DSdsV2_2 Weibull_7:FzJ Ball SizeDExperimentResponse`P  . Ball Size A@B@C@D@@C@C@C@C@D@@B@C@D@@D@D@E@@D@D@D@A@B@D@D@C@@E@D@E@E@ ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? h/?h/?h/h/h/?h/?h/h/h/?h/?h/h/h/?h/?h/h/h/?h/?h/h/h/?i/h/?h/?h/i/h/?h/?h/h/?h/h/h/?h/?h/h/h/?i/h/?h/?h/i/h/?h/?h/h/?h/h/h/?h/?h/h/h/?i/h/?h/?h/i/h/?h/?h/h/?h/h/h/? qDZA@q1B@qqB@qqC@qqC@qC@q1C@qqC@q1D@qqB@sqC@qqC@sqD@qD@qqE@qqGD@qqD@qD@qqB@qqB@rqC@rqD@qq\D@qqE@qq\D@rqD@qqE@ 88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?88?C@c?qq? ?    I        A        B        C        D        AB        AC        AD        BC        BD        CD                 4@e @Model;3?UUUUUu[@ @~5&@A:Force).s??*6@ @0jL1@B:PowerfRJk?qDZO@ @\՘H@C:TimeMu٪?2@ @~5&? D:TemperatureQJg?@8? @R*g?ABv21А?qq? @?AC)Q?? @rv ?ADd`?pq?  @ResidualUUUUUU&@ @P.5 Lack of FitP.5UUUUUU&@   C@P.5SYMD@|~C@ Intercept=Dڊ?jA|3hb@ qqqq{u,%A[1]47?%ŲL?ʀ qq?qq?Bu?vG?A[2]0ɇ?%ŲL?_ZT{N? UUUUUUUUUUUUm]:/B[1]FR?%ŲL?CzW 98?98@HXn?\Ea?B[2]W)?%ŲL?2C@ qqqq(d5mſo C[1]?%ŲL?38& qq̿qqܿD?2C[2]rH?%ŲL?38& rqѿrq e?X"KD[1]v^̑?%ŲL?@ qq?qq??<[@D[2]fc ?%ŲL?38&? qq?qq?|?3FA[1]B[1]bf?Dڊ?v ? qq?qq?9o6?bNA[1]B[2]fOi?Dڊ?W\? qq?qq?rr?sA[2]B[1]F>?Dڊ?W\? qq?qq?9o6?bNA[2]B[2]fOi?Dڊ?W\? UUUUUU?UUUUUU?U6j?VA[1]C[1]]9?Dڊ?E_P? UUUUUUſUUUUUUտljWQ? A[1]C[2]7_?Dڊ?E_PԿ UUUUUUſUUUUUUտljWQ? A[2]C[1]7_?Dڊ?E_PԿ UUUUUU?UUUUUU?U6j?VA[2]C[2]]9?Dڊ?E_P? qqqq̿s?rrA[1]D[1]F>?Dڊ?V\˿ UUUUUU?UUUUUU?U6j?VA[1]D[2]]9?Dڊ?E_P? qq?qq?9o6?bNA[2]D[1]fOi?Dڊ?V\? UUUUUUտUUUUUUV?U6jA[2]D[2]]9?Dڊ?E_P                     C@qqqq?UUUUUU98?qqqq̿rqѿqq?qq?qq?qq?qq?UUUUUU?UUUUUUſUUUUUUſUUUUUU?qqUUUUUU?qq?UUUUUUտ   ?????????????????????????????????????????????????????????????????????????     P.5       Ball SizeDExperimentResponse@0  . Ball Size A@B@C@D@@C@C@C@C@D@@B@C@D@@D@D@E@@D@D@D@A@B@D@D@C@@E@D@E@E@ ????????????????????????????????????????????????????????????????????????????????? h/?h/?h/h/h/?h/?h/h/h/?h/?h/h/h/? VUUUUA@A@UUUUUB@q1C@rqC@q1D@88C@88C@88D@VUUUUB@B@UUUUUC@q1D@rqD@q1E@88D@88D@88E@B@VUUUUB@C@qqD@qqD@qqE@98#D@8xD@88#E@ { %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?{ %?C@yO?-؂-? ?    I        A        B        C        D        AB        AC        AD        BC        BD        CD                 @[ִ4@Model=#};ǁ>88Z@ @ـl*@A:Force0,?*6@ @ B@B:PowerqQP>qDZO@ @ـl@&@C:TimeG&CB?2@  4@Residualrq0@ 4@P.5 Lack of FitP.5rq0@   C@P.5C@b0C@ Interceptx?@_l@ qqqq:N!p6RA[1]@je ?MO^?̂ qq?qq??MO^?D6ˏ-@ UUUUUUUUUUUU`+zbB[1]`>MO^?h+b! 98?98@7.S?1=?B[2]u:?MO^?.w@ qqqq}_ݿ:C[1]I_?MO^?B\؆ qq̿qqܿFY? űyC[2]hͰ?MO^?B\؆                     C@qqqq?UUUUUU98?qqqq̿  ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????     P.5       Reduced ModelDFolio08  1234567 K     L27 (3^13)      54015155 ???? ? A@    54020160 ??@@ ?  B@    54025165 ??@@ ?  C@    55015160 ?@?@ ? D@    55020165 ?@@@ ? @C@    55025155 ?@@? ? C@    56015165 ?@?@ ? C@    56020155 ?@@? ? C@    56025160 ?@@@ ? D@     104015155 @??? ? @B@     104020160 @?@@ ? C@     104025165 @?@@ ? D@     105015160 @@?@ ? @D@     105020165 @@@@ ? D@    105025155 @@@? ?  E@    106015165 @@?@ ? @D@    106020155 @@@? ? D@    106025160 @@@@ ? D@    154015155 @??? ? A@    154020160 @?@@ ? B@    154025165 @?@@ ?  D@    155015160 @@?@ ? D@    155020165 @@@@ ? C@    155025155 @@@? ?  @E@    156015165 @@?@ ? D@    156020155 @@@? ? E@    156025160 @@@@ ? 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B:Power~@ yDZO@W2ı?@y&1B@[z> C:Time~@B>٬2@{/L"@qh@&@a2U0*C?Residual~4@,Ԛ0@*D?   Lack of Fit~ 4@ ,Ԛ0@ *D?  Total  :@ @^@  !