DSdsV2_2 Weibull_72s܏3 Levels One FactorDFolio08  1234567 K          Type A ? ? FF@    Type B @ ? Fh@    Type C @ ? F`@    Type A ? ? Fd@    Type B @ ? Fl@    Type C @ ? Fpw@    Type A ? ? F`l@    Type B @ ? Fs@    Type C @ ?   F}@    Type A ? ?  Fl@    Type B @ ?  F{@    Type C @ ?  S@@    Type A ? ?  F`r@    Type B @ ? S@@    Type C @ ? S@@    Type A ? ? F s@    Type B @ ? S@@    Type C @ ? S@@    Type A ? ? Fw@    Type B @ ?  S@@    Type C @ ?  S@@    Type A ? ? Fy@    Type B @ ?  S@@    Type C @ ? S@@    Type A ? ? S@@    Type B @ ? S@@    Type C @ ? S@@    Type A ? ? S@@    Type B @ ?  S@@    Type C @ ? S@@             @  Type AType BType C    Materials  Time@   I        A                 ?@@ @?@@?@@?@@?@@?@@?@@?@@?@@?@@?@@????????????????????      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Bounds @ 90%" &MDCR-T7;27;0; &MDCR-F &MDCR-S ! User's Name; ! &MDCR-T6;0;0; &MDCR-F &MDCR-S !CompanyS!! &MDCR-T6;0;0; &MDCR-F &MDCR-S !3/9/2008Z"! &MDCR-T6;0;0; &MDCR-F &MDCR-S ! 7:44:04 AM #! &MDCR-T6;0;0; &MDCR-F &MDCR-S-#!#& &MDCR-T6;0;0; &MDCR-F &MDCR-}J--"Systeme fe !-TimeDExperimentResponse@0  .Time  @?@@?@@?@@?@@?@@?@@?@@?@@?@@?@@????????????????????    ?    I        A         @@z8y@ zh?VDB:\ @P.5P.5t][ =e?B'7@|Z@WYb2:?Beta+;>sfNW}?4h>@  X@ @P.58Ǘ8@yL@ InterceptLϓ?TB@ "հ#S߿"հ#Sݠ_ΈĿ묱A[1] E?DbM?GKHh J.?J.?H;E?ZnP̿A[2]f,?j>?,p@?    !W`2UType A - Type BVK?=UJE uwrst%` )bjbjٕ .rP3  H/H/H/8/4/ .E00:111Z4Z4Z4DDDDDDD$&GhID Z444@Z4Z4D11D<<<Z421 1D<Z4D<<?  ?10 ]H/B8?1@|D0.E?,J8J?J ?DZ4Z4<Z4Z4Z4Z4Z4DDX<jZ4Z4Z4.EZ4Z4Z4Z4 !- -  Example One factor reliability DOE can be used in design comparison and factor effect identification. Suppose that there are three different materials that can be used in a product. The engineer wants to know if there is a difference between these three choices and, if there is a difference, which material is the best choice in terms of the product life. Ten samples were tested for each material. The test was stopped at 500 hours. Design the Experiment The design matrix and the data are given in the 3 Levels One Factor 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 One Factor Reliability 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 Next to view the design summary, then click Finish to create the Standard Folio containing the one factor 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 3 Levels One Factor 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 3 Levels One Factor Folio to open it. The Design tab will be displayed. Step 2: Select the Weibull distribution on the Control Panel. Step 3: Click the Calculate icon. Several tables of results are provided on the Analysis tab, which is added to the Folio upon calculation. The first one is the Likelihood Ratio Test Table, which is shown next. Likelihood Ratio Test TableModelDegrees of FreedomLn(Likelihood Value)Likelihood RatioP ValueReduced2-112.90746.88130.032Full4-109.4667 This table provides the test for the overall effect of the factor. A small P value indicates that the factor (treatment) has a significant effect on the response. The second table is the MLE Information table, as shown next. MLE InformationTermEffectCoefficientStandard ErrorLow CIHigh CIZ ValueP ValueBeta1.85170.42951.26422.7121Intercept6.42190.17056.14156.702437.67450A[1]-0.997-0.49850.2055-0.8366-0.1604-2.42590.0153A[2]0.27660.13830.2185-0.22120.49780.63290.5268 This table gives the value of the estimated parameters in the model. A small P value indicates that the parameter is significantly different from 0. The third table, the Life Characteristic Summary table, displays the fitted life characteristic. For the Weibull distribution, the life characteristic is eta, the scale parameter, as shown next. Life Characteristic SummaryFactor LevelNumber in LevelEtaStandard Deviation of EtaLow CIHigh CIType AF=8/S=2373.691471.3904272.906511.6974Type BF=4/S=6706.4274203.4664439.81931134.647Type CF=3/S=7881.9385301.5749502.47691547.963 The last table, the Life Comparisons table, shows paired comparisons of the life at each level, as shown next. Life ComparisonsContrastLn(Eta) DifferencePooled Standard ErrorLow CIHigh CIZ ValueP ValueType A - Type B-0.63680.3474-1.2084-0.0652-1.83290.0668Type A - Type C-0.85870.3939-1.5068-0.2106-2.17980.0293Type B - Type C-0.22190.4144-0.90370.4599-0.53540.5923 Step 4: Click the Plot icon to add the Plot tab to the Folio. Step 5: Select Response vs. Level from the Plot Type drop-down in the Control Panel. The Response vs. Level plot is shown next.  From this plot, it is difficult to tell which material is the best. Step 6: Select Life Characteristic from the Plot Type drop-down in the Control Panel. The life characteristic plot is shown next.  You can see that material type C has the largest eta value, which means it has the longest expected life. Conclusions From the Likelihood Ratio Test Table, we can see that there is a significant difference between the three types of material. Most notably, from the paired comparison, we see that there are significant differences between A and B and between A and C. The difference between B and C is not particularly significant.      HYPERLINK "http://www.reliasoft.com/Weibull/weibull7.htm"  Page  PAGE 6 of  NUMPAGES 6 2008 ReliaSoft Corporation. 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