品质管理相关知识(英文版).ppt

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1、FractionalFactorialDesignsBeltonGroupRexWongScreeningDesignsAtthebeginningofinvestigations,itisnotuncommontohavealonglistoffactorsaspotentiallyimportantinfluencesontheresponseunderstudy.Asthenumberoffactorsina2kfactorialdesignincreases,thenumberofrunsrequiredforacomple

2、tereplicateofthedesignincreasesexponentially:FactorsRunsRequired416532664712882569512101,0242ScreeningDesignsAscreeningdesignisanexperimentaldesignwhosepurposeistodistinguishinfluentialfactorsfromnon-influentialfactors,asefficientlyaspossible.Afractionalfactorialdesign

3、isasubsetoftherunsofacompletefactorialdesign.3ExampleForacertainprocess,thereare4factorsofpotentialinterest.A24factorialdesign(16runs)wouldhavebeenasuitableexperimentaldesign.However,resourcesoftimeandcostpermitonly8runs.4ExampleConsiderthe24factorialdesign:Twopossible

4、setsof8runs:a)thesetforwhichX1X2X3X4=1b)thesetforX1X2X3X4=-15ExampleThesetof8runsforwhichX1X2X3X4=1isshownbelow:ItcanbeseenthatthepatternoflevelsforfactorX4isidenticaltothepatternoflevelsfortheinteractionX1X2X3.Infact,forthisdesignthepatternoflevelsforeveryindividualfa

5、ctorandinteractionisidenticaltooneotherindividualfactororinteraction.6FractionalFactorialDesignThedesigninlastexampleiscalleda24-1fractionalfactorialdesign,where2=numberoflevelsforeachfactor4=numberoffactors1=degreeoffractionationofthecorrespondingfullfactorialdesign(i

6、nthiscase2-1=½ofthecorresponding24factorialdesign)Thegeneralnotationfora2-levelfractionalfactorialdesignis2k-p,where2=numberoflevelsforeachfactork=numberoffactorsp=degreeoffractionation,ornumberofgenerators7ExampleStatDOEFactorialCreateFactorialDesign8ExampleFactori

7、alDesignFractionalFactorialDesignFactors:4BaseDesign:4,8Resolution:IVRuns:8Replicates:1Fraction:1/2Blocks:noneCenterpts(total):0DesignGenerators:D=ABC9AliasRelationshipsAsmentionedearlier,thepatternoflevelsforfactorX4infirstexampleisidenticaltothepatternoflevelsforthei

8、nteractionX1X2X3.X4andX1X2X3arecalledaliasesofeachother.Analiasisanindividualfactororinteractionwhosepatternoflevelsi