品質控制

(統計製程管制)余德成國立高雄海洋科技大學運籌管理系2007.5.13POM2007國立中山大學人力資源管理研究所Unit6大綱前言基本的控制模式TQCSPC抽樣方法品質管制方法More前言TQM失敗的原因管理有兩種連續改善基本的控制模式TQM失敗的原因連續改善Concepts如何連續改善?5-Why改善工具Concept-1Concept-2如何連續改善?5-Why?????改善工具魚骨圖基本的控制模式基本概念TQC戴明獎審查檢點表SPC統計製程管制(StatisticalProcessControl;SPC)統計思維(StatisticalThinking)品質特性(QualityCharacteristics)資料型態(TypesOfData)變異型態(TypesofVariations)統計方法(StatisticalMethods)抽樣方法(SamplingMethods)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Characteristicsforwhichyoufocusondefects其特性著重於缺點Classifyproductsaseither‘good’or‘bad’,orcount#defects以產品的好.壞,缺點數量來看e.g.,radioworksornot如收音機是否可以播放Categoricalordiscreterandomvariables屬不連續的雖機變數Attributes計數值Variables計量值Characteristicsthatyoumeasure,e.g.,weight,length其特性可被量測而得,如重量,長度等Maybeinwholeorinfractionalnumbers可以以整數或分數表達Continuousrandomvariables連續的隨機變數品質特性Attributedata計數資料Productcharacteristicevaluatedwithadiscretechoice產品資料特性以離散的評估方式選定Good/bad,yes/no良品/不良品,好/壞Variabledata計量資料Productcharacteristicthatcanbemeasured產品特性能被量測而得Length,size,weight,height,time,velocity

長度,大小,重量,高度,時間,,速度資料型態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Processcontrol製程管制Processstability製程的穩定性變異型態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...何事阻礙完美?製程變異…變異的原因Productspecification產品規格desiredrangeofproductattribute產品屬性之期望範圍partofproductdesign產品設計的一部份length,weight,thickness,color,…長度,重量,厚度,顏色…等nominalspecification(公稱規格)upperandlowerspecificationlimits(規格上下限)Processvariability製程變異inherentvariationinprocesses製程中固有的變異limitswhatcanactuallybeachieved其實際能被達成之界限值definesandlimitsprocesscapability定義並限制製程能力Processmaynotbecapableofmeetingspecification!製程是有可能無法達到規格的要求!產品規格與品變異Grams(a)LocationAverage(平均值)共同原因(a)LocationGramsAverage特殊原因統計方法統計圖表統計分配管制圖檢定迴歸讓資料說話….Know-why-3s-2s-1s+1s+2s+3sMean平均值68.26%95.44%99.74%=Standarddeviation=標準差TheNormalDistribution常態分配Mean平均值CentralLimitTheoremStandarddeviation樣本標準差TheoreticalBasisofControlChartsUCL管制規格上限Nominal中心線LCL管制規格下限123SamplesControlCharts管制圖123SamplesUCL管制規格上限管制圖Assignablecauseslikely可能的特殊原因123SamplesUCL管制規格上限Nominal中心線LCL管制規格下限管制圖FrequencyLowercontrollimitSizeWeight,length,speed,etc.Uppercontrollimit(b)Instatisticalcontrol,butnotcapableofproducingwithincontrollimits.Aprocessincontrol(onlynaturalcausesofvariationarepresent)butnotcapableofproducingwithinthespecifiedcontrollimits;共同原因變異and(c)Outofcontrol.Aprocessoutofcontrolhavingassignablecausesofvariation.特殊原因變異Instatisticalcontrolandcapableofproducingwithincontrollimits.Aprocesswithonlynaturalcausesofvariationandcapableofproducingwithinthespecifiedcontrollimits.正常型製程管制的三種顯示型態UniformNormalBetaDistributionofsamplemeans樣本平均值分配Standarddeviationofthesamplemeans(mean)Threepopulationdistributions群體分配群體與樣本間之關係TargetAtafixedpointintime固定時間TimeTargetOvertime連續時間Thinkofamanufacturingprocessproducingdistinctpartswithmeasurablecharacteristics.Thesemeasurementsvarybecauseofmaterials,machines,operators,etc.Thesesourcesmakeupchancecausesofvariation.製造各零件之量測特性會因4M等機遇原因而發生變異機遇原因之觀察ProcessControlCharts製程管制圖ControlChartsVariablesChartsAttributesChartsContinuous連續的NumericalDataCategoricalorDiscrete離散的NumericalData計量計數管制圖型態QualityCharacteristicvariableattributen>1?n>=10orcomputer?xandMRnoyesxandsxandRnoyesdefectivedefectconstantsamplesize?p-chartwithvariablesamplesizenopornpyesconstantsamplingunit?

