Plackett-Burman Design of Experiments

Plackett-BurmanDesignofExperiments1.Statisticsdevelopedintheearly20thcentury2.Tooltohelpimproveyieldsinfarming3.Manytypesofexperiments/techniques4.Designofexperimentswhenandwho?ByJamesD.WhiteJr.DesignsofExperimentsbyPlackettandBurman1.Werefirstwrittenin19462.R.L..Plackett3.J.P.Burman4.Matrixdesigninstructure5.ImprovequalitycontrolprocessHowdoesithelpImprovethequalitycontrolProcess?1.Upperandlowerlevellimitsofavariables2.Findsinfluencingfactors3.Helpswithefficientestimatingofprocess4.HelpstoimprovetheoverallqualityoftheproductImprovingQualityofProduct1.Experimentalproceduresrequireastructuredapproach2.Reliableresults3.Minimalwastageoftimeandmoney4.Experimentaldesign5.Statisticalprinciples6.LimitednumberofexperimentsImprovingQualityofProduct(continued)1.Optimizeaprocess2.Definewhichvariablesneedmostcontrol3.Maintaintherepeatabilityofaprocess4.Amathematicalmodeloftheprocess5.PredictresultsofchangedvariablesBenefitsofKnowingexpectedResultswhenvariableschanged1.Variablesonsystemcanbeenhanced2.Designfeasibility3.Productrobustness4.Allowsintelligentdecisionmaking5.Whichvariabletochangeinasystem?ChangingVariablesInASystem1.Modifyingonevariableisineffective2.Interactionscauseunforeseenproblems3.StudyEffectssointelligentdecisionscanbemade4.Orthogonalarray5.Plackett-BurmanDesignPlackett-BurmanExperiments1.Twolevelfractionalfactorials2.Efficientestimations3.Interactionsbetweenfactorsignored4.UsedInMatrixFormPlackett-Burman(continued)1.Columnsrepresentfactors2.Specifyleveltosetforfactors3.Rowscontainprocessruns4.post-processingofresultsPlackett-Burman(continued)1.StartwithFactors2.MorefactorsThebetter3.Factorsgoacrossthetop4.labeledf1,f2,....f7.Plackett-Burman(continued)1.Thenumberofrunswillgodowncolumns2.Multiplesof4butnotpowerof23.Onthelastrunwewilluseall(-)signs4.PossibledesignofPlackett-Burmandesignlookslikethefollowing:MatrixPatternof7FactorsRowf1f2f3f4f5f6f7r1+++-+--r2-+++-+-r3--+++-+r4+--+++-r5-+--+++r6+-+--++r7++-+--+r8-------MatrixExplained1.(-)willhavelowerlimitspervariable2.(+)willhaveupperlimitspervariable3.r1istestone4.f1isvariableone5.(r1,f1)positiveupperlimitMatrixexplained(continued)1.(r2,f2)negativelowerlimit2.Fillintherestofthematrixthesameway3.Lowerlimitsfromtestgoin(-)4.Upperlimitsfromtestgoin(+)MatrixExplained(continued)1.FindUpperlevelandLowerlevellimit2.L=¼(r1+r4+r6+r7)3.-¼(r2+r3+r5+r8)4.Variablef1,r1-r8goingdownnotacross.5.Nowhaveupperandlowerlimitsoff1MatrixExplained(continued)1.GetValueofupperlevellimitandvalueoflowerlevellimit2.OncewehavethevaluesofLowerlevellimitandupperlevellimitwecanthenfindthemeanofthatvariable.3.Whatdoesallthismean?Meaningbehindthemeans1.Variablescanbechanged2.Change1variable3.Wenowhavemathematicalformula4.Changenumbersandseechangetotheprocess5.VeryadvantageousHowcouldthistoolbeusedinyourorganization?1.Canyouseethebenefits?2.Whereelsecouldyouseethisworking?3.Woulditworkinyourorganization?4.Examples5.WorkingexampleExampleofmatrix1.Letsusea2variablematrix2.Wewillhave8runs3.Matrixwilllooklikethefollowing:ExampleMatrixstructureRowf1f2R1++R2-+R3--R4+-R5-+R6+-R7++r8--Examplematrix(continued)1.Wewillhave8runsforvariable12.Wewillhave8runsforvariable23.Foreaseofexamplewewillmakeupsomenumbers4.Matrixwilllooklikefollowingwithnumbersinit:ExamplematrixstructurewithvaluesRowf1f2R133.1R222.7R32.21.9R43.12.0R52.33.5R62.92.1R72.83.0r82.02.0Findingupperandlowerlimits1.Formula:L=¼(r1+r4+r6+r7)2.-¼(r2+r3+r5+r8)3.F1-UL=2.95,LL=-2.124.F2-UL=2.0,LL=-2.525.Findthemeans.Meansofexamplematrix1.Meanofvariable1is(.415)2.Meanofvariable2is-(.26)3.Change2runs4.Newtableisasfollows:Examplematrixafterchangeofrun2and5Rowf1f2R133.1R245R32.21.9R43.12.0R53.52.9R62.92.1R72.83.0r82.02.0Meansofvariablesafterchangeinoriginalvariableruns1.Changeofr2to(4)and(5)2.Changeofr5to(3.5)and(2.9)3.f1:UL=2.95,LL=2.924.Newmeanofvariable1=(.06)5.f2:UL=2.55,LL=2.956.Newmeanofvariable2=-(.185)Meansofvariablesafterchange:netchange1.Netchangeofvariable1=(.355)2.Netchangeofvariable2=(.075)3.WecanpredictwhatchangeswillbewithoutanychangesinprocessatthistimeConclusiontoPlackettandBurmandesigns1.Change1toasmanyasNvariables2.Changesinvariablesarebeneficialtocalculate3.NottotallyconclusiveConclusiontoPlackettandBurmanDesigns1.Severalprogramsavailableforhelp2.Somethatareavailableareasfollows:3.Minitab4.S-plus5.MINU6.Calculators7.GoodluckinyoufutureofqualitymanagementReferencescitedpage1.DraperN.R.,“PlackettBurmanDesigns”,EncyclopediaofStatisticalSciencesVolume6,EdJohnsonKotz,9volumes;Wiley,1982-19882.TrutnaLedi,“ProcessImprovements”,EngineeringStatisticsHandbook,Ed.CarollCroarkin;NoDate,