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Pareto ChartI &MDCR-T3;0;0; &MDCR-F &MDCR-S  \"Tahoma ww 0wfi-!.Std = 0.1589; Alpha = 0.05; Threshold = 1.9600F&2 &MDCR-T3;0;0; &MDCR-F &MDCR-S-R&R&' &MDCR-T2;0;0; &MDCR-F >"Tahoma ww 0wfi-!Standardized Effect (Z Value)%h &MDCR-T3;0;0; &MDCR-F &MDCR-S>"Tahoma ww 0wfi-!TermU &MDCR-T3;0;0; &MDCR-F &MDCR-S# &MDCR-T4;0;0; &MDCR-F\"Tahoma ww 0wfi- !0.000R#W &MDCR-T5;0;0; &MDCR-F &MDCR-S#n!n! &MDCR-T4;0;0; &MDCR-F !5.000R# &MDCR-T5;0;0; &MDCR-F &MDCR-S-#66 &MDCR-T4;0;0; &MDCR-F#nn &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F-#  &MDCR-T4;0;0; &MDCR-F !1.000R#m &MDCR-T5;0;0; &MDCR-F &MDCR-S-#L L &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-#cc &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F#   &MDCR-T4;0;0; &MDCR-F-#AA &MDCR-T4;0;0; &MDCR-F !3.000R# &MDCR-T5;0;0; &MDCR-F &MDCR-S-#yy &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F# &MDCR-T4;0;0; &MDCR-F#   &MDCR-T4;0;0; &MDCR-F-#WW &MDCR-T4;0;0; &MDCR-F !4.000R# &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#6 6 &MDCR-T4;0;0; &MDCR-F !1.960R#E &MDCR-T5;0;0; &MDCR-F &MDCR-S-##n! &MDCR-T4;0;0; &MDCR-Fn! &MDCR-T4;0;0; &MDCR-F-  1 &MDCR-T4;0;0; &MDCR-F!AB 1 &MDCR-T11;0;0; &MDCR-F &MDCR-Suu1 &MDCR-T4;0;0; &MDCR-F!C:CD &MDCR-T11;1;0; &MDCR-F &MDCR-S1 &MDCR-T4;0;0; &MDCR-F!A:AD &MDCR-T11;2;0; &MDCR-F &MDCR-Sjj1 &MDCR-T4;0;0; &MDCR-F!E:ED  &MDCR-T11;3;0; &MDCR-F &MDCR-S  1 &MDCR-T4;0;0; &MDCR-F!B:BD  &MDCR-T11;4;0; &MDCR-F &MDCR-S__1 &MDCR-T4;0;0; &MDCR-F!D:DD &MDCR-T11;5;0; &MDCR-F &MDCR-S--\"&2MDCR-T*8;0;1;AB Non-Significant Z Value = 0.788 &MDCR-F &3MDCR-T+8;1;1;C:C Non-Significant Z Value = 0.828 &MDCR-FQ~&3MDCR-T+8;2;1;A:A Non-Significant Z Value = 1.888 &MDCR-F-&/MDCR-T'8;3;1;E:E Significant Z Value = 2.439. &MDCR-FF O &/MDCR-T'8;4;1;B:B Significant Z Value = 3.337. &MDCR-F&/MDCR-T'8;5;1;D:D Significant Z Value = 4.392. &MDCR-F#-%#&MDCR-T8;502;0;Critical Value &MDCR-F ! 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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 ! 10:18:05 AM; #6" &MDCR-T6;0;0; &MDCR-F &MDCR-S#6"#& &MDCR-T6;0;0; &MDCR-F &MDCR-}K--"Systemifi !-  =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@ 0 8 0 @ 0   x@@ x@ x  @ 8@ 8 8 0@ 0 0 8@ 8  < 0 @ 0 0   2008-08-04 12:43:48   dMbP?_*+%&A Page &P&?'?(?)?"d??$Q@}F}& F} F}F}% F}& F@@   @@@@@@@@@@@@@@@@ @!@"@#@2008-08-04 12:43:48 Alpha: 0.05+3"All selected terms are alias free.+3"Terms selected to be in the model: Main Effects A, B, C, D, E2-Way Interaction AB1 3(Independent terms included in the model:  Main Effects  A, B, C, D, E 2-Way Interaction AB Distribution: Lognormal$Likelihood Ratio Test TableModelEffectDegrees of FreedomLn(Likelihood Value)Likelihood RatioP Value Reduced A:A~?<,Ԛ3ǘ @Qkw?  B:B~?) 0y6iq"@_vOf?  C:C~?$~K29#J{?+ h?  D:D~?3ı.n8m4+@-C6*?  E:E~?_vO~4gDioE@HP?  AB~?jMC2V}b?ףp= ?   Full!~! @!R!1!!"#$MLE Information%%%%%%& 'Term(Effect( Coefficient(Standard Error(Low CI(High CI(Z Value)P Value *Std++ͪV?+(\¥?+Mb?+v/? +,- Intercept++9#J{@+.!u?+S:@+/n@+58EGF@~. *A:A+<,Ԛ?+<,Ԛ?+??+;Onr+X9v?+-C6?,h|?5? -B:B+Ӽٿ+nɿ+?W[?+PkwԿ+/L F+V- .-C6J? *C:C +&1 +&1 + ? +Xƿ +Biޱ? +]m{ ,%u? !-D:D!+_v!+ŏ1wѿ!+z):˯?!+Bٿ!+z6>Wÿ!+J4!/È> "-E:E"+ q?"+ q?"+Ǻ?"+Q?"+`TR'?"+鷯@".%u? #0AB#1(\#1HP#1??#1(\ſ#1(\?#1D9#2Zd;O?>dd' TimeDExperimentResponse  6Time   @?@@@@@@ @?@@@@@@ @?????????????????????????@????????@????????@????????@????????@???????? /m]?CÜG?G茓 ?Q#Q4d$~Sgh2dϯ?eG2 m ?m ? ʠ?f?E:EjXA"?8?ȃ@ )r)r3JM?~ſAB yߊ?7d}?i9                    /m]?CÜG?G茓 ?Q#Q4d$~S 463qe%` `bjbj"x"x 4T@@3HHH R  2228&33T D 4:D4:~4~4~4777CCCCCCC$ FhtHC 8~77@88C^^~4~4C;;;8^2~4 ~4C;8C;;>  ?~43 o2Z:>@C0D>,H;H??&H C?7"7;78777CC;d777D8888 'd ' ^^^^^^ Example Consider an experiment to improve the reliability of fluorescent lights.