cuyesno管制圖的選定ProduceGoodProvideServiceStopProcessYesNoAssign.Causes?TakeSampleInspectSampleFindOutWhyCreateControlChartStartStatisticalProcessControlSteps1)Selecttheprocesstobecharted選擇需要被圖表化之製程2)Get20-25groupsofsamples選擇樣組及樣本大小(usually5-20pergroupforXandR-chartorn≥50forp-chart)3)ConstructtheControlChart建立管制圖4)Analyzethedatarelativetothecontrollimits.Pointsoutsideofthelimitsshouldbeexplained分析關聯於管制界線之資料,點超出界限需能被解釋5)Oncetheyareexplained,eliminatethemfromthedataandrecalculatethecontrolchart一旦澄清,消除異常點及原因,並重算管制圖資料6)Usethechartfornewdata,butDONOTrecalculatethecontrollimits利用此新資料,但無須重算管制界限如何使用管制圖Typeofvariablescontrolchart計量管制圖Intervalorratioscalednumericaldata間距或比率量測數字資料Showssamplemeansovertime

算出樣本平均值Monitorsprocessaverage

間控製程平均數Example:Measure5samplesofsolderpaste&computemeansofsamples;Plot

如計算錫膏厚度之平均值,再點圖XChart平均值管制圖usehistoricaldatatakenfromtheprocesswhenitwas“known”tobeincontrol當製程穩定時,利用過去所產生之歷史資料usuallydataisintheformofsamples(preferablywithfixedsamplesize)takenatregularintervals樣本資料是在一定間隔的時間裡取得processmeanmestimatedastheaverageofthesamplemeans(thegrandmeanornominalvalue)假設製程平均值m與樣本平均值相同processstandarddeviationsestimatedby:製程標準差s估算由standarddeviationofallindividualsamples所有個別值樣本之標準差ORmeanofsamplerangeR/d2,where或樣本平均值/d2samplerangeR=(Rmax-Rmin),d2=valuefromlook-uptable,全距為R,d2可由查表得知,平均值與標準差估計Rchartsmonitorvariability:Isthevariabilityoftheprocessstableovertime?Dotheitemscomefromonedistribution?R管制圖監控變異性,是否整個製程處於安定狀態?有項目超出此一分配嗎?X-barchartsmonitorcentering(oncetheRchartisincontrol):Isthemeanstableovertime?X-Bar管制圖監控中心(一旦R管制圖處於管制狀態):平均值於爭個製程是否穩定?>>BringtheR-chartundercontrol,thenlookatthex-barchart(先看R圖,再看Xbar圖)X-barvs.Rcharts1.Takesamplesandmeasurethem.取樣量測2.Foreachsubgroup,calculatethesampleaverageandrange.每個群組,計算平均值與全距3.Settrialcenterlineandcontrollimits.製作解析用管制圖之中心線與管制界限4.PlottheRchart.Removeout-of-controlpointsandrevisecontrollimits.畫R圖,移除異常點,再修正管制界限5.Plotx-barchart.Removeout-of-controlpointsandrevisecontrollimits.畫R圖,移除異常點,再修正管制界限6.Implement-sampleandplotpointsatstandardintervals.Monitorthechart.管制用管制圖,於標準間隔時間取樣,監控此管制圖如何建立管制圖AlarmNoAlarmIn-Control管制內Out-of-Control失控Type1andType2ErrorOnepointoutsideofeithercontrollimit

