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Chapter14StatisticalApplicationsinQualityandProductivityManagementBusinessStatistics,AFirstCourse4thEditionChap14-1BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.LearningObjectivesInthischapter,youlearn:

ThebasicthemesofqualitymanagementandDeming’s14pointsThebasicaspectsofSixSigmaManagementHowtoconstructvariouscontrolchartsWhichcontrolchartstouseforaparticulartypeofdata2BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ChapterOverviewQualityManagementandToolsforImprovementDeming’s14PointsSixSigma?ManagementPhilosophyofQualityToolsforQualityImprovementControlChartspchartRchartXchart3BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TotalQualityManagementPrimaryfocusisonprocessimprovementMostvariationinaprocessisduetothesystem,nottheindividualTeamworkisintegraltoqualitymanagementCustomersatisfactionisaprimarygoalOrganizationtransformationisnecessaryFearmustberemovedfromorganizationsHigherqualitycostsless,notmore4BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.1.Createaconstancyofpurposetowardimprovement

becomemorecompetitive,stayinbusiness,andprovidejobs2.AdoptthenewphilosophyBettertoimprovenowthantoreacttoproblemslater3.Stopdependingoninspectiontoachievequality--buildinqualityfromthestartInspectiontofinddefectsattheendofproductionistoolate4.StopawardingcontractsonthebasisoflowbidsBettertobuildlong-runpurchaser/supplierrelationshipsDeming’s14Points5BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.5.Improvethesystemcontinuouslytoimprovequalityandthusconstantlyreducecosts6.InstitutetrainingonthejobWorkersandmanagersmustknowthedifferencebetweencommoncauseandspecialcausevariation7.InstituteleadershipKnowthedifferencebetweenleadershipandsupervision8.Driveoutfearsothateveryonemayworkeffectively.9.Breakdownbarriersbetweendepartmentssothatpeoplecanworkasateam.(continued)Deming’s14Points6BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.10.Eliminateslogansandtargetsfortheworkforce

Theycancreateadversarialrelationships11.Eliminatequotasandmanagementbynumericalgoals12.Removebarrierstoprideofworkmanship13.Instituteavigorousprogramofeducationandself-improvement14.Makethetransformationeveryone’sjob(continued)Deming’s14Points7BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TheShewhart-DemingCycleTheShewhart-DemingCycleThekeyisacontinuouscycleofimprovementActPlanDoStudy8BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.SixSigmaManagementAmethodforbreakingaprocessintoaseriesofsteps:ThegoalistoreducedefectsandproducenearperfectresultsTheSixSigmaapproachallowsforashiftofasmuchas1.5standarddeviations,soisessentiallya±4.5standarddeviationgoalThemeanofanormaldistribution±4.5standarddeviationsincludesallbut3.4outofamillion9BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TheSixSigmaDMAICModelDMAICrepresentsDefine--definetheproblemtobesolved;listcosts,benefits,andimpacttocustomerMeasure–needconsistentmeasurementsforeachCritical-to-QualitycharacteristicAnalyze–findtherootcausesofdefectsImprove–useexperimentstodetermineimportanceofeachCritical-to-QualityvariableControl–maintaingainsthathavebeenmade10BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TheoryofControlChartsAprocessisarepeatableseriesofstepsleadingtoaspecificgoal

ControlChartsareusedtomonitorvariationinameasuredvaluefromaprocessInherentvariationreferstoprocessvariationthatexistsnaturally.Thisvariationcanbereducedbutnoteliminated11BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TheoryofControlChartsControlchartsindicatewhenchangesindataaredueto:SpecialorassignablecausesFluctuationsnotinherenttoaprocessRepresentsproblemstobecorrectedDataoutsidecontrollimitsortrendChanceorcommoncausesInherentrandomvariationsConsistofnumeroussmallcausesofrandomvariability(continued)12BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ProcessVariationTotalProcessVariationCommonCauseVariationSpecialCauseVariation=+Variationisnatural;inherentintheworldaroundusNotwoproductsorserviceexperiencesareexactlythesameWithafineenoughgauge,allthingscanbeseentodiffer13BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TotalProcessVariationTotalProcessVariationCommonCauseVariationSpecialCauseVariation=+PeopleMachinesMaterialsMethodsMeasurementEnvironmentVariationisoftenduetodifferencesin:14BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.CommonCauseVariationTotalProcessVariationCommonCauseVariationSpecialCauseVariation=+Commoncausevariation

naturallyoccurringandexpectedtheresultofnormalvariationinmaterials,tools,machines,operators,andtheenvironment15BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.SpecialCauseVariationTotalProcessVariationCommonCauseVariationSpecialCauseVariation=+Specialcausevariationabnormalorunexpectedvariationhasanassignablecausevariationbeyondwhatisconsideredinherenttotheprocess

16BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ProcessMeanControlLimitsUCL=ProcessMean+3StandardDeviations

LCL=ProcessMean–3StandardDeviationsUCLLCL+3σ-

3σtimeFormingtheUppercontrollimit(UCL)andtheLowercontrollimit(LCL):17BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ProcessMeanControlChartBasicsUCL=ProcessMean+3StandardDeviations

LCL=ProcessMean–3StandardDeviationsUCLLCL+3σ-

3σCommonCauseVariation:rangeofexpectedvariabilitySpecialCauseVariation:Rangeofunexpectedvariabilitytime18BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ProcessMeanProcessVariabilityUCL=ProcessMean+3StandardDeviations

LCL=ProcessMean–3StandardDeviationsUCLLCL±3σ→99.7%ofprocessvaluesshouldbeinthisrangetimeSpecialCauseofVariation:Ameasurementthisfarfromtheprocessmeanisveryunlikelyifonlyexpectedvariationispresent19BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.UsingControlChartsControlChartsareusedtocheckforprocesscontrol H0:Theprocessisincontroli.e.,variationisonlyduetocommoncauses H1:Theprocessisoutofcontroli.e.,specialcausevariationexistsIftheprocessisfoundtobeoutofcontrol,stepsshouldbetakentofindandeliminatethespecialcausesofvariation20BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.In-controlProcessAprocessissaidtobeincontrolwhenthecontrolchartdoesnotindicateanyout-of-controlconditionContainsonlycommoncausesofvariationIfthecommoncausesofvariationissmall,thencontrolchartcanbeusedtomonitortheprocessIfthecommoncausesofvariationistoolarge,youneedtoaltertheprocess21BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ProcessInControlProcessincontrol:pointsarerandomlydistributedaroundthecenterlineandallpointsarewithinthecontrollimitsUCLLCLtimeProcessMean22BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ProcessNotinControlOut-of-controlconditions:Oneormorepointsoutsidecontrollimits8ormorepointsinarowononesideofthecenterline8ormorepointsmoving

inthesamedirection23BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ProcessNotinControlOneormorepointsoutsidecontrollimitsUCLLCLEightormorepointsinarowononesideofthecenterlineUCLLCLEightormorepointsmovinginthesamedirectionUCLLCLProcessMeanProcessMeanProcessMean24BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.Out-of-controlProcessesWhenthecontrolchartindicatesanout-of-controlcondition(apointoutsidethecontrollimitsorexhibitingtrend,forexample)ContainsbothcommoncausesofvariationandspecialcausesofvariationThespecialcausesofvariationmustbeidentifiedIfdetrimentaltothequality,specialcausesofvariationmustberemovedIfincreasesquality,specialcausesmustbeincorporatedintotheprocessdesign25BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.StatisticalProcessControlChartsStatisticalProcessControlChartsXchartandRchartUsedformeasurednumericdataUsedforproportions(attributedata)pchart26BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.pChartControlchartforproportionsIsanattributechartShowsproportionofnonconformingitemsExample--Computerchips:CountthenumberofdefectivechipsanddividebytotalchipsinspectedChipiseitherdefectiveornotdefectiveFindingadefectivechipcanbeclassifieda“success”27BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.pChartUsedwithequalorunequalsamplesizes(subgroups)overtimeUnequalsizesshouldnotdifferbymorethan±25%fromaveragesamplesizesEasiertodevelopwithequalsamplesizesShouldhavenp>5andn(1-p)>5(continued)28BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.CreatingapChartCalculatesubgroupproportionsGraphsubgroupproportionsComputeaverageproportionComputetheupperandlowercontrollimitsAddcenterlineandcontrollimitstograph29BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.pChartExampleSubgroupnumberSamplesizeNumberofsuccessesSampleProportion,ps123…150150150151217….1000.0800.1133…Averagesubgroupproportion

=

p30BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.AverageofSubgroupProportionsTheaverageofsubgroupproportions=

pwhere:pi=sampleproportion forsubgroupik=numberofsubgroups ofsizenwhere:

Xi=thenumberofnonconforming itemsinsamplei

ni=totalnumberofitems sampledinksamplesIfequalsamplesizes:Ifunequalsamplesizes:31BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ComputingControlLimitsTheupperandlowercontrollimitsforapchartareThestandarddeviationforthesubgroupproportionsisUCL=AverageProportion+3StandardDeviations

LCL=AverageProportion–3StandardDeviations32BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ComputingControlLimitsTheupperandlowercontrollimitsforthepchartare(continued)Proportionsarenevernegative,soifthecalculatedlowercontrollimitisnegative,setLCL=033BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.pChartExample

