sc统计制程管制培训教案

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StatisticalProcessControl

統計製程管制3

ChapterOutline概述StatisticalThinkingandStatisticalMethods統計思維與統計方法StatisticalProcessControl(SPC)統計製程管制Typesofdata資料型態Constructingcontrolcharts如何架構管制圖Interpretingcontrolcharts管制圖之說明Processcapability製程能力Acceptancesampling允收水準Inspectionprocess檢驗程序Qualitymeasures品質的量測Samplingvs.screening抽樣與篩選4

Process製程Variation變異Data資料StatisticalTools統計方法StatisticalThinking統計思維StatisticalMethods統計方法StatisticalThinkingand

StatisticalMethods

統計思維與統計方法

5

StatisticalThinking

統計思維KeyConcepts主要觀念

Processandsystemsthinking製程與系統的思維Variation變異Analysisincreasesknowledge分析可以增加知識Takingaction可以採取行動Improvement可以用來改善RoleofData資料的角色Quantifyvariation量化的變異(變動)Measureeffects量測的效應6

“Youcan’timproveaprocessthatyoudon’tunderstand”

你若對製程不懂,就無法改善製程WithoutaProcessView

若無製程的觀點Peoplehaveproblemsunderstandingtheproblemandtheirroleinitssolution(turf).吾人在其問題的理解與對策執行的角色扮演上會有問題Itisdifficulttodefinethescopeoftheproblem.難以定義問題範圍Itisdifficulttogettorootcauses.難以找到真正的要因Peoplegetblamedwhentheprocessistheproblem(80/20Rule).吾人在當製程是真正問題時,會遭到責備Processmanagementisineffective製程管理沒有效果Improvementisslowed改善緩慢7

WithoutUnderstandingVariation若不了解其變異Managementbythelastdatapoint永遠是用最後的資料作管理(永遠在頭痛醫頭,腳痛一腳,沒有源頭置根本的觀念)There’slotsoffirefighting火災不斷Usingspecialcausemethodstosolvecommoncauseproblems用特別的方法處理共同要因的(一般性)問題Tamperingandmicromanagingabound修改與小事的管理老是存在Goalsandmethodstoattainthemfail目標與方法無法達成Understandingtheprocessishandicapped只知道製程是個問題

Learningisslowed學習慢Processmanagementisineffective製程管理沒有效果Improvementisslowed改善慢8

WithoutData

若是手上沒有資料Everyoneisanexpert:每個人都是專家Discussionsproducemoreheatthanlight討論不斷Historicalmemoryispoor歷史的記憶模糊Difficulttogetagreementon:難以得到協議若Whattheproblemis無法得知問題是什麼Whatsuccesslookslike無法得知其成果將如何Progressmade或由哪一製程所產出Processmanagementisineffective製程管理是無效的Improvementisslowed改善慢9

“Earlyon,wefailedtofocusadequatelyoncoreworkprocessesandstatistics.”

初期若核心工作製程與統計無法適當集中,其結果…

WithoutStatisticalThinking

若無製程統計的思維Yourmanagementandimprovementprocessesarehandicapped吾人的管理與改善將有障礙It’slike其像Footballwithoutapassingattack足球未經核准即攻擊Growingalawnwithoutfertilizer草地未經施肥Doingresearchwithoutmeasurements研究未做量測資料Playinggolfwithoutyourirons不用自己的球竿打高爾書球10