一點超出管制界線2outof3pointsbeyondUCL-2sigma3點有2點在2個標準差或以外7successivepointsonsamesideofthecentralline

連續7點在中心線之同一側of11successivepoints,atleast10onthesamesideofthecentralline

連續11點有10點在中心線之同一側of20successivepoints,atleast16onthesamesideofthecentralline

連續20點有16點在中心線之同一側管制圖異常之判定

Test ProbabilityType1Error2/37/710/1116/201/12(0.00135)0.00270.0052(0.5)70.00780.005860.0059Type1ErrorsfortheseTestsSupposem1>mType2Error=

whereF(z)denotesthethecumulativeprobabilityofastandardnormalvariateatzPower=1-Type2Error.Powerincreasesas…nincreases,as(m1-m)increases,andassdecreases.Extensiontom1<misstraightforwardType2ErrorSampleRangeatTimei#SamplesSampleMeanatTimeiFrom

TableXChartControlLimits管制圖之係數表Typeofvariablescontrolchart計量管制圖Intervalorratioscalednumericaldata間距或比率量測數字資料ShowssamplerangesovertimeDifferencebetweensmallest&largestvaluesininspectionsample樣本中最大值與最小值之差Monitorsvariabilityinprocess間控製程變異性Example:CalculateRangeofsamplesofsolderpaste;Plot計算全距並點圖RChart全距管制圖SampleRangeatTimei某時間間隔之全距Samplessize樣本大小FromTable查表RChartControlLimitsTakeabout20-25samplegroups(n)oftheprocessresult.Eachsampleshouldcontain4or5observations.Foreachsamplecalculatetheaverageandtherange.Averageallthesampleaverages=X-BAR.Averageallthesampleranges=R-BAR.Calculatetheupper&lowercontrollimitforX-BARCalculatetheupper&lowercontrollimitforR-BAR建立X-barR管制圖UCLLCLIstheprocessincontrol?Arethespecificationsbeingmet?Howcanwetellifthevariabilityisincontrol?X-barChartTheRchartmeasuresthechangeinthespreadovertime.PlotR,therangeforeachsample.LowerControlLimit=UpperControlLimit=UCLLCLR-ChartTypeofattributescontrolchart計數管制圖Nominallyscaledcategoricaldata以絕對資料分類e.g.,good-bad如好,壞Shows%ofnonconformingitems顯示不合格項目%Example:Count#defectivechairs÷bytotalchairsinspected;Plot計算椅子的不良數除以椅子總檢驗數,點圖Chairiseitherdefectiveornotdefective椅子只有好與壞兩種pChart