Youarethemanagerofa500-roomhotel.Youwanttoachievethehighestlevelofservice.Forsevendays,youcollectdataonthereadinessof200rooms.Istheprocessincontrol?34BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.pChartExample:

HotelData #Not

Day #Rooms Ready Proportion 1 200 16 0.080

2 200 7 0.035

3 200 21 0.105

4 200 17 0.085

5 200 25 0.125

6 200 19 0.095

7 200 16 0.08035BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.pChart

ControlLimitsSolution36BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.p=.0864pChart

ControlChartSolutionUCL=.1460LCL=.02680.000.050.100.151234567PDayIndividualpointsaredistributedaroundpwithoutanypattern.Theprocessisincontrol.Anyimprovementintheprocessmustcomefromreductionofcommon-causevariation,whichistheresponsibilityofmanagement.__37BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.UnderstandingProcessVariability:

RedBeadExperimentTheexperiment:Fromaboxwith20%redbeadsand80%whitebeads,have“workers”scoopout50beadsTelltheworkerstheirjobistogetwhitebeads10redbeadsoutof50(20%)istheexpectedvalue.Scoldworkerswhogetmorethan10,praiseworkerswhogetlessthan10Someworkerswillgetbetterovertime,somewillgetworse38BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.Moralsofthe

RedBeadExperimentVariationisaninherentpartofanyprocess.Thesystemisprimarilyresponsibleforworkerperformance.Onlymanagementcanchangethesystem.Someworkerswillalwaysbeaboveaverage,andsomewillbebelow.Settingunrealisticgoalsisdetrimentaltoafirm’swell-being.UCLLCLpproportionSubgroupnumber39BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.

RchartandXchartUsedformeasurednumericdatafromaprocessStartwithatleast20subgroupsofobservedvaluesSubgroupsusuallycontain3to6observationseachFortheprocesstobeincontrol,boththeRchartandtheX-barchartmustbeincontrol40BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.Example:SubgroupsProcessmeasurements:SubgroupmeasuresSubgroupnumberIndividualmeasurements(subgroupsize=4)Mean,XRange,R123…151217…171621…15918…111520…14.513.019.0…674…Meansubgroupmean

=

Meansubgrouprange=

R41BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TheRChartMonitorsdispersion(variability)inaprocess ThecharacteristicofinterestismeasuredonanumericalscaleIsavariablescontrol

chartShowsthesamplerangeovertimeRange=differencebetweensmallestandlargestvaluesinthesubgroup42BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.Findthemeanofthesubgroupranges(thecenterlineoftheRchart)ComputetheupperandlowercontrollimitsfortheRchartUselinestoshowthecenterandcontrollimitsontheRchartPlotthesuccessivesubgrouprangesasalinechartStepstocreateanRchart43BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.AverageofSubgroupRangesMeanofsubgroupranges:where:

Ri=ithsubgrouprange k=numberofsubgroups44BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.RChartControlLimitsTheupperandlowercontrollimitsforan Rchartarewhere: d2andd3aretakenfromthetable (AppendixTableE.10)forsubgroupsize=n45BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.RChartExample Youarethemanagerofa500-roomhotel.Youwanttoanalyzethetimeittakestodeliverluggagetotheroom.For7days,youcollectdataon5deliveriesperday.Isthevariationintheprocessincontrol?46BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.R

ChartExample:

SubgroupDataDaySubgroupSizeSubgroupMeanSubgroupRange123456755555555.326.594.895.704.077.346.793.854.273.282.993.615.044.2247BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.RChartCenterand

ControlLimitsD4andD3arefromTableE.10(n=5)48BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.RChart

ControlChartSolutionUCL=8.232024681234567MinutesDayLCL=0R=3.894_Conclusion:Variationisincontrol49BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.TheXChartShowsthemeansofsuccessivesubgroupsovertimeMonitorsprocessmeanMustbeprecededbyexaminationoftheRcharttomakesurethatthevariationintheprocessisincontrol50BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.Computethemeanofthesubgroupmeans(thecenterlineofthechart)ComputetheupperandlowercontrollimitsforthechartGraphthesubgroupmeansAddthecenterlineandcontrollimitstothegraphStepstocreateanXchart51BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.MeanofSubgroup

MeansMeanofsubgroupmeans:where: Xi=ithsubgroupmean k=numberofsubgroups52BusinessStatistics,AFirstCourse(4e)?2006Prentice-Hall,Inc.ComputingControlLimitsTheupperandlowercontrollimitsforanXchartaregenerallydefinedasUsetoestimatethestandarddeviation oftheprocessmean,whered2 isfromappendixTableE.10UCL=ProcessMean+3StandardDeviations

LCL=ProcessMean–3S