SECURESTOREKITLoadProgramLoadPick/PlaceLoadReflowProfileLoadStencilScreenSolderPastePartsSMTPlacementI/RReFlowCleanPEMParts(ASIC,ADC,DAC)Placement&HandSolderCleanSecondLevelAssy.Touch-upsolderjointsMechanicalInstallationsStaking/BondingCleanElectricalFunctionalTestCleanBakeConformalCoatPostTestInspectionAcceptanceTestElectricalControlledStorageInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointThrough-holeandPlasticPartsPreparationTinComponentsForm&CutAxialLeadsThrough-holeComponentPlacement&HandSolderClean&InspectionCheckpointPWBPreparation:CleanInkStampBakeProductionOperationInspectionOperationTestOperationMaterialControlOperationKEYManufacturingFlowDiagramofPWBAssemblyPWB組裝之製造流程圖11SECURESTOREKITLoadProgramLoadPick/PlaceLoadReflowProfileLoadStencilScreenSolderPastePartsSMTPlacementI/RReFlowCleanPEMParts(ASIC,ADC,DAC)Placement&HandSolderCleanSecondLevelAssy.Touch-upsolderjointsMechanicalInstallationsStaking/BondingCleanElectricalFunctionalTestCleanBakeConformalCoatPostTestInspectionAcceptanceTestElectricalControlledStorageInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointInspectionCheckpointThrough-holeandPlasticPartsPreparationTinComponentsForm&CutAxialLeadsThrough-holeComponentPlacement&HandSolderClean&InspectionCheckpointPWBPreparation:CleanInkStampBakeProductionOperationInspectionOperationTestOperationMaterialControlOperationKEYManufacturingFlowDiagramofPWBAssemblyPWB組裝之製製造流程程圖12Dependsonlevelsofactivityandjobresponsibility.依據活動動的層級級與工作作執掌Wherewe'reheaded我們朝何何方Managerialprocessestoguideus用管理的的程序來來指導我我們WheretheworkgetsDone讓所需的的工作被被執行完完成Strategic策略上的的Managerial管理上的的Operational作業性的的Executives高階決策策層Managers經理階層層Workers現場員工工UseofStatisticalThinking運用統計計思維13Executivesusesystemsapproach.決策者運運用系統統導向策策略Coreprocesseshavebeenflowcharted主要程序序已被流流程圖表表化Strategicdirectiondefinedanddeployed.策略方向向的訂定定與展開開Measurementsystemsinplace.適當的量量測系統統Employee,customer,andbenchmarkingstudiesareusedtodriveimprovement.是以員工工,客戶與benchmarking的研究被被用來主主導改善善Experimentationisencouraged.鼓勵實驗驗StatisticalThinkingattheStrategicLevel決策者之之統計思思維14.Managersusemeetingmanagementtechniques經理利用用會議管管理技巧巧Standardizedprojectmanagementsystemsareinplace.適當的標標準化專專案管理理系統Bothprojectprocessandresultsarereviewed.此專案的的流程與與結果已已被審核核Processvariationisconsideredwhensettinggoals.當設定目目標時,流程的變變異已被被考慮Measurementisviewedasaprocess.量測點被被視為一一個流程程Thenumberofsuppliersisreduced供應者數數目減少少Avarietyofcommunicationmediaareused.廣泛的傳傳訊媒體體被採用用StatisticalThinkingattheManagerialLevel經理階層層統計思思維15Workprocessesareflowcharted&documented工作程序序已被流流程圖表表化與書書面化Keymeasurementsareidentified.主要量測測點已被被確認Timeplotsdisplayed時間的圖圖示被展展現Processmanagementandimprovementutilize:製程管理理與改善善採用Knowledgeofvariation,and變異觀念念的知識識及Dataanalysis資料分析析Improvementactivitiesfocusontheprocess,notblamingemployees.改善工具具著重於於製程,而非責備備員工StatisticalThinkingattheOperationalLevel現場員工工的統計計思維範範例16StatisticalThinkingattheOperationalLevel現場員工工的統計計思維範範例ARecentExperience最近的經經驗Hugequantitiesofdata大量的資資料Limitedunderstandingofstructure在有限度度理解的的結構上上Consultantsappliedartificialneuralnets顧問群運運用人工工神經網網狀系統統Didn’twork但不成功功17StatisticalThinkingattheOperationalLevel現場員工工的統計計思維範範例ARecentExperience最近的經經驗ArtificialNeuralNetsapplynicelyinmanysituations(NISTExamples):人工神經經網狀系系統出色色地運用用於許多多領域:OpticalCharacterRecognition光學文字字辨識系系統FingerPrinting指紋辨識識FacePrintingfortheFBI相貌辨識識Example等案例上上18….But,但Unlessyousampletheprocesstakingtherightamountoftherightkindofdata(rationalsubgroups)youwillneverapproachprocessunderstanding.