* The purpose was to find the best factor setting to improve the life time. Five two-level factors denoted by A-E were studied using a  EMBED Equation.3  design with the factor generator D = AC and E = BC. In addition to the main effects, the experimenter also thought that the AB (= DE) interaction might be important. Each treatment had two replicates (i.e. two lights were tested) and the experiment was conducted over 20 days with inspections every two days (the failure times were short because the lights were subjected to an accelerating factor that stressed the lights at higher than normal conditions). If a light had not failed by the 20th day, its failure time was recorded as right censored at 20. Design the Experiment The design matrix and the data are given in the Fluorescent Light Life Test 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 Reliability DOE then click Next.  Step 3: In the second step of the Design Wizard, select 2 Level Fractional Factorial Reliability Design then click Next.  Step 4: In the third step of the Design Wizard, use the settings shown next.  Step 5: Click the Fraction Generator button and, in the Fraction Generator window, set the generators to be D = AC and E = BC, as shown next, then click OK.  Step 6: Click Next to view the design summary, then click Finish to create the Standard Folio containing the two level fractional factorial reliability 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 Fluorescent Light Life Test 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 Fluorescent Light Life Test Folio to open it. The Design tab will be displayed. Step 2: On the Options page of the Control Panel, change the risk level (alpha) to 0.05 and select to use Individual Terms. Step 3: Return to the Main page of the Control Panel and click the Select Effects icon. In the Effects window, use the settings shown next then click OK.  Step 4: Select the Lognormal distribution on the Control Panel and click the Calculate icon. The Likelihood Ratio Test table and the MLE Information table for the model are provided on the Analysis tab, which is added to the Folio upon calculation. The model coefficients are: MLE InformationTermEffectCoefficientStandard ErrorLow CIHigh CIZ ValueP ValueStd0.15890.04250.0940.2685Intercept2.93920.06432.81313.065345.70530A:A0.23360.11680.0618-0.00450.2381.88840.059B:B-0.4029-0.20150.0604-0.3198-0.0831-3.3370.0008C:C-0.102-0.0510.0616-0.17190.0698-0.82760.4079D:D-0.5457-0.27290.0621-0.3947-0.1511-4.39181.12E-05E:E0.30540.15270.06260.030.27542.43930.0147AB-0.0975-0.04880.0618-0.170.0725-0.78830.4305 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. The pareto chart shows that effects B, D and E are significant.  Conclusion From the MLE Information table, we can see the model for the ln-mean or the scale parameter EMBED Equation.3 in the lognormal distribution is:  EMBED Equation.3  We can determine that in order to improve the reliability, factors B, C and D should be set to their low (-1) level, indicated by their negative coefficients, while A and E should be at their high (+1) level, indicated by their positive coefficients. This setting is also good for the AB interaction term. Under this setting, the predicted scale parameter in lognormal distribution is 3.7829. Therefore, the life distribution under this factor setting is a lognormal distribution with standard deviation of 0.1589 and ln-mean of 3.7829. To do more advanced analysis, you can enter the data into ReliaSofts ALTA for accelerated life data analysis to further investigate the life stress relationship. Since factors A and C are not shown to be significant, they can be removed in further analysis. * Wu, Jeff and Hamada, Michael, Experiments: Planning, Analysis, And Parameter Design Optimization, John Wiley & Sons, New York, 2000.      HYPERLINK "http://www.reliasoft.com/Weibull/weibull7.htm"  Page  PAGE 4 of  NUMPAGES 5 2008 ReliaSoft Corporation. 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