質量管理相關知識簡介 (英文版)

質量管理相關知識簡介(英文版)ResponseSurfaceMethodologyWhatisResponseSurfaceMethodology(RSM)ResponseSurfaceMethodology(RSM)isacollectionofmathematicalandstatisticaltechniquesthatareusefulforthemodelingandanalysisofproblemsinwhicharesponseofinterestisinfluencedbyseveralquantifiablevariables(orfactors),withtheobjectiveofoptimizingtheresponse.ResponseSurfaceTheyieldofaprocess(Y)wasdeterminedtobeinfluencedbytheamountofnitrogen(X1)andphosphoricacid(X2),i.e. Y=?(X1,X2)+

whereisthenoiseorerrorobservedintheresponse.Ifwedenotetheexpectedresponseby E(Y)=?(X1,X2)=

thenthesurfacerepresentedby

=?(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.ExleAnengineerhasdeterminedthattwofactors–reactiontime(X1)andreactiontemperature(X2)–havesignificanteffectontheyield(Y)ofaprocess.Theprocessiscurrentlyoperatingwithareactiontimeof35minutesandreactiontemperatureof155°C,resultinginyieldsofabout40%.Theengineerdecidestoexploretheprocessregionof[30,40]minutesand[150,160]°C.ExleTheexperimentaldesignandaccompanyingresults(availableinResponseSurfaceMethodology.MTW)areshownbelow:ExleStat

DOEFactorialAnalyzeFactorialDesignExleSessionWindowFractionalFactorialFit: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.ExleSessionWindowFractionalFactorialFit:YieldversusTime,Temperature(InteractionExcluded)EstimatedEffectsandCoefficientsforYield(codedunits)TermEffectCoefSECoefTPConstant40.42500.09341432.780.000Time1.55000.77500.093418.300.000Temperature0.65000.32500.093413.480.018CtPt0.03500.125320.280.791TheFirst-OrderModel isvalid.ExleAnalysisofSecond-OrderModelsMethodstoanalyzeSecond-OrderResponseSurfacesinclude:3kFactorialDesignsBox-BehnkenDesignsCentralCompositeDesignsWewillcompare3-factorvariantsofthesedesigns.3kFactorialDesigns3kFactorialDesignsEachofthekfactorsarerunat3levels.Pro: a)Abletoestimatealllinearandquadraticeffects,and allpossiblesimpleandhigherorderinteractions.Con: a)Numberofrunscanbeexcessive.

k Runs 2 9 3 27 4 81 5 243 6 7293kFactorialDesignsStat

DOEFactorialCreateFactorialDesign(2)(3)(1)(4)3kFactorialDesignsCreateFactorialDesign

Design FactorsBox-BehnkenDesignsBox-BehnkenDesignsEachofthekfactorsarerunat3levels.Pro: a)Abletoestimatealllinearandquadraticeffects,and 2-factorinteractions. b)Lessrunsrequired,comparedvs3kFactorialDesigns. c)Doesnotincludeanycornerpoints.Con:a)Numberofrunsislargeenoughtoestimateallquadratic and2-factorinteractions,regardlessofneed. b)Cannotbebuilt-upfroma2k-pFactorialDesign.Box-BehnkenDesignsStat

DOEResponseSurfaceCreateResponseSurfaceDesign(2)(3)(1)CentralComposite(Box-WilsonDesign)

=nf?wherenfisnumberofrunsinfactorialportionofCCD

CentralComposite(Box-WilsonDesign)FactorialPoints(8runs)+CenterPoints&AxialPoints(6+6runs)=CentralComposite(Box-Wilson)Design(20runs)CentralComposite(Box-WilsonDesign)Eachofthekfactorscanberunat5levels.Pro: a)Abletoestimatealllineareffects,andselectedquadratic effectsand2-factorinteractio