> 5S = 0.9159 R-sq = 86.1341% R-sq(adj) = 81.9743%2Regression Information333334%&&&&&' (Term) Coefficient)Standard Error)Low CI)High CI)T Value*P Value%&&&&&'+ Intercept~,C@,Tt$?, +C@,xC@,jMl@~- +A[1],Biq,EGr?,46 +B[2],ZӼ?,EGr?,MJ?,S㥛?,Ǻ@--C6:? +C[1],Biq,EGr?,o_,K7A`ݿ,I&† -ŏ1w-!_? /C[2]0镲 q̿0EGr?0;pΈ0?0I +1#?>dd&  =8X1Tahoma1Tahoma1Tahoma1Tahoma1Tahoma"$"#,##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&    GF???d Upper Legend Lower LegendCurrent Upper TitleCurrent Lower TitleCurrent Main TitleCurrent X-Axis TitleCurrent Y-Axis TitleColorColor = Size = X = Y =  Starts at:  Ends at:  Duration: ???*****Z @@@@v@v@TahomaDBTahomaDB ????{Gz?{Gz?{Gz??333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahoma|Z    ????{Gz?{Gz?{Gz??333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomatTahoma|Z  @@@@v@v@TahomaDBTahomaDB    Taguchi OA L27(3^13)DFolioP8  1234567 K     L27 (3^13)      54015155 ???? ? A@    54020160 ??@@ ?  B@    54025165 ??@@ ?  C@    55015160 ?@?@ ? D@    55020165 ?@@@ ? @C@    55025155 ?@@? ? C@    56015165 ?@?@ ? C@    56020155 ?@@? ? C@    56025160 ?@@@ ? D@     104015155 @??? ? @B@     104020160 @?@@ ? C@     104025165 @?@@ ? D@     105015160 @@?@ ? @D@     105020165 @@@@ ? D@    105025155 @@@? ?  E@    106015165 @@?@ ? @D@    106020155 @@@? ? D@    106025160 @@@@ ? D@    154015155 @??? ? A@    154020160 @?@@ ? B@    154025165 @?@@ ?  D@    155015160 @@?@ ? D@    155020165 @@@@ ? C@    155025155 @@@? ?  @E@    156015165 @@?@ ? D@    156020155 @@@? ? E@    156025160 @@@@ ? E@   ư>?      @@@@v@v@TahomaDBTahomaDB ????{Gz?{Gz?{Gz??333333?TahomaTahoma|Tahoma|TahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahomaDBTahoma|Z   GF ???d Upper Legend Lower LegendCurrent Upper TitleCurrent Lower TitleCurrent Main TitleCurrent X-Axis TitleCurrent Y-Axis TitleColorColor = Size = X = Y =  Starts at:  Ends at:  Duration: ???*****Z            51015 405060 152025 155160165 !???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????  Force Power Time  Temperature   Ball Size`   I        A        B        C        D        AB        AC        AD        BC        BD        CD                           Block 1      L27 (3^13)1     51015 405060 123 123 152025 123 123 155160165 123 123 123 123 123   Force Power C D Time F G  Temperature J K L M N    51015 405060 152025 155160165  =2%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 @  p @ p@ p p  p@ p p   p  Design   dMbP?_*+%&A Page &P&?'?(?)?"d?? Q Ball Size D:Temperature C:Time B:Power A:Force Block Number Run OrderStandard Order}F}F}GF}F                           <?@?????A@?<@&@???@@B@@<@*@???@@C@@<@@??@?@D@@<@???@@@@C@@<@ @??@@?C@@<@1@??@?@C@@< @@??@@?C@ @<"@6@??@@@D@"@< $@7@?@???@B@$@< &@2@?@?@@C@&@< (@;@?@?@@D@(@< *@5@?@@?@@D@*@< ,@.@?@@@@D@,@<.@(@?@@@?E@.@<0@9@?@@?@@D@0@<1@:@?@@@?D@1@<2@@?@@@@D@2@<3@8@?@???A@3@<4@@?@?@@B@4@<5@$@?@?@@D@5@<6@@?@@?@D@6@<7@,@?@@@@C@7@<8@"@?@@@?@E@8@<9@3@?@@?@D@9@<:@4@?@@@?E@:@<;@ 0@ ?!@!@!@!@"E@;@>dd ` =T$g 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 0 x@@ x@ x  @ Sheet1   dMbP?_*+%&A Page &P&?'?(?)?"d??,I@}F}n F}& F@@@@@@@@@ @ @ @ @ @@@@@@@@@@@@@@@@@ @!@"@#@$@%@&@'@(@)@*@+@! 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Example Taguchi orthogonal array (OA) designs are often used in design experiments with multiple level factors. Taguchi OA can be thought of as a general fractional factorial design. Consider an experiment to study the effect of four 3-level factors on a fine gold wire bonding process in an IC chip-package.