品质管理相关知识(英文版)(ppt 24页).ppt

FractionalFactorialDesigns BeltonGroupRexWong 2 ScreeningDesigns Atthebeginningofinvestigations itisnotuncommontohavealonglistoffactorsaspotentiallyimportantinfluencesontheresponseunderstudy Asthenumberoffactorsina2kfactorialdesignincreases thenumberofrunsrequiredforacompletereplicateofthedesignincreasesexponentially FactorsRunsRequired416532664712882569512101 024 3 ScreeningDesigns Ascreeningdesignisanexperimentaldesignwhosepurposeistodistinguishinfluentialfactorsfromnon influentialfactors asefficientlyaspossible Afractionalfactorialdesignisasubsetoftherunsofacompletefactorialdesign 4 Example Foracertainprocess thereare4factorsofpotentialinterest A24factorialdesign 16runs wouldhavebeenasuitableexperimentaldesign However resourcesoftimeandcostpermitonly8runs 5 Example Considerthe24factorialdesign Twopossiblesetsof8runs a thesetforwhichX1X2X3X4 1b thesetforX1X2X3X4 1 6 Example Thesetof8runsforwhichX1X2X3X4 1isshownbelow ItcanbeseenthatthepatternoflevelsforfactorX4isidenticaltothepatternoflevelsfortheinteractionX1X2X3 Infact forthisdesignthepatternoflevelsforeveryindividualfactorandinteractionisidenticaltooneotherindividualfactororinteraction 7 FractionalFactorialDesign Thedesigninlastexampleiscalleda24 1fractionalfactorialdesign where2 numberoflevelsforeachfactor4 numberoffactors1 degreeoffractionationofthecorrespondingfullfactorialdesign inthiscase2 1 ofthecorresponding24factorialdesign Thegeneralnotationfora2 levelfractionalfactorialdesignis2k p where2 numberoflevelsforeachfactork numberoffactorsp degreeoffractionation ornumberofgenerators 8 Example Stat DOE Factorial CreateFactorialDesign 9 Example FactorialDesignFractionalFactorialDesignFactors 4BaseDesign 4 8Resolution IVRuns 8Replicates 1Fraction 1 2Blocks noneCenterpts total 0DesignGenerators D ABC 10 AliasRelationships Asmentionedearlier thepatternoflevelsforfactorX4infirstexampleisidenticaltothepatternoflevelsfortheinteractionX1X2X3 X4andX1X2X3arecalledaliasesofeachother Analiasisanindividualfactororinteractionwhosepatternoflevelsinanexperimentisidenticaltothatofanotherfactororinteraction 11 AliasRelationships Inafractionalfactorialdesign everyindividualfactorandinteractionhasanalias Thecalculatedeffectofanyfactororinteractionisanestimateofthesumoftheeffectsofthealiasedvariables e g thecalculatedeffectofX4 orofX1X2X3 isanestimateofthesumoftheeffectsofX4andX1X2X3 TheeffectofthefactorX4issaidtobeconfoundedwiththeeffectoftheX1X2X3interaction 12 Example Forthe24 1fractionalfactorialdesigninExample1 determinethealiasforeachfactorandinteraction Note X4 X1X2X3 i e X4isgeneratedfromX1X2X3 13 Example FromX4 X1X2X3MultiplybothsidesbyX4 X4X4 X1X2X3X4I X1X2X3X4 1 Note XiXi I 1 Multiplybothsidesof 1 byX1 X1 X1X1X2X3X4 X2X3X4Multiplybothsidesof 1 byX2 X2 X1X2X2X3X4 X1X3X4Multiplybothsidesof 1 byX3 X3 X1X2X3X3X4 X1X2X4 14 Example FactorialDesignDesignGenerators D ABCAliasStructureI ABCDA BCDB ACDC ABDD ABCAB CDAC BDAD BC 15 DesignResolutions Fractionalfactorialdesignscanbeclassifiedbytheirresolution ResolutionIIIdesignsarethoseforwhichnoindividualfactorisaliasedwithanotherindividualfactor butforwhichatleastonefactorisaliasedwitha2 factorinteraction ResolutionIVdesignsarethoseforwhichnoindividualfactorisaliasedwithanotherindividualfactororwithany2 factorinteraction butatleastone2 factorinteractionisaliasedwithanother2 factorinteraction andatleastoneindividualfactorisaliasedwitha3 factorinteraction ResolutionVdesignsarethoseforwhichnoindividualfactoror2 factorinteractionisaliasedwithanyotherindividualfactoror2 factorinteraction butatleastone2 factorinteractionisaliasedwitha3 factorinteraction andatleastoneindividualfactorisaliasedwitha4 factorinteraction 16 DesignResolutions Theresolutionofa2 levelfractionalfactorialdesignisthesmallestsumoftheordersofaliasedeffects ResolutionSmallestSumofOrdersofAliasedEffectsIII1 2IV1 3 2 2V1 4 2 3Theresolutionofafractionalfactorialdesignisoftenincludedasasubscriptinthedesignationofthedesign e g 2design Wherepossible avoidResolution III RIII designs 17 Example Stat DOE Factorial CreateFactorialDesign 18 Plackett BurmanDesigns Plackett BurmanDesignsaretwo levelfractionalfactorialdesigns ofResolutionIII usedforstudyingK N 1variablesinNruns whereNisamultipleof4 Thedesigncanbespecifiedbygivingjustthefirstcolumn 8Runs 12Runs 16Runs 20Runs 24Runs 19 Plackett Burman Example 8RunPlackett BurmanDesign RunABCDEFG1 2 3 4 5 6 7 8 EachPlackett BurmanDesigncanhaveuptok n 1 factors Ifk n 1 onlythefirstkcolumnsareused 20 Example Anengineerplanstoinvestigatethemaineffectsof5factors Hecanonlyperform10experimentalrunsatbest Selectanappropriateexperimentaldesign 21 Example Stat DOE Factorial CreateFactorialDesign 22 Example StdOrderRunOrderCenterPtBlocksABCDE12111 1 11 1251111 1 113311111 1 14111 1111 157111 11116411 11 1117611 1 11 118811