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页数:24页
时间:2020-05-11
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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,ornumberofgenerators7ExampleStatDOEFactorialCreateFactorialDesign8ExampleFactori
7、alDesignFractionalFactorialDesignFactors:4BaseDesign:4,8Resolution:IVRuns:8Replicates:1Fraction:1/2Blocks:noneCenterpts(total):0DesignGenerators:D=ABC9AliasRelationshipsAsmentionedearlier,thepatternoflevelsforfactorX4infirstexampleisidenticaltothepatternoflevelsforthei
8、nteractionX1X2X3.X4andX1X2X3arecalledaliasesofeachother.Analiasisanindividualfactororinteractionwhosepatternoflevelsi
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