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P.5       Reduced ModelDFolio8  1234567 K           1425200 @?? ? @     1230250 @@@ ? @    1230200 @@? ? @    1030250 ?@@ ? ?    1230200 @@? ? @    1425200 @?? ? @    1430250 @@@ ? &@     1425250 @?@ ? @     1225250 @?@ ?  ?    1030250 ?@@ ?  ?    1225250 @?@ ?  @    1225200 @?? ?      1030200 ?@? ?      1230250 @@@ ? @    1025250 ??@ ?     1430200 @@? ? "@     1430250 @@@ ? $@    1025200 ??? ?      1025200 ??? ?     1030200 ?@? ?     1025250 ??@ ?     1430200 @@? ? @    1225200 @?? ? ?    1425250 @?@ ? @               @@@  101214 2530 200250    ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????   Carbonation % Operating Pressure Speed  Height Deviation   I        A        B        C        AB        AC        BC        ABC                          Block 1    1 @@@  101214 2530 200250   Carbonation % Operating Pressure Speed    101214 2530 200250  ==X1Tahoma1Tahoma1Tahoma1Tahoma1Tahoma"$"#,##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 p p   p@@ p@ p @  p8 @ p@ p p8 8 p@ p p   p8 8 Design   dMbP?_*+%&A Page &P&?'?(?)?"d??QHeight Deviation C:SpeedB:Operating PressureA:Carbonation % Block Number Run OrderStandard Order}F}'F}F}F}F}F     6"@??,@9@i@@"@64@@?(@>@@o@@4@6@@?(@>@i@@@60@@?$@>@@o@?0@63@@?(@>@i@@3@65@@?,@9@i@@5@6(@@?,@>@@o@&@(@6$@ @?,@9@@o@@$@6@"@?(@9@@o@?@6 @$@?$@>@@o@?@6 2@&@?(@9@@o@@2@6 @(@?(@9@i@@6 @*@?$@>@i@@6  @,@?(@>@@o@@ @6@.@?$@9@@o@@6&@0@?,@>@i@"@&@68@1@?,@>@@o@$@8@6*@2@?$@9@i@*@6?3@?$@9@i@?6.@4@?$@>@i@.@6,@5@?$@9@@o@,@67@6@?,@>@i@@7@61@7@?(@9@i@?1@66@ 8@ ?!,@!9@!@o@"@6@>dd  =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   @   8@ 8 0  < 8   @ 0  x@@$x@$x  @$ @   8@ 8 8 0@ 0  < 8 0 @ 0 0 x@@$x@$x  @$ Sheet1   dMbP?_*+%&A Page &P&?'?(?)?"d??I@}F} F} F}I F}& F@@@@@@@@@ @ @ @ @@@@@@@@@@@@@@" ANOVA Table#####$Source of VariationDegrees of Freedom!Sum of Squares [Partial]Mean Squares [Partial]F RatioP ValueModel~@䃞ͪVt@JY8K@  A:Carbonation %@o@_@( g@Lk(= B:Operating Pressure?F@F@1*4Q@wPƍ> C:Speed~?B>٬ 6@B>٬ 6@ŏ1@@eSP->  AB@@@ZB>@jM? Residual~ 1@ {/Lj&@ HP?   Lack of Fit~ @  0@ K=U?  h"lx? D?   Pure Error (@!@ 7d?  Total  7@ u@  !>5S = 0.8120 R-sq = 96.6704% R-sq(adj) = 95.4952%2Regression Information333334%&&&&&' (Term) Coefficient)Standard Error)Low CI)High CI)T Value*P Value%&&&&&'+ Intercept~, @,=yX5?,oŏ@,~:pN @, g2@-AWOk= +A[1]~, ,X?,6yX5˿,ioT.{?+B:Operating Pressure~,,=yX5?,"u, c,m4 -wPƍ>+C:Speed,7d,=yX5?,m{,q= ףp,T㥛 -eSP->+A[1]B~,?,X?,>yX5?,JY?,ioT@.{?/A[2]B~00X?0镲 0a+e?0^)1b48?>dd&  =8X1Tahoma1Tahoma1Tahoma1Tahoma1Tahoma"$"#,##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&  Soft Drink Bottling ExperimentDFolio8  1234567 K           1025200 ??? ?     1025250 ??@ ?     1030200 ?@? ?      1030250 ?@@ ?  ?    1225200 @?? ?      1225250 @?@ ?  ?    1230200 @@? ? @    1230250 @@@ ? @    1425200 @?? ? @     1425250 @?@ ? @     1430200 @@? ? 