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X = 86.9463;% &MDCR-T3;0;0; &MDCR-F &MDCR-S ! Temperature;$ &MDCR-T3;0;0; &MDCR-F &MDCR-S ! X = 176.5293%z &MDCR-T3;0;0; &MDCR-F &MDCR-S>"Tahoma  fww 0wf- ! 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GF4@@?d Pareto Chart)User Name Company 8/5/2008 10:20:22 AM#ReliaSoft DOE++ - www.ReliaSoft.comAlpha = 0.1; Threshold = 1.8946 Pareto ChartStandardized Effect (T Value)TermColor T Value = X = Y =  Starts at:  Ends at:  Duration: ???*****#ReliaSoft DOE++ - www.ReliaSoft.comZ @@@@v@v@TahomaDBTahomaDB o_?VF?{Gz?c]Kȵ?gj+?ͪժ?y):?;S.?333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahoma|Z YieldNon-Significant EffectsYield(Effect Points)Non-Significant Effects Yield Y' = Yd?YieldSignificant EffectsYield(Effect Points)Significant Effects Yield Y' = Yd?YieldDistribution LineYield(Distribution Line)Distribution Line Yield Y' = Yd?Non-SignificantNon-SignificantNon-SignificanthA Significant Significant Significanto@  ABABABd?I? B:Temperature B:Temperature B:Temperatured?z-@BBBBBBd?#쮯#@A:TimeA:TimeA:Timed?\o5u(%@AAAAAAd?BWJ+@Special Pareto Target Pareto Target Yield Y' = Yd? 1P?1P?Critical ValueCritical ValueCritical Value Yield Y' = Yd?1P?1P?@Non-SignificantNon-SignificantNon-SignificanthA Significant Significant Significanto@   ????{Gz?{Gz?{Gz??333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomatTahoma|Z  @@@@v@v@TahomaDBTahomaDB        bƚK & "  '' & MDCR-O. &MDCR-{  --'' &MDCR-T1;0;-1; &MDCR-F \"Tahoma 8ww 0w fn-!#ReliaSoft DOE++ - www.ReliaSoft.com2 &MDCR-T3;0;0; &MDCR-F &MDCR-S-' &MDCR-T2;0;0; &MDCR-F "Tahoma Uww 0w fn- ! Pareto Chart &MDCR-T3;0;0; &MDCR-F &MDCR-S  \"Tahoma :ww 0w fn-!Alpha = 0.1; Threshold = 1.8946F&2 &MDCR-T3;0;0; &MDCR-F &MDCR-S-R&R&' &MDCR-T2;0;0; &MDCR-F >"Tahoma Www 0w fn-!Standardized Effect (T Value)4% &MDCR-T3;0;0; &MDCR-F &MDCR-S>"Tahoma <ww 0w fn-!TermU &MDCR-T3;0;0; &MDCR-F &MDCR-S#vv &MDCR-T4;0;0; &MDCR-F\"Tahoma Yww 0w fn- !0.000R# &MDCR-T5;0;0; &MDCR-F &MDCR-S#n!n! &MDCR-T4;0;0; &MDCR-F !20.000# &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-F-#  &MDCR-T4;0;0; &MDCR-F !4.000R#f &MDCR-T5;0;0; &MDCR-F &MDCR-S-#- - &MDCR-T4;0;0; &MDCR-F#K K &MDCR-T4;0;0; &MDCR-F#ii &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F-# &MDCR-T4;0;0; &MDCR-F !8.000R# &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 !12.000#r &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 !16.000#  &MDCR-T5;0;0; &MDCR-F &MDCR-S-# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F#11 &MDCR-T4;0;0; &MDCR-F#O O &MDCR-T4;0;0; &MDCR-F !1.895R#u &MDCR-T5;0;0; &MDCR-F &MDCR-S-#D#n! &MDCR-T4;0;0; &MDCR-FDn! &MDCR-T4;0;0; &MDCR-F-m Dm  &MDCR-T4;0;0; &MDCR-F!AB  &MDCR-T11;0;0; &MDCR-F &MDCR-SD &MDCR-T4;0;0; &MDCR-F ! B:Temperature;h &MDCR-T11;1;0; &MDCR-F &MDCR-S-D- &MDCR-T4;0;0; &MDCR-F!BB &MDCR-T11;2;0; &MDCR-F &MDCR-S D  &MDCR-T4;0;0; &MDCR-F !A:Time'  &MDCR-T11;3;0; &MDCR-F &MDCR-SD &MDCR-T4;0;0; &MDCR-F!AA &MDCR-T11;4;0; &MDCR-F &MDCR-S--"v&2MDCR-T*8;0;1;AB Non-Significant T Value = 1.880 &MDCR-F-u %v"&9MDCR-T18;1;1;B:Temperature Significant T Value = 5.477 &MDCR-FXv&.MDCR-T&8;2;1;BB