design-expert软件响应面分析的官方教程之多因素分析

DX7-04C-MultifactorRSM-P1.docRev.4/12/06Design-Expert7User’sGuideMultifactorRSMTutorial–Part1•1MultifactorRSMTutorial(Part1–TheBasics)ResponseSurfaceDesignandAnalysisThistutorialshowstheuseofDesign-Expert®softwareforresponsesurfacemethodology(RSM).Thisclassofdesignsisaimedatprocessoptimization.Acasestudyprovidesareal-lifefeeltotheexercise.Duetothespecificnatureofthecasestudy,anumberoffeaturesthatcouldbehelpfultoyouforRSMwillnotbeexercisedinthistutorial.ManyofthesefeaturesareusedintheGeneralOneFactor,RSMOneFactororTwo-LevelFactorialtutorials.Ifyouhavenotcompletedallofthesetutorials,considerdoingsobeforestartinginonthisone.WewillpresumethatyoucanhandlethestatisticalaspectsofRSM.Foragoodprimeronthesubject,seeRSMSimplified(AndersonandWhitcomb,Productivity,Inc.,NewYork).YouwillfindoverviewsonRSMandhowit’sdoneviaDesign-Expertintheon-lineHelpsystem.TogainaworkingknowledgeofRSM,werecommendyouattendourResponseSurfaceMethodsforProcessOptimizationworkshop.CallStat-Easeorvisitourwebsite,“y”,are:•y1-Conversion(%ofreactantsconvertedtoproduct)•y2-Activity.Theexperimenterchosethreeprocessfactorstostudy.Theirnamesandlevelscanbeseeninthefollowingtable.FactorUnitsLowLevel(-1)HighLevel(+1)A–Timeminutes4050B-TemperaturedegreesC8090C-Catalystpercent23FactorsforresponsesurfacestudyYouwillstudythechemicalprocesswithastandardRSMdesigncalledacentralcompositedesign(CCD).It’swellsuitedforfittingaquadraticsurface,whichusuallyworkswellforprocessoptimization.Thethree-factorlayoutfortheCCDispicturedbelow.Itiscomposedofacorefactorialthatformsacubewithsidesthataretwocodedunitsinlength(from-1to+1asnotedinthetableabove).Thestarsrepresentaxialpoints.Howfaroutfromthecubetheseshouldgoisamatterformuchdiscussionbetweenstatisticians?Theydesignatethisdistance“alpha”–measuredintermsofcodedfactorlevels.AsyouwillseeDesign-Expertoffersavarietyofoptionsforalpha.2•MultifactorRSMTutorial–Part1Design-Expert7User’sGuideCentralCompositeDesignforthreefactorsAssumethattheexperimentswillbeconductedoveratwo-dayperiod,intwoblocks:1.Twelveruns:composedofeightfactorialpoints,plusfourcenterpoints.2.Eightruns:composedofsixaxial(star)points,plustwomorecenterpoints.DesigntheExperimentStarttheprogrambyfindinganddoubleclickingtheDesign-Expertsoftwareicon.Takethequickestroutetoinitiatinganewdesignbyclickingtheblank-sheeticonontheleftofthetoolbar.TheotherrouteisviaFile,NewDesign(orassociatedAltkeys).MainmenuandtoolbarClickontheResponseSurfacefoldertabtoshowthedesignsavailableforRSM.ResponsesurfacedesigntabThedefaultselectionistheCentralCompositedesign,whichwillbeusedforthiscasestudy.ClickonthedownarrowintheNumericFactorsentryboxandSelect3.Ignoretheoptionofincludingcategoricfactorsinyourdesigns(leaveatdefaultof0).DX7-04C-MultifactorRSM-P1.docRev.4/12/06Design-Expert7User’sGuideMultifactorRSMTutorial–Part1•3ToseealternativeRSMdesignsforthreefactors,clickonthechoicesforBox-Behnken(17runs)andMiscellaneousdesigns,whereyoufindthe3-LevelFactorialoption(32runs,including5centerpoints).Nowgobackandre-selecttheCentralCompositedesign.Beforeenteringthefactorsandranges,clicktheOptionsatthebottomoftheCCDscreen.NoticethatitdefaultstoaRotatabledesignwiththeaxial(star)pointssetat1.68719codedunitsfromthecenter–aconventionalchoicefortheCCD.ForCenterpointsincreasethenumbertothenormaldefaultof6andpresstheTabkey.DefaultCCDoptionforalphasetsodesignwillberotatableManyoftheoptionsarestatisticalinnature,butonethatproduceslessextremefactorrangesisthe“Practical”valueforalpha.Thisiscomputedbytakingthefourthrootofthenumberoffactors(inthiscase3¼or1.31607).SeeRSMSimplifiedChapter8“EverythingYouShouldKnowAboutCCDs(butdarenotask!)”fordetailsonthispracticalversusotherlevelssuggestedforalphainCCDs–themostpopularofwhichmaybethe“FaceCentered”(alphaequalone).PressOKtoaccepttherotatablevalue.Usingtheinformationprovidedinthetableonpage1ofthistutorial(oronthescreencapturebelow),typeinthedetailsforfactorName(A,B,C),Unitsandlevelsforlow(-1)andhigh(+1),bytabbingorclickingtoeachcellandenteringthedetailsgivenintheintroductiontothiscasestudy.Completedfactorform4•MultifactorRSMTutorial–Part1Design-Expert7User’sGuideYou’venowspecifiedthecubicalportionoftheCCD.Asyoudidthis,Design-Expertcalculatedthecodeddistance“alpha”forplacementonthestarpointsinthecentralcompositedesign.Alternatively,byclickinganoptionfurtherdownthisscreen,youcouldhaveenteredvaluesforalphalevelsandletthesoftwarefigureouttherest.Thiswouldbehelpfulifyouwantedtoavoidgoingoutofoperatingconstraints.Nowgobacktothebottomofthecentralcompositedesignform.LeavetheTypeatitsdefaultvalueofFull(theotheroptionisa“small”CCD,whichwedonotrecommendunlessyoumustcutthenumberofrunstothebareminimum).Youwillneedtwoblocksforthisdesign,oneforeachday,soclickontheBlocksfieldandselect2.SelectingthenumberofblocksNoticethatthesoftwaredisplayshowthisCCDwillbelaidoutinthetwoblocks.ClickontheContinuebuttontoreachthesecondpageofthe“wizard”forbuildingarespon