在抽驗的的流(製)程裡若你你無法取取得正確確的數量量與資料料(合理的樣樣組),你將無法法深入了了解此一一流(製)程Withoutprocessunderstanding,thereisnoprocesscontrol.流(製)程若不了了解,就無所謂謂的流(製)程管制19KeyLearningsfromStatisticalThinkingEfforts由統計思思維的努努力中,吾人學到到的要點點Statisticiansdon’tunderstandStatisticalThinkingaswellastheythinktheydo.統計的思思維不僅僅要懂而而且也要要會做Thosewhodounderstandithavelimitedaccesstomanagerialandstrategiclevels.真正了解統統計思維的的人,在管理與決決策上之能能力較少受受限制There’smuchmoreworktobedone.較多的事能能被完成Spreadtheword口令的展開開Focusonprocess著重製程QualityCharacteristics品質特性Variables計量值Characteristicsthatyoumeasure,e.g.,weight,length其特性可被被量測而得得,如重量,長度等Maybeinwholeorinfractionalnumbers可以以整數數或分數表表達Continuousrandomvariables連續的隨機機變數Attributes計數值Characteristicsforwhichyoufocusondefects其特性著重重於缺點Classifyproductsaseither‘‘good’or‘bad’,orcount#defects以產品的好好.壞,缺點數量來來看e.g.,radioworksornot如收音機是是否可以播播放Categoricalordiscreterandomvariables屬不連續的的雖機變數數21TypesOfData資料型態Attributedata計數資料Productcharacteristicevaluatedwithadiscretechoice產品資料特特性以離散散的評估方方式選定Good/bad,yes/no良品/不良品,好/壞Variabledata計量資料Productcharacteristicthatcanbemeasured產品特性能能被量測而而得Length,size,weight,height,time,velocity長度,大小,重量,高度,時間,,速度TypesofVariations變異型態CommonCause共同原因Random隨機Chronic長期的Small影響小Systemproblems系統問題Mgtcontrollable管理上的控控制Processimprovement製程改善Processcapability製程能力SpecialCause特殊原因Situational局部Sporadic偶而發生Large影響大Localproblems局部問題Locallycontrollable可局部控制制Processcontrol製程管制Processstability製程的穩定定性StatisticalProcessControl統計製程管管制Statisticaltechniqueusedtoensureprocessismakingproducttostandard統計技術用用於確保製製程所製出出的產品合合乎標準Allprocessaresubjecttovariability所有製程受受變異性所所支配NaturalorCommoncauses自然或共同同原因:Randomvariations隨機變異如如設備損耗耗Assignablecauses特殊原因:Correctableproblems可改善的問問題Machinewear,unskilledworkers,poormaterial如生手,材料不良…Objective:Identifyassignablecauses目標:確認特殊原原因Usesprocesscontrolcharts利用管制圖圖表24CausesofVariation變異的原因因Inherenttoprocess固有製程Random隨機Cannotbecontrolled不可控Cannotbeprevented無法預防Examples如:Weather氣候accuracyofmeasurements量測精度capabilityofmachine設備能力Exogenoustoprocess外來因子影影響製程Notrandom非隨機Controllable可控Preventable可預防Examples如toolwear工具磨耗“Monday”effect週一效應poormaintenance維護差CommonCauses共同原因AssignableCauses特殊原因Whatpreventsperfection?Processvariation...何事阻礙完完美?製程變異…ProductSpecificationandProcessVariation產品規格與與品變異Productspecification產品規格desiredrangeofproductattribute產品屬性之之期望範圍圍partofproductdesign產品設計的的一部份length,weight,thickness,color,……長度,重量,厚度,顏色…等nominalspecification(公稱規規格)upperandlowerspecificationlimits(規格上上下限限)Processvariability製程變變異inherentvariationinprocesses製程中中固有有的變變異limitswhatcanactuallybeachieved其實際際能被被達成成之界界限值值definesandlimitsprocesscapability定義並並限制制製程程能力力Processmaynotbecapableofmeetingspecification!製程是是有可可能無無法達達到規規格的的要求求!26Grams(a)LocationAverage(平平均值值)CommonCauses共同原原因27(a)LocationGramsAverageAssignableCauses特殊原原因28-3s-2s-1s+1s+2s+3sMean平均值68.26%95.44%99.74%=Standarddeviation=標準差差TheNormalDistribution常態分分配29Mean平均值值CentralLimitTheoremStandarddeviation樣本標標準差差TheoreticalBasisofControlCharts30UCL管制規規格上上限Nominal中心線線LCL管制規規格下下限123SamplesControlCharts管制圖圖31123SamplesControlCharts管制圖圖UCL管制規格上限Nominal中心線LCL管制規格下限32Assignablecauseslikely可能的的特殊殊原因因123SamplesControlCharts管制圖圖UCL管制規格上限Nominal中心線LCL管制規格下限33ProcessControl:ThreeTypesofProcessOutputs製程管管制的的三種種顯示示型態態FrequencyLowercontrollimitSizeWeight,length,speed,etc.Uppercontrollimit(b)Instatisticalcontrol,butnotcapableofproducingwithincontrollimits.Aprocessincontrol