Significant T Value = 9.927 &MDCR-F4A v&3MDCR-T+8;3;1;A:Time Significant T Value = 10.579 &MDCR-FDv&/MDCR-T'8;4;1;AA Significant T Value = 13.645. &MDCR-F#-%#&MDCR-T8;502;0;Critical Value &MDCR-F ! Pareto Chart6" &MDCR-T6;0;0; &MDCR-F &MDCR-S-6"& &MDCR-T6;0;0; &MDCR-Fv6"v& &MDCR-T6;0;0; &MDCR-F#-6"" &MDCR-T7;502;0; &MDCR-F !Critical ValueKb# &MDCR-T7;502;0; &MDCR-F &MDCR-S--"0h" &MDCR-T7;0;0; &MDCR-F!Non-Significant;b# &MDCR-T7;0;0; &MDCR-F &MDCR-S-E"h"&MDCR-T 7;1001;0; &MDCR-F ! Significant;b#&MDCR-T 7;1001;0; &MDCR-F &MDCR-S ! User Name 6" &MDCR-T6;0;0; &MDCR-F &MDCR-S !CompanyS!6" &MDCR-T6;0;0; &MDCR-F &MDCR-S !8/5/2008Z"6" &MDCR-T6;0;0; &MDCR-F &MDCR-S ! 10:20:22 AM; #6" &MDCR-T6;0;0; &MDCR-F &MDCR-S#6"#& &MDCR-T6;0;0; &MDCR-F &MDCR-}I--"Systemn fn !- =X1Tahoma1Tahoma1Tahoma1Tahoma1Tahoma1 Tahoma"$"#,##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 x@@ x@ x  @ 8@ 8   (@ 0  < 8  @   @ 0       x@@ x@ x  @ 8@ 8 8 8@ 0 8  < 0@ 0 8 @ 0  <   2008-08-04 14:17:42   dMbP?_*+%&A Page &P&?'?(?)?"d??*Q}rF}F}F}F}F@@@    @@@@@@@@@@@@@@ @"@#@$@%@&@'@(@)@2008-08-04 14:17:42 Alpha: 0.1Transform: Y' = Y+7"All selected terms are alias free.+7"Terms selected to be in the model:Linear Effects A, B Interaction Effects AB Quadratic Effects AA, BB1 7(Independent terms included in the model: Linear Effects A, BInteraction Effects ABQuadratic EffectsAA, BB ANOVA TableSource of VariationDegrees of Freedom!Sum of Squares [Partial]Mean Squares [Partial]F RatioP ValueModel~@8gDi?<@ +@AfS@wo> A:Time~?vq @vq @ 0[@'s^)> B:Temperature~?HP@HP@8d>@H}M?   AB???lxz,C @ y)?  AA~?'1Z*@'1Z*@Fg@0=l>  BB~?a+@a+@;M X@R> Residual~@3?r?  Lack of Fit~@9#?x&1?9#J{?:pΈ? Pure Error~@A`"?A`"? !Total~"(@"X5;<@"""# $S =%/$?&PRESS =%48@$R-sq ='ݳr?& R-sq(pred) ='SKc? $ R-sq(adj) = 'ƽ ? &%"(Regression Information")))))* #+Term#, Coefficient#,Standard Error#,Low CI#,High CI#,T Value#-P Value$. Intercept$/\(S@$/X9v?$//nS@$/ T@$/K=@~$0%.A:Time%/ףp= ?%/?%/9#?%/ڬ\m?%/ r(%@%1's^)>&. B:Temperature&/?ܵ|?&/?&/ rh?&/|a2U0?&/)\@&0H}M? '2AB~'/?'//$?'/Mb`'/Mb?'/Ps?'3 y)? (.AA(/&S(/1*Թ?(/(/؁sF(/'†WJ+(10=l> )4BB)5&S)51*Թ?)52U0*)5()5B>٬#)6R>>dd  Reduced ModelDFoliopB  1234567           U   ;f?  L27 (3^13)       80170  ?  S@    90170 ? ? S@    80180 ? ?  @S@    90180 ?? ? S@    77.929175  - ? fffffR@    92.071175  -? ?  S@    85167.929  - ? @S@    85182.071  -? ? S@    85175  ? S@     85175  ? 33333T@     85175  ?  T@     85175  ?  S@     85175  ?  33333S@     YieldR@T@P.5??  Timeffffffhfffff?P.5   Temperatureffffffhfffff?P.5   Optimal Solution 1 kv"?5v? ;g^$ H T@H T@ H T@ ư>?   Optimal Solution 1 kv"?5v? ;g^$ H T@H T@ H T@ @@@@v@v@TahomaDBTahomaDB o_?k)3?{Gz?7A`?gj+?ZӼ?o_?Oz1?333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahoma|Z ' Folio Data SetContinuous FunctionContinuous FunctionContinuous FunctionFactor vs Responsed?' Folio Data SetA:Time vs YieldA:Time vs YieldContinuous FunctionFactor vs Responsed?' Folio Data SetB:Temperature vs YieldB:Temperature vs YieldContinuous FunctionFactor vs Responsed?Folio Data Set Factor Value Factor Value Factor Valued ?Folio Data SetResponse ValueResponse ValueResponse Valued ?  