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Prof.RobLeachmanIEOR130Fall,2014

9/11/2014 1RobLeachmanIntrotoSixSigma

SixSigmaisanengineeringmanagementparadigmoriginallydevelopedatMotorola.Itsapplicationhasspreadfromhitechmanufacturingtogeneralbusinessprocessesinmanyindustries.

SixSigmaseekstoimprovethequalityofprocessoutputsbyidentifyingandremovingthecausesofdefects (errors)andvariability. Itinvolvesstatisticalmethodsandusuallyreliesonaspecialinfrastructureofpeoplewithintheorganizationwhoareexpertsinthesemethods.

ASixSigmaprojecttypicallyhasspecificfinancialgoalsforcostreductionorprofitgain.9/11/2014 2RobLeachmanIntrotoSixSigma

FirstwrittenformulationbyBillSmithofMotorolain1986.

BUT,SixSigmadrawsheavilyonthepreviouslypublishedqualityparadigmsandmethodologies(statisticalqualitycontrol,TQM,ZeroDefects,etc.)developedbyShewart,Deming,Juran,Ishikawa,Taguchiandothersfromthe1930suptothe1980s.

9/11/2014 3RobLeachmanIntrotoSixSigma

Adefectisanythingthatcouldleadtocustomerdissatisfaction.Defectsareverycostly.

Theremustbecontinuousefforttoachievestableandpredictableprocessresults(i.e.,toreduceprocessvariationandhencedefects).

Processeshavecharacteristicsthatcanbemeasured,analyzed,improvedandcontrolled.

Achievingsustainedqualityimprovementrequirescommitmentfromtheentireorganization.

9/11/2014 4RobLeachmanIntrotoSixSigma

Consideraprocessgeneratinganongoingstreamofoutput.

Ifonanongoingbasisweplottheaveragesofparametermeasurementsforgroupsoffiveormoreoutputunitsoftheprocess,thenbytheCentralLimitTheoremofstatistics,weshouldseeanormaldistribution .

PROVIDEDTHATtheprocessisstable,i.e.,providedthatconsecutivemeasurementsareindependentandidenticallydistributed(IID)randomvariables. IfnotIID,thentheprocessisnotinstatisticalcontrol andissaidtobeoutofcontrol(OOC).

9/11/2014 5RobLeachmanIntrotoSixSigma

Foranormaldistribution,99.9%ofthemassliesbetween[3,+3],where denotesthemean and denotesthestandarddeviation.Thus,aspreadof6 containsvirtuallyalltheoutputoftheprocess:

9/11/2014 6RobLeachmanIntrotoSixSigma

Weassumeforeachimportantprocessparameterthattheengineersdefinespecificationlimits,wherebyiftheparameterfallsbelowthelowerspecificationlimit(LSL) orabovetheupperspecificationlimit(USL),thentheoutputunitisdefectiveandnogoodforthecustomer.

Howmanydefectsweexperiencecanbecharacterizedbycomparingthespeclimitstothe6spreadofthenormaldistributionfortheprocess

9/11/2014 RobLeachmanIntrotoSixSigma 7

Averywellcontrolledprocess.Thedistributioniswellcenteredbetweenthespeclimits,andthe6 spreadishalfthe12 spreadofthespeclimits.

9/11/2014 8RobLeachmanIntrotoSixSigma

Processcapabilityconcernstheabilityoftheprocesstogenerateoutputwithinthespeclimits.Motoroladevelopedsomemetricsforthispurpose:

Cp ={USL LSL}/6 istermedtheprocesscapabilityindex,whereUSLdenotestheupperspecificationlimitandLSLdenotesthelowerspecificationlimit. Cp >>1meansgoodprocesscapability.Cp

Cp =1mightseemliketherewouldbelittlescrap.Butthatwouldonlybethecaseiftheprocesswasperfectlycentered(i.e.,themeanliesexactlyhalfwaybetweenLSLandUSL).

Toallowforthefactthataprocessmightnotbewellcentered,anewmetricwasdeveloped:

Cpk =Min{(LSL)/3,(USL)/3 }iscalledtheprocessperformanceindex.

Cpk >1indicatesthemeanismorethan3 awayfromthenearestspeclimit,i.e.,thereislittleornoscrap.

9/11/2014 10RobLeachmanIntrotoSixSigma

Itisfoundinpracticethattheprocessmeanisoftennotstationarybuttendstodrift overtime.

ThusCpk =1doesnotimplyqualityisreallygreat,becauseiftheprocessdriftsunfavorablywewillstartgettingscrap.

AcommonindustrygoalistoraiseCpk forallimportantprocessparameterstoatleast1.5,i.e.,thenearestspeclimitshouldbeatleast4.5awayfromtheprocessmean.

