0v<".A:Aperture Setting"/@&@/@@"/"u?"/uq `@"/r@"/C+@"0k7[>#.B:Exposure Time#/@@/0@#/"u?#/d]F80@#/#1@#/6>W[)E@#0!E=$.C:Develop Time$/%@/@$/"u?$/uq @$/r@$/_,+@$0]@@a> %1AB%2@2 @%2"u?%26@%2r@%2vq -!@%3ύ!>>dd YieldDExperimentResponse`P  6Yield  @"@A@J@0@6@F@N@@$@>@I@.@5@F@O@ ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? ????????????????  @"@A@J@0@6@F@N@@$@>@I@.@5@F@O@ ????????????????P>@ ?    I  IABCDE ?     A  ABCDE ?     B  BACDE ?     C  CABDE ?     D  DABCE ?     E  ABCDABCD ?     AB  ABCDE ?     AC  ACBDE ?     AD  ADBCE ?     AE  BCDBCD ?     BC  BCADE ?     BD  BDACE ?     BE  ACDACD ?     CD  CDABE ?     CE  ABDABD ?     DE  ABCABC ?     ABC  ABCDE ?     ABD  ABDCE ?     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ABCDE  ABCDEI ?              @^ڕ@ModelO v=@s@ ?cp>&h@A:Aperture SettingLl.~7[>~@ ?@B:Exposure TimeH7lE=@ ?18g@C:Develop TimefH@a>}@ ?28qR@ABH/<>g@  &@Residual0<@ @zelW? Lack of Fith~?`#@  @ Pure Error2@   P>@P.50?@p=@ Intercept<̜?V1R@ @@@&@h<@A `@A:Aperture Setting~7[>̜?C+@ 0@@@01@p80@B:Exposure TimeE=̜?ɎZ)E@ @%@h<@A @C:Develop TimeH@a>̜?n ,+@  @@h<@.@ABH/<>̜? g-!@                     P>@@@0@@ @  ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????ffffff?     P.5          I  IABCDE ?     A  ABCDE ?     B  BACDE ?     C  CABDE ?     D  DABCE ?     E  ABCDABCD ?     AB  ABCDE ?     AC  ACBDE ?     AD  ADBCE ?     AE  BCDBCD ?     BC  BCADE ?     BD  BDACE ?     BE  ACDACD ?     CD  CDABE ?     CE  ABDABD ?     DE  ABCABC ?     ABC  ABCDE ?     ABD  ABDCE ?     ABE  ABECD ?     ACD  ACDBE ?     ACE  ACEBD ?     ADE  ADEBC ?     BCD  BCDAE ?     BCE  BCEAD ?     BDE  BDEAC ?     CDE  CDEAB ?     ABCD  ABCDE ?     ABCE  ABCED ?     ABDE  ABDEC ?     ACDE  ACDEB ?     BCDE  BCDEA ?     ABCDE  ABCDEI ?    ?   1 aAa_MainProject '2 Level Fractional Factorial Design.doc,C:\DOCUME~1\MCAROL~1\LOCALS~1\Temp\RSFE6.tmpࡱ> >@=A%` bjbj"x"x 4h@@c3::: D  @1@1@18x1|1 ~A22: 3 3 3P6P6P6@@@@@@@$$ChE#A 8 66@88#APP 3 38Aj:j:j:8P2 3 3@j:8@j:j:I=  = 32 @18a=I?NA0~Ai=, F~9 F= F =P6Z6@j:647P6P6P6#A#A:dP6P6P6~A8888 |# |# PPPPPP Example Consider a manufacturing process for an integrated circuit.* The objective is to improve the process yield. The five factors that may affect the process are: FactorNameUnitLowHighAAperture SettingsmalllargeBExposure Timemins2040CDevelop Timeseconds3045DMask DimensionsmalllargeEEtch Timemins14.515.5 It is too expensive to run a full factorial design, which has  EMBED Equation.3 runs. Therefore, the engineers decide to run a half fractional factorial design using generator E = ABCD. Design the Experiment The design matrix and the data are given in the Fractional Factorial Design Model 1 Folio. You can also reproduce the design by the following steps. Step 1: Add a new Standard Folio by selecting Add Folio from the Project menu. Step 2: In the first step of the Design Wizard, select Factorial Design then click Next.  Step 3: In the second step of the Design Wizard, select 2 Level Fractional Factorial Design then click Next.  Step 4: In the third step of the Design Wizard, use the settings shown next.  Step 5: Click the Factor Properties button and, in the Factor Properties window, use the settings shown next then click OK.  Step 6: Click the Fraction Generator button and, in the Fraction Generator window, make sure the generator is Etch Time = ABCD, as shown next, then click OK.  Step 7: Click the Response Properties button and, in the Response Properties window, enter the name of the response, as shown next, then click OK.  Step 8: Click Next to view the design summary, then click Finish to create the Standard Folio containing the two level fractional factorial design. Alternatively, you can skip the design review step by clicking Finish in the third step of the Design Wizard. The run order is randomly generated when you create the design. It may be different from the Folio in the example file. You can conduct the experiment according to the run order in the design matrix and record all the response values. Analysis and Results The design and the data are provided in the Fractional Factorial Design Model 1 Folio. You can proceed using this Folio or you can copy the data to the Folio you just created. Make sure you sort both Folios by the Standard Order column before you copy and paste the data: select Standard Order in the Sort By area in the Control Panel to sort the Data Sheet by the Standard Order column. Once the data set has been entered in the Data Sheet, you can analyze it. Step 1: Double-click the Fractional Factorial Design Model 1 Folio to open it. The Design tab will be displayed. Step 2: Specify to include all effects up to two-way interactions in the model. To do this, click the Select Effects icon and, in the Effects window, use the settings shown next, then click OK.  Step 3: On the Options page of the Control Panel, select to use Individual Terms in the analysis. Step 4: Return to the Main page of the Control Panel and click the Calculate icon. The ANOVA table and the Regression Information table for the model are provided on the Analysis tab, which is added to the Folio upon calculation. Step 5: Click the Plot icon to add the Plot tab to the Folio. From the normal probability plot, which is created by default, we can see that effects A, B, C and AB are significant.  Therefore, in model 2, only effects A, B, C and AB are included in the model. The results for the reduced model and the optimization are given in the Fractional Factorial Design Model 2 Folio. You can also reproduce the Folio by the following steps. Step 6: Right-click the Fractional Factorial Design Model 1 Folio in the Project Explorer and select Duplicate Item from the shortcut menu that appears. Rename the new Folio. Step 7: Click the Select Effects icon and click the Select Significant Effects button to select only the significant effects to calculate the new model, then click OK.  Step 8: Click Calculate. The coefficients for A, B, C and AB are: TermCoefficientsA5.5625B16.9375C5.4375AB3.4375Conclusions Each of the effects in model 2 has a positive effect on the yield. Therefore, in order to increase the yield, the high level setting of factors A, B, and C should be applied. * Montgomery, D. C. Design and Analysis of Experiments, 5th edition, John Wiley & Sons, New York.      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