VU e@f@#tR@H T@?d Reduced Model(User Name Company 8/4/2008 2:17:50 PM#ReliaSoft DOE++ - www.ReliaSoft.comOptimal Solution 1  ColorColor = Size = X = Y =  Starts at:  Ends at:  Duration: ???*****#ReliaSoft DOE++ - www.ReliaSoft.comS@W@A:Time X = 86.8074e@f@B:Temperature X = 176.2863#tR@H T@Yield (Maximize) Y = 80.1861Z   ' Folio Data SetContinuous FunctionContinuous FunctionContinuous FunctionFactor vs Responsed?' 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GF4@@?d Pareto Chart)User Name Company 8/5/2008 10:20:15 AM#ReliaSoft DOE++ - www.ReliaSoft.comAlpha = 0.1; Threshold = 1.8595 Pareto ChartStandardized Effect (T Value)TermColor T Value = X = Y =  Starts at:  Ends at:  Duration: ???*****#ReliaSoft DOE++ - www.ReliaSoft.comZ @@@@v@v@TahomaDBTahomaDB o_?VF?{Gz?c]Kȵ?gj+?ͪժ?y):?ao?333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahoma|Z yxYieldSignificant EffectsYield(Effect Points)Significant Effects Yield Y' = Yd?YieldDistribution LineYield(Distribution Line)Distribution Line Yield Y' = Yd? 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P.5          I   A   B   AB   AA   BB  ?   1 aAa_MainProject PCentral Composite Design.docs-C:\DOCUME~1\MCAROL~1\LOCALS~1\Temp\RSF1FF.tmpࡱ> %` t"bjbj 4̟̟7c3::: D  PPP8QQl |dSS:VSVSVSVVVccccccc$Xfhh!d RXVVZV@RXRX!dPPVSVS6dZZZRXP2VS VScZRXcZZ]  !^VSS `P:Y]W_Ld0|d],@iY@i!^!^&@i G^VZV@Z4W4hWVVV!d!dZdVVV|dRXRXRXRX &\3 \3 PPPPPP Example Central composite design is the most commonly used response surface methodology (RSM) design. RSM design is usually used to study the quadratic effects of factors. A chemical engineer is interested in determining the operating conditions that maximize the yield of a process.* Two controllable variables influence process yield: reaction time and reaction temperature. NameUnitLevel -Level +Timemin8090TemperatureF170180 A central composite design with 5 center points and alpha = 1.414 is used to conduct the experiment. A full quadratic model is fitted to the data. Design the Experiment The design matrix and the data are given in the Central Composite Design 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 Response Surface Method Design then click Next.  Step 3: In the second step of the Design Wizard, select Central Composite 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 Response Properties button and, in the Response Properties window, enter the name of the response, as shown next, then click OK.  Step 7: Click Next to view the design summary, then click Finish to create the Standard Folio containing the central composite 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 Composite Design 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 Composite Design Folio to open it. The Design tab will be displayed. Step 2: Specify to include all effects (i.e. full quadratics) 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. ANOVA TableSource of VariationDegrees of FreedomSum of Squares [Partial]Mean Squares [Partial]F RatioP ValueModel528.24775.649579.83445.11E-06A:Time17.91987.9198111.91561.47E-05B:Temperature12.12322.123230.00260.0009AB10.250.253.53280.1022AA113.17613.176186.19142.67E-06BB16.97386.973898.54772.25E-05Residual70.49540.0708Lack of Fit30.28340.09451.78210.2896Pure Error40.2120.053Total1228.7431 From the ANOVA table, we can see that effects A, B, AA and BB are significant. This also can be seen in the pareto chart. Step 5: Click the Plot icon to add the Plot tab to the Folio. Step 6: Select Pareto Chart from the Plot Type drop-down in the Control Panel.  