DOEexample_minitab

GeneratingFull-FactorialModelsinMinitabWewanttogenerateadesignfora23fullfactorialmodel.2x2x2=8runsClickondownarrowandselectnumberoffactors.Forthisexampleit’s3.Highlightdesireddesignfromlist.For3factors,therearetwooptions.Enter2replicates.GeneratingFull-FactorialModelsinMinitabAfterselectingthedesign,youcannamethefactors(X’s)anddefinetheirlowandhighvaluesClickonFactorsbuttonGeneratingFull-FactorialModelsinMinitabAfterenteringyourfactors,ClickontheOptionsbutton&De-Selectthe“Randomizeruns”Thenclick“OK”twice…WhatDoYouSeeNoticeMinitabgivesyouthevaluesyouneedtorunyourexperiment—not–1and+1.Sincewedidn’trandomizeandwemadeStartAnglefactorC,weonlyneedtochangestartangleonce.ItisrecommendedtoRANDOMIZEYOUREXPERIMENTNotes:1)Anewworksheetwillbecreatedforthedesign.2)TheMinitabdefaultistorandomizetherunorder.ForourDesignAnalyzingtheResultsoftheDOE:Step9Let’slookatsomegraphsAnalyzingtheResultsoftheDOE:Step9ClickonthedoublearrowbuttontotransferallavailabletermsintoselectedtermsMakesureyouhave“Distance”intheResponsesboxPerformthesestepsinbothsetup—MainEffects&InteractionsAnalyzingtheResultsoftheDOE:Step9ItlookslikeStartAngleandPinPositionhadabigeffectonourY--DistanceAnalyzingtheResultsoftheDOE:Step9Sincethelinesarenearlyparallel,thetwo-wayinteractionswillprobablybeinsignificantAnalyzingtheResultsoftheDOE:Step9GotoStatDOEAnalyzeFactorialDesignAnalyzingtheResultsoftheDOE:Step92.ClickonGraphs3.ThenParetowithAlpha=0.054.FinallyclickOk1.PutDistanceinResponses:3.Clickonthese3PlotsAnalyzingtheResultsoftheDOE:Step91.ThenclickonStorage2.SelectFits&Residuals3.ThenOkandOkAnalyzingtheResultsoftheDOE:Step9These3graphsgiveyouagoodideaaboutwhat’sgoingonAnalyzingtheResultsoftheDOE:Steps10&11Steps10&11:Plot&InterprettheResiduals•ResidualsarethedifferencebetweentheactualYvalueandtheYvaluepredictedbytheregressionequation.•Residualsshould»berandomlyandnormallydistributedaboutameanofzero»notcorrelatewiththepredictedY»notexhibittrendsovertime(ifdatachronological)•StatDOEAnalyzeFactorialDesign,Graphsbutton»Selectnormalplotofresidualsresidualsagainstfitsresidualsagainstorder•Anytrendsorpatternsintheresidualplotsindicatesinadequaciesintheregressionmodel,suchasmissingXsornonlinearrelationships.AnalyzingtheResultsoftheDOE:Steps10&11Let’slookateachgraphindividuallyAnalyzingtheResultsoftheDOE:Steps10&11ButfirstletsperformaNormalitytestonTheresidualsbygoingto:StatBasicStatisticsNormalityTestInvariable,selectRESI1ThenclickOkAnalyzingtheResultsoftheDOE:Steps10&11-3-2-10123-1.5-1.0-0.50.00.51.01.5NormalScoreResidualNormalProbabilityPlotoftheResiduals(responseisDistance)Average:0.0000000StDev:1.49443N:16Anderson-DarlingNormalityTestA-Squared:0.322P-Value:0.497-202.001.01.05.20.50.80.95.99.999ProbabilityRESI1NormalProbabilityPlotResidualsLooknormalP-value:0.497Ifresidualsarenotnormal,yourmodelmaynotpredictverywellAnalyzingtheResultsoftheDOE:Steps10&11246810121416-3-2-10123ObservationOrderResidualResidualsVersustheOrderoftheData(responseisDistance)NotrendsinthisgraphAnalyzingtheResultsoftheDOE:Steps10&11100110120130140150160170180190-3-2-10123FittedValueResidualResidualsVersustheFittedValues(responseisDistance)Thisgraphindicatestheremightbemorevariabilityinthesmallerdistances,butwithonlytworeps,we’llpresson!AnalyzingtheResultsoftheDOE:Step12ExaminetheFactorEffectsWe’llkeepAnythingwithAlowP-valueLowerthan0.05Sincewe’rekeepingthe3-wayinteraction,weneedtoincludestoppositioninthemodelAnalyzingtheResultsoftheDOE:Step12ExaminetheFactorEffectsGobackinStatDOEAnalyzeFactorialDesignandclickonTerms,thenremovethetwo-wayinteractionsPut2-wayinteractionsbackinAvailableTermsStep13:DevelopPredictionModelsCoefficientsfortheCodedmodelCoefficientsfortheUncodedmodelY=145.4–11.3A+0.7B+29.2C–1.31ABCY=-339.4–9.4A+2.9B+2.9CFortheCodedModelY=145.4–11.3A+0.7B+29.2C–1.31ABC145=145.4–11.3(PinPosition)+0.7(StopPosition)+29.2(StartAngle)–1.3(ABC)•Let’sjustarbitrarilysetA&BtosomevaluesincetheyarediscreteSetPinPositionto0(coded)whichequatesto2(actual:whatyousetinyourdesign)StopPositionat–1(coded)whichequatesto2(actual:whatyousetinyourdesign)•Let’sfigureoutStartAngle145=145.4–11.3(0)+0.7(-1)+29.2(StartAngle)–1.31(0*-1*C)145=145.4–0–0.7+29.2(StartAngle)-0145–145.4+0.7=29.2(StartAngle)0.3=29.2(StartAngle)0.01=StartAngleConvertingfromthecodedunits:160180-1+11700170.10.01FortheUn-codedModelY=-339.4–9.4A+2.9B+2.9C–0.0ABC145=-339.4–9.4(PinPosition)+2.9(StopPosition)+2.9(StartAngle)•Let’sjustarbitrarilysetA&BtosomevaluesincetheyarediscreteSetPinPositionto2StopPositionat2•Let’sfigureoutStartAngle145=-339.4–9.4(2)+2.9(2)+2.9(StartAngle)145=-339.4–18.8+5.8+2.9(StartAngle)497.4=2.9(StartAngle)497.4/2.9=(StartAngle)171.5=StartAngle