质量管理相关知识简介英文

ResponseSurfaceMethodologyWhatisResponseSurfaceMethodology(RSM)ResponseSurfaceMethodology(RSM)isacollectionofmathematicalandstatisticaltechniquesthatareusefulforthemodelingandanalysisofproblemsinwhicharesponseofinterestisinfluencedbyseveralquantifiablevariables(orfactors),withtheobjectiveofoptimizingtheresponse.ResponseSurfaceTheyieldofaprocess(Y)wasdeterminedtobeinfluencedbytheamountofnitrogen(X1)andphosphoricacid(X2),i.e. Y=ƒ(X1,X2)+whereisthenoiseorerrorobservedintheresponse.Ifwedenotetheexpectedresponseby E(Y)=ƒ(X1,X2)=thenthesurfacerepresentedby

=ƒ(X1,X2)iscalledaresponsesurface.ResponseSurfacePlotsResponseSurfacePlotsshowhowaresponsevariablerelatestotwoquantifiablefactorsbasedonamodelequation.ResponseSurfaceDesignsDesignsforfittingresponsesurfacesarecalledresponsesurfacedesigns.Whenchoosingadesignidentifythenumberofcontrolfactorsunderinvestigationdeterminethelimitingnumberofexperimentalrunsensureadequatecoverageoftheregionofinterestdeterminetheimpactofeconomics–cost,time,availability,etcResponseSurfaceMethodology–Why?ResponseSurfaceMethods

areusedtoexaminetherelationshipbetweenoneormoreresponsesandasetofquantifiablefactorstosearchforthesettingofcriticalcontrolfactorsthatwouldoptimizetheresponsewhencurvatureintheresponsesurfaceissuspectedResponseSurfaceMethodology–When?ResponseSurfaceMethods

maybeemployedtofindfactorsettingsthatproducethe“best”responsefindfactorsettingsinwhichoperatingorprocessspecificationsaresatisfiedidentifynewoperatingconditionsthatwouldproducetherequiredimprovementinproductqualitymodelarelationshipbetweenthecontrolfactorsandtheresponseResponseSurfaceFunctionsFirst-OrderModelResponsesurfacewillbeplanar.Second-OrderModelResponsesurfacewillbecurvi-planarResponseSurfaceFunctionsRSMseekstoidentifytherelationshipbetweentheresponseandthecontrolfactors.Itisasequentialprocedure,startingfromcurrentoperatingconditionsandmovingtowardstheoptimumcondition.Pointsontheresponsesurfacethatareremotefromtheoptimumcondition,suchascurrentoperatingconditions,oftenexhibitlittlecurvature.Afirst-ordermodelwillbeappropriate.Attheregionoftheoptimum,curvatureisoftenpresent,andthesecond-ordermodelwillbecomenecessary.ExampleAnengineerhasdeterminedthattwofactors–reactiontime(X1)andreactiontemperature(X2)–havesignificanteffectontheyield(Y)ofaprocess.Theprocessiscurrentlyoperatingwithareactiontimeof35minutesandreactiontemperatureof155°C,resultinginyieldsofabout40%.Theengineerdecidestoexploretheprocessregionof[30,40]minutesand[150,160]°C.ExampleTheexperimentaldesignandaccompanyingresults(availableinResponseSurfaceMethodology.MTW)areshownbelow:ExampleStatDOEFactorialAnalyzeFactorialDesignExampleSessionWindowFractionalFactorialFit:YieldversusTime,TemperatureEstimatedEffectsandCoefficientsforYield(codedunits)TermEffectCoefSECoefTPConstant40.42500.1037389.890.000Time1.55000.77500.10377.470.002Temperature0.65000.32500.10373.130.035Time*Temperature-0.0500-0.02500.1037-0.240.821CtPt0.03500.13910.250.814Ignore““time-temperature””interaction,i.e.analyzeasaFirst-OrderModel.ExampleSessionWindowFractionalFactorialFit:YieldversusTime,Temperature(InteractionExcluded)EstimatedEffectsandCoefficientsforYield(codedunits)TermEffectCoefSECoefTPConstant40.42500.09341432.780.000Time1.55000.77500.093418.300.000Temperature0.65000.32500.093413.480.018CtPt0.03500.125320.280.791TheFirst-OrderModelisvalid.ExampleAnalysisofSecond-OrderModelsMethodstoanalyzeSecond-OrderResponseSurfacesinclude:3kFactorialDesignsBox-BehnkenDesignsCentralCompositeDesignsWewillcompare3-factorvariantsofthesedesigns.3kFactorialDesigns3kFactorialDesignsEachofthekfactorsarerunat3levels.Pro:a)Abletoestimatealllinearandquadraticeffects,andallpossiblesimpleandhigherorderinteractions.Con:a)Numberofrunscanbeexcessive.kRuns29327481524367293kFactorialDesignsStatDOEFactorialCreateFactorialDesign(2)(3)(1)(4)3kFactorialDesignsCreateFactorialDesignDesignFactorsBox-BehnkenDesignsBox-BehnkenDesignsEachofthekfactorsarerunat3levels.Pro:a)Abletoestimatealllinearandquadraticeffects,and2-factorinteractions.b)Lessrunsrequired,comparedvs3kFactorialDesigns.c)Doesnotincludeanycornerpoints.Con:a)Numberofrunsislargeenoughtoestimateallquadraticand2-factorinteractions,regardlessofneed.b)Cannotbebuilt-upfroma2k-pFactorialDesign.Box-BehnkenDesignsStatDOEResponseSurfaceCreateResponseSurfaceDesign(2)(3)(1)CentralComposite(Box-WilsonDesign)=nf¼wherenfisnumberofrunsinfactorialportionofCCDCentralComposite(Box-WilsonDesign)FactorialPoints(8runs)+CenterPoints&AxialPoints(6+6runs)=CentralComposite(Box-Wilson)Design(20runs)CentralComposite(Box-WilsonDesign)Eachofthekfactorscanberunat5levels.Pro:a)Abletoestimatealllineareffects,andselectedquadraticeffectsand2-factorinteractions.b)Canbebuilt-upfroma2k-qscreeningdesign,byaddingaxialpoints.Con:a)Bestsuitedforquantitativef