6sigma introduction

16SigmaIntroductionContents•6SigmaHistory•What’s6Sigma?•6Stepsto6Sigma•6SigmaToolsQuickView26SigmaHistory(I)•Theguesttoachieve6sigmahaditsbirthatMotorolain1979whenexecutiveArtSundrystoodupandproclaimed,”TherealproblematMotorolaisthatourqualitystinks!”•Atthetime,Motorolawasspending5~10%ofannualrevenues,andinsomecasesasmuchas20%ofrevenues,correctingpoorquality.THECOSTOFQUALITYSIGMADEFECTSPERMILLIONOPPORTUNITIESCOQ2308,537(Noncompetitivecompanies)Notapplicable366,80725~40%ofsales46,210(Industrialaverage)15~25%ofsales52335~15%ofsales63.4(Worldclass)1%ofsalesEachsigmashiftprovidesa10percentnetincomeimprovement.36SigmaHistory(II)COMPUTINGTHECOSTOFQUALITYINTERNALFAILUREAPPRAISALScrapInspectionReworkTestingSupplierscrapandreworkQualityauditInitialcostandmaintenanceoftestequipmentEXTERNALFAILUREPREVENTIONCosttocustomerQualityplanningWarrantycostProcessplanningComplaintadjustmentProcesscontrolReturnedmaterialTraining46SigmaHistory(III)•In1984,Dr.MikelHarryatMotorola’sGovernmentElectronicsGroup,begantoexperimentwithproblemsolvingthroughstatisticalanalysisandfinallyformulatedamethodforapplying6sigmathroughoutthecompany•In1988,MotorolawonthecovetedprizeoftheMalcolmBaldrigeNationalQualityAwardastheresultofachievingtenfoldimprovementoverafiveyearperiod.•In1990,HarrystartedupandleadMotorola’s6sigmaresearchinstituteinSchaumburgwhichwasfundedbyMotorola,IBM,TI,ABB,Kodak,andDigitalElectronics.•In1991,applying6sigmainearlydesignstage,BanditpagerwasdesignedtobeproducedinitsautomatedfactoryinBBwithin72min.fromthetimetheorderwasplacedinanysalesoffice.56SigmaHistory(IV)•In1993,Dr.MikelHarryleftMotorolaandjoininABB,withtheshiftofdefectcontrollingfocustoreducingcosts,theABBachieveda68percentreductionindefectlevelsanda30%reductionproductcosts,resultinginan$898Msavings/costreductioneachyearoveratwo-yearperiod.•In1994,Dr.Harryopenedthedoorstothe6sigmaacademyinScottsdale,Arizona,takingonGeneralElectricandAlliedSignalasthefirstclients.Withinashorttime,6sigmabegantospreadlikewildfiretootherindustries6What’s6SigmaContents•Why3.4ppm?•DPU&DPMO•ApplySigmaforBenchmarking•6SigmaGoal7Why3.4ppm?CourseGoals(I):Aftercompletingthissection,youwillbeableto:•Calculatetheyieldundernormaldistribution.•Applyexcelfunctionof‘Normsdist()’tocalculatetheyieldanddefectrateofnormaldistribution.•Understandtheppmdifferencebetweencenteredand1.5shiftednormaldistribution.σ8Yield--NormalDistribution161116212631364146515661667199.73%σ1σ2σ3σ4σ5σ6σ0σ-1σ-2σ-3σ-4σ-5σ-6USLLSL68.27%95.45%99.994%99.99994%99.9999998%9151101151201251µ+xOne-tailedµ=Average(a1,a2….)σ=Stdev(a1,a2….)z=(x-µ)/σyield=Normsdist(z)USL151101151201251µ-xLSL+xUSLTwo-tailedz1=(x-µ)/σz2=(-x-µ)/σyield=Normsdist(z1)-Normsdist(z2)HowtoCalculateYield?(I)10HowtoCalculateYield?(II)ExampleMSMD110Resistancewasspecifiedas72~102ohms,onebatchofmaterialwascenteredat90ohms,iftheresistancevariation(sigma)ofthisbatchis8ohms,what’stheyield?151101151201251LSLUSL9010272z1=(x1-µ)/σ=(102-90)/8=1.5z2=(x2-µ)/σ=(72-90)/8=-2.25yield=Normsdist(1.5)-Normsdist(-2.25)=92.1%11Yield--CenteredDistribution161116212631364146515661667199.73%σ1σ2σ3σ4σ5σ6σ0σ-1σ-2σ-3σ-4σ-5σ-6USLLSL68.27%95.45%99.994%99.99994%99.9999998%z1=(x-µ)/σ=3z2=(-x-µ)/σ=-3yield=normsdist(3)-normsdist(-3)=99.73%Take+/-3σasexample12VariationisNatureSub-group1Sub-group2Sub-group3Sub-group4Sub-group51.Eachsub-grouprepresentedashort-termcapabilitystudy,anditisameasureoftechnological(design)capability.---(UCL-LCL)/2=62.Along-termcapabilitystudycombiningseveralsub-groupsrepresentedameasureofdesignandprocesscapability.---(UCL-LCL)/2=4.53.Typically,a1.5sigmadifferenceiscalculatedfromlong-termandshort-termcapabilitystudy.---6-4.5=1.513Yield--1.5SigmaShifted1611162126313641465156616671σ1σ2σ3σ4σ5σ6σ0σ-1σ-2σ-3σ-4σ-5σ-6USLLSLσ1.530.85%69.15%93.32%99.38%99.98%99.9997%Take+/-3σasexamplez1=(x-µ)/σ=1.5z2=(-x-µ)/σ=-4.5yield=?14151101151201251µ-xOne-tailedµ=Average(a1,a2….)σ=Stdev(a1,a2….)z=(-x-µ)/σdefect%=Normsdist(z)USL151101151201251µ-xLSL+xUSLTwo-tailedz1=(-x-µ)/σz2=(x-µ)/σdefect%=Normsdist(z1)+[1-Normsdist(z2)]Defect%--NormalDistribution15Defect%--CenteredDistribution161116212631364146515661667115.87%σ1σ2σ3σ4σ5σ6σ0σ-1σ-2σ-3σ-4σ-5σ-6USLLSL2.27%1350ppm32ppm0.287ppm1ppb15.87%2.27%1350ppm32ppm0.287ppm1ppbDefect%=Normsdist(n)σDefect%=1-Normsdist(n)σ16Defect%--1.5SigmaShifted1611162126313641465156616671σ1σ2σ3σ4σ5σ6σ0σ-1σ-2σ-3σ-4σ-5σ-6USLLSLσ1.569.15%30.85%6.68%6210ppm233ppm3.4ppm6210ppm233ppm3.4ppm19ppb0.04ppb3.4ppmDefect%=Normsdist((n-1.5))σDefect%=1-Normsdist((n-1.5))σ17455002700633085386680762102330.5740.0023.41.0E-031.0E-021.0E-011.0E+001.0E+011.0E+021.0E+031.0E+041.0E+051.0E+061.02.03.04.05.06.07.0SigmaLevelppmCentered1.5sigmashift151101151201251LSLUSL151101151201251USLLSL1.5σshiftCenteredOne-tailedTwo-tailedCenteredvs.1.5SigmaShifted18DPU,DPMO&BenchmarkingCourseGoals(II)Aftercompletingthissection,youwillbeableto:•CalculatetheDPU&DPMOofyourownproductsorservice.•Applyexcelfunctionof‘Normsinv()’tocalculatethesigmalevelofyourjob.•Understandhowtoapply6sigmatoolsforbench