(onlynaturalcausesofvariationarepresent)

butnotcapableofproducingwithinthespecifiedcontrollimits;

共同原因變異and(c)Outofcontrol.Aprocessoutofcontrolhaving

assignablecauses

ofvariation.特殊原因變異Instatisticalcontrolandcapableofproducingwithincontrollimits.Aprocesswithonlynaturalcausesofvariationandcapableofproducingwithinthespecifiedcontrollimits.正常型34TheRelationshipBetweenPopulationandSamplingDistributions群體與與樣本本間之之關係係UniformNormalBetaDistributionofsamplemeans樣本平均值分配Standarddeviationofthesamplemeans(mean)Threepopulationdistributions群體分配35VisualizingChanceCauses機遇原原因之之觀察察TargetAtafixedpointintime固定時時間TimeTargetOvertime連續時時間Thinkofamanufacturingprocessproducingdistinctpartswithmeasurablecharacteristics.Thesemeasurementsvarybecauseofmaterials,machines,operators,etc.Thesesourcesmakeupchancecausesofvariation.製造各各零件件之量量測特特性會會因4M等機遇遇原因因而發發生變變異36ProcessControlCharts製程管管制圖圖37Control

Charts

Variables

Charts

Attributes

Charts

Continuous連續的NumericalDataCategoricalorDiscrete離散的NumericalDataControlChartTypes管制圖圖型態態計量計數38ControlChartSelection管制圖圖的選選定QualityCharacteristicvariableattributen>1?n>=10orcomputer?xandMRnoyesxandsxandRnoyesdefectivedefectconstantsamplesize?p-chartwithvariablesamplesizenopornpyesconstantsamplingunit?cuyesno39ProduceGoodProvideServiceStopProcessYesNoAssign.Causes?TakeSampleInspectSampleFindOutWhyCreateControlChartStartStatisticalProcessControlSteps統計製製程管管制控控制步步驟40StatisticalThinkingisaphilosophyoflearningandActionbasedonthefollowingfundamentalprinciples:統計計思思維維哲哲學學之之學學習習與與行行動動基基於於以以下下原原則則Allworkoccursinasystemofinterconnectedprocesses,Variationexistsinallprocesses,andUnderstandingandreducingvariationarekeystosuccess.所有有工工作作的的產產生生源源於於系系統統互互相相連連結結之之製製程程,而變變異異存存在在於於所所有有製製程程,了解解並並降降低低製製程程的的變變異異是是成成功功的的關關鍵鍵41UsingControlCharts如何何使使用用管管制制圖圖1)Selecttheprocesstobecharted選擇擇需需要要被被圖圖表表化化之之製製程程2)Get20-25groupsofsamples選擇擇樣樣組組及及樣樣本本大大小小(usually5-20pergroupforXandR-chartorn≥≥50forp-chart)3)ConstructtheControlChart建立立管管制制圖圖4)Analyzethedatarelativetothecontrollimits.Pointsoutsideofthelimitsshouldbeexplained分析析關關聯聯於於管管制制界界線線之之資資料料,點超超出出界界限限需需能能被被解解釋釋5)Oncetheyareexplained,eliminatethemfromthedataandrecalculatethecontrolchart一旦旦澄澄清清,消除除異異常常點點及及原原因因,並重重算算管管制制圖圖資資料料6)Usethechartfornewdata,butDONOTrecalculatethecontrollimits利用用此此新新資資料料,但無無須須重重算算管管制制界界限限`XChart平均均值值管管制制圖圖Typeofvariablescontrolchart計量量管管制制圖圖Intervalorratioscalednumericaldata間距距或或比比率率量量測測數數字字資資料料Showssamplemeansovertime算出出樣樣本本平平均均值值Monitorsprocessaverage間控控製製程程平平均均數數Example:Measure5samplesofsolderpaste&computemeansofsamples;Plot如計計算算錫錫膏膏厚厚度度之之平平均均值值,再點點圖圖43BasicProbabilitiesConcerningtheDistributionofSampleMeans有關關樣樣本本平平均均數數之之機機率率分分佈佈Std.dev.ofthesamplemeans樣本平均數標準差:44EstimationofMeanandStd.Dev.oftheUnderlyingProcess在製製程程控控制制之之下下之之平平均均值值與與標標準準差差估估計計usehistoricaldatatakenfromtheprocesswhenitwas““known””tobeincontrol當製製程程穩穩定定時時,利用用過