质量管理相关知识简介(英文版).pptx
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质量管理相关知识简介(英文版).pptx
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ResponseSurfaceMethodology,WhatisResponseSurfaceMethodology(RSM),ResponseSurfaceMethodology(RSM)isacollectionofmathematicalandstatisticaltechniquesthatareusefulforthemodelingandanalysisofproblemsinwhicharesponseofinterestisinfluencedbyseveralquantifiablevariables(orfactors),withtheobjectiveofoptimizingtheresponse.,2,ResponseSurface,Theyieldofaprocess(Y)wasdeterminedtobeinfluencedbytheamountofnitrogen(X1)andphosphoricacid(X2),i.e.Y=(X1,X2)+whereisthenoiseorerrorobservedintheresponse.IfwedenotetheexpectedresponsebyE(Y)=(X1,X2)=thenthesurfacerepresentedby=(X1,X2)iscalledaresponsesurface.,3,ResponseSurfacePlots,ResponseSurfacePlotsshowhowaresponsevariablerelatestotwoquantifiablefactorsbasedonamodelequation.,4,ResponseSurfaceDesigns,Designsforfittingresponsesurfacesarecalledresponsesurfacedesigns.Whenchoosingadesignidentifythenumberofcontrolfactorsunderinvestigationdeterminethelimitingnumberofexperimentalrunsensureadequatecoverageoftheregionofinterestdeterminetheimpactofeconomicscost,time,availability,etc,5,ResponseSurfaceMethodologyWhy?
ResponseSurfaceMethodsareusedtoexaminetherelationshipbetweenoneormoreresponsesandasetofquantifiablefactorstosearchforthesettingofcriticalcontrolfactorsthatwouldoptimizetheresponsewhencurvatureintheresponsesurfaceissuspected,6,ResponseSurfaceMethodologyWhen?
ResponseSurfaceMethodsmaybeemployedtofindfactorsettingsthatproducethe“best”responsefindfactorsettingsinwhichoperatingorprocessspecificationsaresatisfiedidentifynewoperatingconditionsthatwouldproducetherequiredimprovementinproductqualitymodelarelationshipbetweenthecontrolfactorsandtheresponse,7,ResponseSurfaceFunctions,First-OrderModelResponsesurfacewillbeplanar.Second-OrderModelResponsesurfacewillbecurvi-planar,8,ResponseSurfaceFunctions,RSMseekstoidentifytherelationshipbetweentheresponseandthecontrolfactors.Itisasequentialprocedure,startingfromcurrentoperatingconditionsandmovingtowardstheoptimumcondition.Pointsontheresponsesurfacethatareremotefromtheoptimumcondition,suchascurrentoperatingconditions,oftenexhibitlittlecurvature.Afirst-ordermodelwillbeappropriate.Attheregionoftheoptimum,curvatureisoftenpresent,andthesecond-ordermodelwillbecomenecessary.,9,Example,Anengineerhasdeterminedthattwofactorsreactiontime(X1)andreactiontemperature(X2)havesignificanteffectontheyield(Y)ofaprocess.Theprocessiscurrentlyoperatingwithareactiontimeof35minutesandreactiontemperatureof155C,resultinginyieldsofabout40%.Theengineerdecidestoexploretheprocessregionof30,40minutesand150,160C.,10,Example,Theexperimentaldesignandaccompanyingresults(availableinResponseSurfaceMethodology.MTW)areshownbelow:
11,Example,StatDOEFactorialAnalyzeFactorialDesign,12,Example,SessionWindowFractionalFactorialFit:
YieldversusTime,TemperatureEstimatedEffectsandCoefficientsforYield(codedunits)TermEffectCoefSECoefTPConstant40.42500.1037389.890.000Time1.55000.77500.10377.470.002Temperature0.65000.32500.10373.130.035Time*Temperature-0.0500-0.02500.1037-0.240.821CtPt0.03500.13910.250.814,Ignore“time-temperature”interaction,i.e.analyzeasaFirst-OrderModel.,13,Example,SessionWindowFractionalFactorialFit:
YieldversusTime,Temperature(InteractionExcluded)EstimatedEffectsandCoefficientsforYield(codedunits)TermEffectCoefSECoefTPConstant40.42500.09341432.780.000Time1.55000.77500.093418.300.000Temperature0.65000.32500.093413.480.018CtPt0.03500.125320.280.791,TheFirst-OrderModelisvalid.,14,Example,15,AnalysisofSecond-OrderModels,MethodstoanalyzeSecond-OrderResponseSurfacesinclude:
3kFactorialDesignsBox-BehnkenDesignsCentralCompositeDesignsWewillcompare3-factorvariantsofthesedesigns.,16,3kFactorialDesigns,17,3kFactorialDesigns,Eachofthekfactorsarerunat3levels.Pro:
a)Abletoestimatealllinearandquadraticeffects,andallpossiblesimpleandhigherorderinteractions.Con:
a)Numberofrunscanbeexcessive.kRuns2932748152436729,18,3kFactorialDesigns,StatDOEFactorialCreateFactorialDesign,
(2),(3),
(1),(4),19,3kFactorialDesigns,CreateFactorialDesignDesignFactors,20,Box-BehnkenDesigns,21,Box-BehnkenDesigns,Eachofthekfactorsarerunat3levels.Pro:
a)Abletoestimatealllinearandquadraticeffects,and2-factorinteractions.b)Lessrunsrequired,comparedvs3kFactorialDesigns.c)Doesnotincludeanycornerpoints.Con:
a)Numberofrunsislargeenoughtoestimateallquadraticand2-factorinteractions,regardlessofneed.b)Cannotbebuilt-upfroma2k-pFactorialDesign.,22,Box-BehnkenDesigns,StatDOEResponseSurfaceCreateResponseSurfaceDesign,
(2),(3),
(1),23,CentralComposite(Box-WilsonDesign),24,CentralComposite(Box-WilsonDesign),25,CentralComposite(Box-WilsonDesign),Eachofthekfactorscanberunat5levels.Pro:
a)Abletoestimatealllineareffects,andselectedquadraticeffectsand2-factorinteractions.b)Canbebuilt-upfroma2k-qscreeningdesign,byaddingaxialpoints.Con:
a)Bestsuitedforquantitativefactors.b)Someaxialpointsmaybeinnon-desirableconditions.,26,CentralComposite(Box-WilsonDesign),StatDOEResponseSurfaceCreateResponseSurfaceDesign,
(2),(3),
(1),27,Comparisonof3-LevelDesign,Numbersinparenthesis=thenumberofreplicatedcenterpoints.ForCCD,Source:
UnderstandingIndustrialDesignedExperimentsStephenRSchmidt&RobertGLaunsby,28,Contour/SurfacePlots,StatDOEResponseSurfaceContour/Surface(Wireframe)Plots,29,EndofPresentation,Rev1:
17July02,
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