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Carbonation % Operating Pressure Speed  Height Deviation   I        A        B        C        AB        AC        BC        ABC                          Block 1    1 @@@  101214 2530 200250   Carbonation % Operating Pressure Speed    101214 2530 200250  =R&X1Tahoma1Tahoma1Tahoma1Tahoma1Tahoma"$"#,##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 p p   p@@ p@ p @  p8 @ p@ p p8 8 p@ p p   p8 8 Design   dMbP?_*+%&A Page &P&?'?(?)?"d??QHeight Deviation C:SpeedB:Operating PressureA:Carbonation % Block Number Run OrderStandard Order}F}'F}F}F}F}F     6?3@?$@9@i@?6@.@?$@9@@o@@6@*@?$@>@i@@6@$@?$@>@@o@?@6@(@?(@9@i@@6@"@?(@9@@o@?@6@@?(@>@i@@@6 @,@?(@>@@o@@ @6"@??,@9@i@@"@6 $@ @?,@9@@o@@$@6 &@0@?,@>@i@"@&@6 (@@?,@>@@o@&@(@6 *@2@?$@9@i@*@6 ,@5@?$@9@@o@,@6.@4@?$@>@i@.@60@@?$@>@@o@?0@61@7@?(@9@i@?1@62@&@?(@9@@o@@2@63@@?(@>@i@@3@64@@?(@>@@o@@4@65@@?,@9@i@@5@66@8@?,@9@@o@@6@67@6@?,@>@i@@7@68@ 1@ ?!,@!>@!@o@"$@8@>dd  ==X1Tahoma1Tahoma1Tahoma1Tahoma1Tahoma1 Tahoma"$"#,##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   @   8@ 8 0  <   @ 0  x@@ x@ x  @  @   8@ 8 8 0@ 0  < 8 0 0 @ 0 0 x@@ x@ x  @ 8 Sheet1   dMbP?_*+%&A Page &P&?'?(?)?"d??#I@}F} F} F}I F}& F@@@@@@@@@ @ @ @ @ @@@@@@@@@@@@@@@@@ @!@"@! ANOVA Table"""""#Source of VariationDegrees of Freedom!Sum of Squares [Partial]Mean Squares [Partial]F RatioP ValueModel&@t@1Z=@  A:Carbonation %@o@_@ŏ1w-Mf@0x`> B:Operating Pressure?F@F@O@aP@.d> C:Speed~?B>٬ 6@B>٬ 6@u?@5-C6?  AB@@@1殥 @56;Nё?  AC~ @ 7d? z6?  cZ? rh|?   BC~ ? &䃞ͪ? &䃞ͪ? +ݓ? ?   ABC~ @ |a2U? K=U?  h"lx? ^)?  Residual (@!@ 7d?   Pure Error (@!@ 7d? Total7@ u@ >5S = 0.8416 R-sq = 97.4749% R-sq(adj) = 95.1603%2Regression Information333334$%%%%%& 'Term( Coefficient(Standard Error(Low CI(High CI(T Value)P Value$%%%%%&* Intercept~+ @+Zڊ?+鷯@+HPs @+{02@,դ= *A[1]~+ +v?+Zd;+K7 +z6>-,P1> *A[2]~++v?+!rh+~jtȿ+Gz-HP?*B:Operating Pressure~++Zڊ?+.1+o_+e ,.d>*C:Speed+7d+Zڊ?+Zd;+Y+q -P--C6?*A[1]B~+?+v?+~jt?+!rh?+Gz@-HP?*A[2]B~++v?+B`"+ʡE?+X9v.Gr?*A[1]C+ ?+v?+47̿+JY?+q= ףp?.&1?*A[2]C+|гY+v?+Q|a޿+镲 ?+ʡEſ..n? *BC+ ?+Zڊ?+9EGr+X9v?+H}8g?.? *A[1]BC + ʿ +v? +JY +47? +q= ףp .&1?!/A[2]BC!0z6?!0v?!0a+e¿!0( 0?!0h|?5?!1†W2?">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&  aAa_MainProject 2!General Full Factorial Design.doc-C:\DOCUME~1\MCAROL~1\LOCALS~1\Temp\RSF7BE.tmpࡱ> #` -bjbjmm 4`3BBB L  >>>8?dd?T S@@:@@@BDBDBDSSSSSSS$UhWCS ECD@EECSXX@@XSrJrJrJEX2@ @SrJESrJrJQM  M@@ PP֪0z>GiMN4nS0SqM,~XTH~XMM~X M8BDZD@rJD4EBDBDBDCSCSJpBDBDBDSEEEE !$. $. XXXXXX Example General full factorial design is used when there are several factors (<5) that have multiple levels. If there are many multiple level factors, the size of a general full factorial design will be prohibitively large. In such cases, Taguchi OA design should be used. Consider that a soft drink bottler is interested in obtaining more uniform fill heights in the bottles.