* Taguchi OA L27 (3^13) is applied to identify the critical parameters in the wire bonding process. The response is the ball size. The smaller the ball size, the better the process. For this example, the 4 factors are: FactorNameLevel 1Level 2Level 3AForce51015BPower405060ETime152025HTemperature155160165 These four factors are assigned to columns 1, 2, 5 and 8 in L27. The remaining columns either represent the interaction effects of these factors or are treated as dummy factors. For example, columns 3 and 4 are the interaction of AB. Columns 6 and 7 are the interaction of AE. Columns 9 and 10 represent the effect of AH. Those columns can be deleted from the design matrix and will not affect the analysis results. More detailed discussion on the properties of Taguchi arrays can be found in the appendix of Taguchis handbook. ** Design the Experiment The design matrix and the data are given in the Taguchi OA L27(3^13) 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 Taguchi OA 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 Taguchi OA 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. Step 8: Delete all unused factor columns, keeping only Force, Power, Time and Temperature in the design matrix. To do this, right-click in each unwanted factor column and select Delete then Selected Factor from the shortcut menu that appears. Once all unused colums have been deleted, Time becomes factor C and Temperature becomes factor D. Analysis and Results The design and the data are provided in the Taguchi OA L27(3^13) 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 Taguchi OA L27(3^13) Folio to open it. The Design tab will be displayed. Step 2: 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 ValueModel20109.83335.4917A:Force222.166711.08335.95520.0376B:Power263.388931.694417.02990.0034C:Time218.66679.33335.01490.0524D:Temperature21.05560.52780.28360.7626AB41.94440.48610.26120.8927AC41.50.3750.20150.9286AD41.11110.27780.14930.9566Residual611.16671.8611Lack of Fit611.16671.8611Total26121 From the ANOVA table, we can see that effects A, B and C 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 5: Right-click the Taguchi OA L27(3^13) Folio in the Project Explorer and select Duplicate Item from the shortcut menu that appears. Rename the new Folio. Step 6: Click the Select Effects icon and select only the significant effects to calculate the new model, as shown next, then click OK.  Step 7: Click Calculate. Step 8: Click the Diagnostics icon on the Analysis tab Control Panel. The Diagnostics window is shown next.  The Fitted Value column is the expected ball size for the factor settings under different runs. Conclusions From the Fitted Value column, it can be seen that run order 4 (standard order 1) gives the best result. The predicted ball size is 35.1667. The settings are Force=5, Power=40 and Time=15. In Taguchi OA 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 3Force51015Power405060Time152025 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. * T. Hou, S. Chen, T. Lin and K. Huang, An integrated system for setting the optimal parameters in IC chip-package wire bonding process, Int. J Adv Manuf Technology, 2006, 30, 247-253. ** G. Taguchi, S. Chowdhury and Y. Wu, Taguchis Quality Handbook, Hoboken, New Jersey, Wiley, 2004.      HYPERLINK "http://www.reliasoft.com/Weibull/weibull7.htm"  Page  PAGE 8 of  NUMPAGES 8 2008 ReliaSoft Corporation. ALL RIGHTS RESERVED  !2q{6 7 8 9   ! 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