From these results, only effects A, B and AA and BB would be included in the reduced model. In fact, you also can include term AB in the model. From the ANOVA table and Pareto chart, we can see that AB is only slightly below the critical value. The inclusion or exclusion of AB is a personal decision that should be made based on the knowledge of the experiment and the statistical results. Here, we will include only A, B, AA and BB in the model. The results for the reduced model are given in the Reduced Model Folio. You can also reproduce the Folio by the following steps. Step 7: Right-click the Central Composite Design Folio in the Project Explorer and select Duplicate Item from the shortcut menu that appears. Rename the new Folio. Step 8: Click the Select Effects icon and click the Select Significant Effects button to select only the significant effects to calculate the new model, as shown next, then click OK.  Step 9: Click Calculate. The coefficients for the parameters in the reduced model are: Regression InformationTermCoefficientStandard ErrorLow CIHigh CIT ValueP ValueIntercept79.940.136579.686280.1938585.61330A:Time0.9950.10790.79431.19579.21971.55E-05B:Temperature0.51520.10790.31450.71584.77370.0014AA-1.37630.1157-1.5915-1.1611-11.8922.30E-06BB-1.00130.1157-1.2165-0.786-8.65162.47E-05 You can use this model as the final model to conduct optimization. Optimization Step 1: Click the Optimization icon in the Control Panel. Step 2: On the Response Settings page of the Optimization Settings window, use the settings shown next.  Step 3: On the Factor Settings page of the Optimization Settings window, set the range of each factor, as shown next. The ranges are the limits of each factor within which the optimal settings should fall.  Step 4: Click OK to close the window and plot the optimal solution, as shown next.  You also can use the contour and surface plot to visually identify the optimal settings for factors A and B. Step 5: Return to the Analysis tab of the Reduced Model Folio and click the Plot icon in the Control Panel. Step 6: In the Plot tab that is added to the Folio, click the Contour/Surface Plot icon in the Control Panel. The Contour/Surface Plot window will open, as shown next.  Step 7: Select Surface Plot from the Plot Type drop-down in the Control Panel.  Conclusions From the contour and surface plots, we can see that the maximum yield occurs at Time = 86.8 and Temperature = 176.3oF, which is the same as the result from the optimization. The predicted maximum yield is 80.1861. Keep in mind that it is necessary to conduct an experiment using this setting to confirm this conclusion. * Montgomery, D. C. 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