9/11/2014 11RobLeachmanIntrotoSixSigma

Identifytheoccurrencesofprocessvariationandestablishcontainmentmeasures Addinspectionsormeasurements(e.g.,SPCcharts)todetectoutofcontrolexcursions

Engineerfixestoeliminaterootcausesofexcursions,OR:

Reengineertheproductsothatthespeclimitscanbewideryetthecustomerwillbejustashappy

9/11/2014 12RobLeachmanIntrotoSixSigma

DMAIC (forexistingprocesses) Definehighlevelgoalsanddefinetheexistingprocess. Measurekeyaspectsoftheprocessandsetupdatacollectionsystems.

Analyzethedatatoverifycauseandeffectrelationships.Determinethoserelationships.

Improveoroptimizetheprocessbasedonapplicationoftechniqueslikedesignofexperiments.

Controltoensurethatanydeviationsfromtargetsarecorrectedbeforetheyresultindefects.

9/11/2014 13RobLeachmanIntrotoSixSigma

DMADV (fornewproductsorprocesses) Definedesigngoalsconsistentwithcustomerdesiresandenterprisestrategy.

MeasureandidentifyCTQs(criticaltoqualitycharacteristics),productcapabilities,productionprocesscapability,andrisks.

Analyzetodevelopanddesignalternatives,createahighleveldesignandevaluatedesigncapabilitytoselectbestdesign.

Designdetails,optimizethedesign,andplanfordesignverification.(Mayrequiresimulation.)

Verifythedesign,setuppilotruns,implementtheproductionprocess,handovertoprocessowners.9/11/2014 14RobLeachmanIntrotoSixSigma

Statisticalprocesscontrolcharts(AKAShewartcontrolcharts,SPCcharts)

Ishikawadiagrams(AKAFishbonediagrams) Designofexperiments(DOE) Failuremodesandeffectsanalysis(FMEA) Faultdetectionandclassification(FDC) Regressionanalysis,Analysisofvariance Taguchimethods,TaguchiLossFunction Manyothers

9/11/2014 15RobLeachmanIntrotoSixSigma

Continuousprocessparameter Xbarchart trackmeanoffixedsizesamples LCL=,UCL= isprocessmean, isprocessstandarddeviation,nissamplesize

Rchart trackrangeoffiveunitsamples LCL=d3R,UCL=d4R,Risaveragerangeofsample,d3andd4areconstantsfromstatisticaltables

=R/d2,d2isconstantfromstatisticaltable (canusethisinXbarchart)

9/11/2014 RobLeachmanIntrotoSixSigma 16

n/3 n/3

Countableparameter(e.g.,particlesonwafer) Cchart LCL=,UCL= c istheaveragecountforafixedsizesample

9/11/2014 RobLeachmanIntrotoSixSigma 17

cc 3 cc 3

nppp /)1(3 nppp /)1(3

Binaryparameter(e.g.,goodornotgood) Pchart

LCL=,UCL= pistheaveragefractionbad,nisthesamplesize

1930s ShewhartinventscontrolchartsatBellLabsandimplementstheminWesternElectric(AT&Tsmanufacturingarm)

1940sWesternElectricandafewothersmakegooduseofSPC,butmostcompaniesresistit

1950s DeminggoestoJapan;SPCisembracedthere

1970s&1980s ManyAmericanindustriesaredecimatedbyJapanesecompetition

1980s&1990sTQMand6movementsinUSA9/11/2014 RobLeachmanIntrotoSixSigma 18

Introducequalitymanagementprofessionalsthatcutacrosstraditionaldept.boundaries ExecutiveLeadership definevision,empowerroleholderswithfreedomandresources

Champions responsibleforimplementation,mentortheBlackBelts

MasterBlackBelt Fulltime,inhousecoaches,ensureconsistentapplicationacrossfunctionsanddepartments

BlackBelt Fulltime,applymethodologytospecificprojects

GreenBelt handleimplementationunderguidanceofBlackBeltsalongwithotherjobduties

YellowBelt trainedinbasicapplicationoftools,workwithBlackBelts,closesttothework9/11/2014 19RobLeachmanIntrotoSixSigma

Fortheperiod1986 2006,MotorolaclaimsitsSixSigmaprogramsachieved$17billioninsavings.

Startinginthe1990s,GeneralElectricunderJackWelchbecameastrongdiscipleofSixSigma,andGEclaimsmajorsuccessesfromit. Subsequently,SixSigmabecameamanagementcraze.Success

atothercompanieshasbeenmixed.

SixSigmaisnotapanacea. Itisnosubstituteforinventingandmarketinggreatproducts. Itisanincrementalimprovementonpreviousqualitytheories.

Ontheotherhand,thereisnosubstituteforgreatquality,andthemethodologiesembracedbySixSigmaembodythebestknowledgewehaveonthesubject.

9/11/2014 RobLeachmanIntrotoSixSigma 20

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