過去去所所產產生生之之歷歷史史資資料料usuallydataisintheformofsamples(preferablywithfixedsamplesize)takenatregularintervals樣本資資料是是在一一定間間隔的的時間間裡取取得processmeanmestimatedastheaverageofthesamplemeans(thegrandmeanornominalvalue)假設製製程平平均值值m與樣本本平均均值相相同processstandarddeviationsestimatedby:製程標標準差差s估算由由standarddeviationofallindividualsamples所有個個別值值樣本本之標標準差差ORmeanofsamplerangeR/d2,where或樣本本平均均值/d2samplerangeR=(Rmax-Rmin),d2=valuefromlook-uptable,全距為為R,d2可由查查表得得知,45X-barvs.Rcharts平均值值VS全距管管制圖圖Rchartsmonitorvariability:Isthevariabilityoftheprocessstableovertime?Dotheitemscomefromonedistribution?R管制圖圖監控控變異異性,是否整整個製製程處處於安安定狀狀態?有項目目超出出此一一分配配嗎?X-barchartsmonitorcentering(oncetheRchartisincontrol):Isthemeanstableovertime?X-Bar管制圖圖監控控中心心(一旦R管制圖圖處於於管制制狀態態):平均值值於爭爭個製製程是是否穩穩定?>>BringtheR-chartundercontrol,thenlookatthex-barchart(先看R圖,再看Xbar圖)46HowtoConstructaControlChart如何建建立管管制圖圖1.Takesamplesandmeasurethem.取樣量量測2.Foreachsubgroup,calculatethesampleaverageandrange.每個群群組,計算平平均值值與全全距3.Settrialcenterlineandcontrollimits.製作解解析用用管制制圖之之中心心線與與管制制界限限4.PlottheRchart.Removeout-of-controlpointsandrevisecontrollimits.畫R圖,移除異異常點點,再修正正管制制界限限5.Plotx-barchart.Removeout-of-controlpointsandrevisecontrollimits.畫R圖,移除異異常點點,再修正正管制制界限限6.Implement-sampleandplotpointsatstandardintervals.Monitorthechart.管制用用管制制圖,於標準準間隔隔時間間取樣樣,監控此此管制制圖47Type1andType2Error第一種種與第第二種種錯誤誤AlarmNoAlarmIn-Control管制內內Out-of-Control失控48CommonTeststoDetermineiftheProcessisOutofControl管制圖圖異常常之判判定Onepointoutsideofeithercontrollimit一點超超出管管制界界線2outof3pointsbeyondUCL-2sigma3點有2點在2個標準準差或或以外外7successivepointsonsamesideofthecentralline連續7點在中中心線線之同同一側側of11successivepoints,atleast10onthesamesideofthecentralline連續11點有10點在中中心線線之同同一側側of20successivepoints,atleast16onthesamesideofthecentralline連續20點有16點在中中心線線之同同一側側49Type1ErrorsfortheseTests第一種種錯誤誤TestProbabilityType1Error2/37/710/1116/201/12(0.00135)0.00270.0052(0.5)70.00780.005860.005950Type2Error第二種種錯誤誤Supposem1>mType2Error=whereF(z)denotesthethecumulativeprobabilityofastandardnormalvariateatzPower=1-Type2Error.Powerincreasesas……nincreases,as(m1-m)increases,andassdecreases.Extensiontom1<misstraightforward51`XChartControlLimitsSampleRangeatTimei#SamplesSampleMeanatTimeiFromTable52FactorsforComputingControlChartLimits管制圖圖之係係數表表TableRChart全距管管制圖圖Typeofvariablescontrolchart計量管管制圖圖Intervalorratioscalednumericaldata間距或或比率率量測測數字字資料料ShowssamplerangesovertimeDifferencebetweensmallest&largestvaluesininspectionsample樣本中中最大大值與與最小小值之之差Monitorsvariabilityinprocess間控製製程變變異性性Example:CalculateRangeofsamplesofsolderpaste;Plot計算全距距並點圖圖54SampleRangeatTimei某時間間間隔之全全距Samplessize樣本大小小FromTable查表RChartControlLimitsR管制圖管管制界限限公式SettingupaX-BARRChart建立X-barR管制圖Takeabout20-25samplegroups(n)oftheprocessresult.Eachsampleshouldcontain4or5observations.Foreachsamplecalculatetheaverageandtherange.Averageallthesampleaverages=X-BAR.Averageallthesampleranges=R-BAR.Calculatetheupper&lowercontrollimitforX-BARCalculatetheupper&lowercontrollimitforR-BARUsingans-ChartInsteadofanR-Chart利用標準準差圖取取代R管制圖S-Chartsareusedwhen:Tightcontrolofprocessvariationisessential.Samplesizeequals10ormore.acomputercanbeusedtosimplify&speedupcalculations.Formulas:ControlLimitsfors-ChartControlLimitsforX-barChart57Example:Thefirst20dayssamplesareasfollows:58UCLLCLX-barChartIstheprocessincontrol?Arethespecificationsbeingmet?Howcanwetellifthevariabilityisincontrol?59R-ChartTheRchartmeasuresthechangeinthespreadovertime.PlotR,therangeforeachsample.LowerControlLimit=UpperControlLimit=UCLLCL60Ex:Control““Commutingtimes”Step1CommutingTimes(min.)-A.M.WEEKMinutesXbar=R=Step2Step3X=74.6R=36n=5UCLL=X+A2*R=74.6+(.58)*(36)=95.48LCLL=X-A2*R=74.6-20.88=53.72UCLR=D4*R=(2.11)*(36.0)=75.96LCLR=D3*R=061Control“Commutingtimes””(cont.)step4Commutingtimes-A.M.UCL=95.48Xbarbar=74.6LCL=53.72XbarChart110234567895010075RChartUCL=75.96Rbar=36.0LCL=0110234567897553562FigurepChart不良率管管制圖Typeofattributescontrolchart計數管制制圖Nominallyscaledcategoricaldata以絕對資資料分類類e.g.,good-bad如好,壞Shows%ofnonconformingitems顯示不合合格項目目%Example:Count#defectivechairs÷bytotalchairsinspected;Plot計算椅子子的不良良數除以以椅子總總檢驗數數,點圖Chairiseitherdefectiveornotdefective椅子只有有好與壞壞兩種SettingupapChart建立p管制圖Takeabout20-25samplesoftheprocessresult.EachsampleshouldbelargeenoughtocontainATLEAST1badobservation.OftenforP-Chartssamplessizesareinexcessof100.Foreachsamplecalculatethepercentageofbadunits.Averageallthesamplepercentagestogether,thisisP-BAR.Calculatetheupper&lowercontrollimitfortheP-BARchartusingthefollowingformulas:65pChartControlLimits不良率管管制圖管管制界限限#DefectiveItemsinSampleiSizeofsampleiIfindividualsamplesarewithin25%oftheaveragesamplesizethencontrollimitscanbecalculatedusingtheaveragesamplesize:z=2for95.5%limits;z=3for99.7%limitsIfsamplesizesvarybymorethan25%oftheaveragesamplesizethencontrollimitsshouldbecomputedforeachsample.66Example:p-ChartM&MMarswantstoinstituteastatisticalprocesscontrolonanewcandybar.Inordertodoso,everyshifttheysample50barsanddeterminethenumberofdefectiveones.Theyobtainthefollowingdata:6720groupsof50=1000samplesTotaldefective=170p-bar=0.17UCL=0.17+3x0.053=0.329LCL=0.17-3x0.053=0.010Plottingthe%defectiveshows:68IdentifyingSpecialCauses確認認特特殊殊要要因因Itappearsthatshifts4,7and12wereoutofcontrol.Uponfurtherinspectionitappearsthattoomuchwaterwasaddedtotheprocessinshifts4and7andthatinshift12anewoperatorstarted.Sinceeachoftheoutofcontrolpointshaveassignablecauses,weeliminatethemfromthedata.Thenewcontrolchartisthen:69Nowitappearsthatshift15isout-of-control.Furthercheckingshowsthatthetemperaturewassettoohighduringthisshift.Therefore,wewanttoeliminatethispointsothatinsubsequenttestswecanidentifywhenthisoccurs.Ifweeliminatethispointthenewcontrolchartis:IdentifyingSpecialCauses70FinalpChartUCL=0.122+3x0.046=0.260LCL=0.122-3x0.046=-0.016=0.0(negativecontrollimitsshouldbesetto0)Nowtheyshouldusethischartforallsubsequentsamplinguntiltheprocesschanges71DeterminingifYourProcessis““OutofControl”決定你的製製程是否在在穩定狀態態EstablishregionsA,B,andCasone,two,andthreesOneormorepointsfalloutsidethecontrollimits.2outof3consecutivepointsfallinthesameregionA4outof5consecutivepointsfallinthesameregionAorB6consecutivepointsincreasingordecreasing9consecutivepointsonthesamesideoftheaverage.14consecutivepointsalternatingupanddown15consecutivepointswithinregionC.ABCABCUsingannpChart建立不良數數管制圖Npchartsfornumberofnonconformingunits.以不合格品品之數統計計Convertedfrombasicp-chart由p管制圖演變變而來Multiplypbysamplesize(n).不良率乘以以樣本大小小Formulas:Settingupacchart建立缺點數數管制圖Takeabout20-25samplesfromtheprocess.Eachsamplecontains1unit.Foreachunitcountthenumberofoccurrencesfortheobservationofinterest.Calculatetheaveragenumberofoccurrencesperunit.ThisisC-BAR.Calculatetheupper&lowercontrollimitfortheC-BARchartusingthefollowingformulas:UsinganuChart建立單位缺缺點數管制制圖Auchartisusedwhentheunitsizeinspectedfordefectsisnotconstant.Inthesecasestheunitisoftenreferredtoasanareaofopportunity(ni).Theaverageoccurrenceperareaofopportunity(i.e.thecenterline)iscalculatedas:Thesame25%variationrulediscussedforp-chartsapplieshereaswell.Controllimitsarecalculatedas:75Figure76425GramsMean平均均值值ProcessDistribution製程程分分配配Distributionofsamplemeans樣本本平平均均值值分分配配SampleMeansandtheProcessDistribution樣本本平平均均值值與與製製程程分分配配77ProcessCapability製程程能能力力µ,Nominalvalue80010001200HoursUpperspecificationLowerspecificationProcessdistribution(a)Processiscapable78ProcessCapability製程程能能力力LowerspecificationMeanUpperspecificationTwosigmaµ,Nominalvalue79ProcessCapability製程程能能力力LowerspecificationMeanUpperspecificationFoursigmaTwosigmaµ,Nominalvalue80ProcessCapability製程程能能力力LowerspecificationMeanUpperspecificationSixsigmaFoursigmaTwosigmaµ,Nominalvalue81ProcessCapability製程程能能力力CapableVerycapableNotcapableLSLUSLSpecProcessvariation82ProcessCapabilityCpk製程程能能力力指指數數Assumesthattheprocessis:undercontrolnormallydistributed假設製程為穩定且為常態分配Cpk=min(Cpu,Cpl)Cpu=(USL-µ)/3Cpl=(µ-LSL)/3Precision精密度Capability準確度83MeaningsofCpkMeasuresCpk量測測之之意意義義Cpk=negativenumberCpk=zeroCpk=between0and1Cpk=1Cpk>184StatisticalProcessControl––IdentifyandReduceProcessVariability統計計製製程程管管制制-確認認並並降降低低製製程程變變異異LowerspecificationlimitUpperspecificationlimit(a)Acceptancesampling(b)Statisticalprocesscontrol(c)cpk>185QualityControlApproaches品質質管管制制方方法法Statisticalprocesscontrol(SPC)統計計製製程程管管制制Monitorsproductionprocesstopreventpoorquality監控控產產品品製製程程以以預預防防不不良良品品質質Acceptancesampling允收收抽抽樣樣Inspectsrandomsampleofproductormaterialstodetermineifalotisacceptable隨機機抽抽樣樣檢檢驗驗產產品品或或物物料料以以決決定定此此批批是是否否允允收收86Samplingvs.Screening抽樣樣與與篩篩選選Sampling抽樣樣Whenyouinspectasubsetofthepopulation群體批中中檢查小小批ScreeningWhenyouinspectthewholepopulation群體批中中檢查全全數Thecostsconsideration成本的考考量,經濟的原原則AcceptanceSampling允收抽樣樣Accept/rejectentir