Design-Expert-8.0使用指南-Multifactor-Response-Surface

DX8-04C-MultifactorRSM-P1.docxRev.4/8/10Design-Expert8User’sGuideMultifactorRSMTutorial–Part11MultifactorRSMTutorial(Part1–TheBasics)ResponseSurfaceDesignandAnalysisThistutorialshowshowtouseDesign-Expert®softwareforresponsesurfacemethodology(RSM).Thisclassofdesignsisaimedatprocessoptimization.Acasestudyprovidesareal-lifefeeltotheexercise.Duetothespecificnatureofthiscasestudy,anumberoffeaturesthatcouldbehelpfultoyouforRSMwillnotbeimplementedinthistutorial.ManyofthesefeaturesareusedintheGeneralOneFactor,RSMOneFactor,orTwo-LevelFactorialtutorials.Ifyouhavenotcompletedallthesetutorials,considerdoingsobeforestartingthisone.WewillpresumethatyouareknowledgeableofthestatisticalaspectsofRSM.Foragoodprimeronthesubject,seeRSMSimplified(AndersonandWhitcomb,Productivity,Inc.,NewYork,2005).YouwillfindoverviewsonRSMandhowit’sdoneviaDesign-Expertintheon-lineHelpsystem.TogainaworkingknowledgeofRSM,werecommendyouattendourResponseSurfaceMethodsforProcessOptimizationworkshop.CallStat-Easeorvisitourwebsiteforascheduleat“y”,are:y1-Conversion(%ofreactantsconvertedtoproduct)y2-Activity.Theexperimenterchosethreeprocessfactorstostudy.Theirnamesandlevelsareshowninthefollowingtable.FactorUnitsLowLevel(-1)HighLevel(+1)A–Timeminutes4050B–TemperaturedegreesC8090C–Catalystpercent23FactorsforresponsesurfacestudyYouwillstudythechemicalprocessusingastandardRSMdesigncalledacentralcompositedesign(CCD).It’swellsuitedforfittingaquadraticsurface,whichusuallyworkswellforprocessoptimization.Thethree-factorlayoutforthisCCDispicturedbelow.Itiscomposedofacorefactorialthatformsacubewithsidesthataretwocodedunitsinlength(from-1to+1asnotedinthetableabove).Thestarsrepresentaxialpoints.Howfaroutfromthecubetheseshouldgoisamatterformuchdiscussionbetweenstatisticians.Theydesignatethisdistance“alpha”–measuredintermsofcodedfactorlevels.Asyouwillsee,Design-Expertoffersavarietyofoptionsforalpha.2MultifactorRSMTutorial–Part1Design-Expert8User’sGuideCentralCompositeDesignforthreefactorsAssumethattheexperimentswillbeconductedoveratwo-dayperiod,intwoblocks:1.Twelveruns:composedofeightfactorialpoints,plusfourcenterpoints.2.Eightruns:composedofsixaxial(star)points,plustwomorecenterpoints.DesigntheExperimentStarttheprogrambyfindinganddoubleclickingtheDesign-Expertsoftwareicon.TakethequickestroutetoinitiatinganewdesignbyclickingNewDesignnearthecenteroftheopeningscreen,asshownbelow.Twootherroutesareavailable:Clicktheblank-sheeticonontheleftofthetoolbar,orchooseFile,NewDesign(orassociatedAltkeys)fromthemainmenuatopyourscreen.Design-ExpertopeningscreenClicktheResponseSurfacefoldertabtoshowthedesignsavailableforRSM.ResponsesurfacedesigntabDX8-04C-MultifactorRSM-P1.docxRev.4/8/10Design-Expert8User’sGuideMultifactorRSMTutorial–Part13ThedefaultselectionistheCentralCompositedesign,whichisusedinthiscasestudy.ClickthedownarrowintheNumericFactorsentryboxandSelect3asshownbelow.Selecting3numericfactorsToseealternativeRSMdesignsforthreefactors,clickatfarleftonBox-Behnken(notice17runsnearthescreenbottom)andMiscellaneousdesigns,whereyoufindthe3-LevelFactorialoption(32runs,including5centerpoints).Nowgobackandre-selectCentralCompositedesign.Beforeenteringfactorsandranges,clickOptionsnearthebottomoftheCCDscreen.NoticethatitdefaultstoaRotatabledesignwiththeaxial(star)pointssetat1.68179codedunitsfromthecenter–aconventionalchoicefortheCCD.DefaultCCDoptionforalphasetsodesignisrotatableManyoptionsarestatisticalinnature,butonethatproduceslessextremefactorrangesisthe“Practical”valueforalpha.Thisiscomputedbytakingthefourthrootofthenumberoffactors(inthiscase3¼or1.31607).SeeRSMSimplifiedChapter8“EverythingYouShouldKnowAboutCCDs(butdarenotask!)”fordetailsonthispracticalversusotherlevelssuggestedforalphainCCDs–themostpopularofwhichmaybethe“FaceCentered”(alphaequalsone).PressOKtoaccepttherotatablevalue.Usingtheinformationprovidedinthetableonpage1ofthistutorial(oronthescreencapturebelow),typeinthedetailsforfactorName(A,B,C),Units,andLowandHighlevels.4MultifactorRSMTutorial–Part1Design-Expert8User’sGuideCompletedfactorformYou’venowspecifiedthecubicalportionoftheCCD.Asyoudidthis,Design-Expertcalculatedthecodeddistance“alpha”forplacementonthestarpointsinthecentralcompositedesign.Alternatively,byclickingthe“enteredfactorrangesintermsofalphas”optionyoucancontrolhowfarouttherunswillgoforeachofyourfactors.Nowreturntothebottomofthecentralcompositedesignform.LeaveTypeatitsdefaultvalueofFull(theotheroptionisa“small”CCD,whichwedonotrecommendunlessyoumustreducethenumberofrunstothebareminimum).Youwillneedtwoblocksforthisdesign,oneforeachday,soclicktheBlocksfieldandselect2.SelectingthenumberofblocksNoticethesoftwaredisplayshowthisCCDwillbelaidoutinthetwoblocks–forexample,4centerpointswillgoinoneand2intheother.ClickContinuetoreachthesecondpageofthe“wizard”forbuildingaresponsesurfacedesign.YounowhavetheoptionofidentifyingBlockNames.EnterDay1andDay2asshownbelow.BlocknamesPressContinuetoenterR