* The filling machine theoretically fills each bottle to the correct target height, but in practice, there is variation around this target, and the bottler would like to understand better the sources of this variability and eventually reduce it. There are 3 control factors. NameUnitLevel 1Level 2Level 3Percent carbonation101214Operating pressurepsi2530Line speedbpm200250 There are two replicates at each factor setting, making a total of 24 runs. The response is the average deviation from the target fill height observed in a production run of bottles. Positive deviations are fill heights above the target. Design the Experiment The design matrix and the data are given in the Soft Drink Bottling Experiment 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 General Full 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 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 general full 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 Soft Drink Bottling Experiment 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 Soft Drink Bottling Experiment Folio to open it. The Design tab will be displayed. Step 2: On the Options page of the Control Panel, select to use Individual Terms in the analysis. Step 3: 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 ValueModel11328.12529.8295A:Carbonation %2252.75126.375178.41181.19E-09B:Operating Pressure145.37545.37564.05883.74E-06C:Deviation122.041722.041731.11760.0001AB25.252.6253.70590.0558AC20.58330.29170.41180.6715BC11.04171.04171.47060.2486ABC21.08330.54170.76470.4869Residual128.50.7083Pure Error128.50.7083Total23336.625 From the ANOVA table shown above, we can see that effects A, B, C and AB are significant. The results for the reduced model are given in the Reduced Model Folio. You can also reproduce the Folio by the following steps. Step 4: Right-click the Soft Drink Bottling Experiment Folio in the Project Explorer and select Duplicate Item from the shortcut menu that appears. Rename the new Folio. Step 5: Click the Select Effects icon and select only the significant effects to calculate the new model, as shown next, then click OK.  Step 5: Click Calculate. Step 6: Click the Diagnostics icon on the Analysis tab Control Panel. The Diagnostics window is shown next.  In order to identify which factor settings can provide the smallest height deviation, you can copy these data to a Spreadsheet. In the example file, the data are shown in the Best Setting Spreadsheet, as shown next.  Conclusions From the Spreadsheet, it can be seen that run order 12 and 23 are the best setting which is A=12, B=25, C=200. Under this setting, the expected deviation is lowest. In general full factorial design, all factors are assumed to be qualitative factors, which means that the factors can only take the discrete values defined in the design, which in this case are: NameLevel 1Level 2Level 3Percent carbonation101214Operating pressure2530Line speed200250 If the factors can be treated as quantitative factors, meaning they can take any value within a range, further analysis using response surface methodology should be conducted to find the optimal settings for the manufacturing process. * Montgomery, D. Design and Analysis of Experiments, 5th edition, John Wiley & Sons, New York.      HYPERLINK "http://www.reliasoft.com/Weibull/weibull7.htm"  Page  PAGE 8 of  NUMPAGES 9 2008 ReliaSoft Corporation. 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