不良率管制圖Takeabout20-25samplesoftheprocessresult.EachsampleshouldbelargeenoughtocontainATLEAST1badobservation.OftenforP-Chartssamplessizesareinexcessof100.Foreachsamplecalculatethepercentageofbadunits.Averageallthesamplepercentagestogether,thisisP-BAR.Calculatetheupper&lowercontrollimitfortheP-BARchartusingthefollowingformulas:建立p管制圖#DefectiveItemsinSampleiSizeofsampleiIfindividualsamplesarewithin25%oftheaveragesamplesizethencontrollimitscanbecalculatedusingtheaveragesamplesize:z=2for95.5%limits;z=3for99.7%limitsIfsamplesizesvarybymorethan25%oftheaveragesamplesizethencontrollimitsshouldbecomputedforeachsample.pChartControlLimitsItappearsthatshifts4,7and12wereoutofcontrol.Uponfurtherinspectionitappearsthattoomuchwaterwasaddedtotheprocessinshifts4and7andthatinshift12anewoperatorstarted.Sinceeachoftheoutofcontrolpointshaveassignablecauses,weeliminatethemfromthedata.Thenewcontrolchartisthen:IdentifyingSpecialCausesNowitappearsthatshift15isout-of-control.Furthercheckingshowsthatthetemperaturewassettoohighduringthisshift.Therefore,wewanttoeliminatethispointsothatinsubsequenttestswecanidentifywhenthisoccurs.Ifweeliminatethispointthenewcontrolchartis:IdentifyingSpecialCausesABCABCEstablishregionsA,B,andCasone,two,andthreesOneormorepointsfalloutsidethecontrollimits.2outof3consecutivepointsfallinthesameregionA4outof5consecutivepointsfallinthesameregionAorB6consecutivepointsincreasingordecreasing9consecutivepointsonthesamesideoftheaverage.14consecutivepointsalternatingupanddown15consecutivepointswithinregionC.DeterminingifYourProcessis“OutofControl”Npchartsfornumberofnonconformingunits.以不合格品之數統計Convertedfrombasicp-chart由p管制圖演變而來Multiplypbysamplesize(n).不良率乘以樣本大小Formulas:建立不良數管制圖Takeabout20-25samplesfromtheprocess.Eachsamplecontains1unit.Foreachunitcountthenumberofoccurrencesfortheobservationofinterest.Calculatetheaveragenumberofoccurrencesperunit.ThisisC-BAR.Calculatetheupper&lowercontrollimitfortheC-BARchartusingthefollowingformulas:建立缺點數管制圖425GramsMean平均值ProcessDistribution製程分配Distributionofsamplemeans樣本平均值分配樣本平均值與製程分配ProcessCapabilityμ

,Nominalvalue80010001200HoursUpperspecificationLowerspecificationProcessdistribution(a)Processiscapable製程能力LowerspecificationMeanUpperspecificationTwosigmaμ,Nominalvalue製程能力LowerspecificationMeanUpperspecificationFoursigmaTwosigmaμ

,Nominalvalue製程能力LowerspecificationMeanUpperspecificationFoursigmaTwosigmaμ

,Nominalvalue製程能力Capable

Verycapable

NotcapableLSLUSLSpecProcessvariation製程能力ProcessCapabilityCpkAssumesthattheprocessis: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準確度製程能力指數Cpk=negativenumberCpk=zeroCpk=between0and1Cpk=1Cpk>1Cpk

量測之意義LowerspecificationlimitUpperspecificationlimit(a)Acceptancesampling(b)Statisticalprocesscontrol(c)cpk>1確認並降低製程變異TYPEIERROR=P(rejectgoodlot)aorproducer’srisk,toonervous5%iscommon第一種錯誤=將好批判成壞批的機率,緊張忙亂的錯誤TYPEIIERROR=P(acceptbadlot)borconsumer’srisk,absent-minded10%istypicalvalue第二種錯誤=將壞批判成好批的機率,心不在焉的錯誤生產者與消費者冒險率Acceptancequalitylevel(AQL)

允收水準

Acceptablefractiondefectiveinalot

允許一批中不良的比例Lottolerancepercentdefective(LTPD)

拒收水準,批容許不良率Maximumfractiondefectiveacceptedinalot

允許一批中最大不良的比例品質的定義OperatingCharacteristicCurveShowsprobabilityoflotacceptance

顯示批允收的機率Basedon是基於:samplingplan抽樣計劃qualityleveloflot批品質的等級Indicatesdiscriminatingpowerofplan

顯示不同計劃的差異性作業特性曲線AQLLTPDb=0.10a=0.05Probabilityofacceptance,Pa{0.600.400.200.020.040.060.080.100.120.140.160.180.200.80{Proportiondefective不良比例1.00OCcurvefornandc樣本大小與c允收數允收機率OperatingCharacteristicCurveOC曲線AverageOutgoingQuality(AOQ)Expectednumberofdefectiveitemspassedtocustomer

期望通過客戶之不良項目數Averageoutgoingqualitylimit(AOQL)is

maximumpointonAOQcurve

平均出廠品質界限是AOQ曲線的最大值平均出廠品質0.0150.0100.0050.010.020.030.040.050.060.070.080.090.10AOQLAverageOutgoingQuality(Incoming)PercentDefectiveAQLLTPDAOQCurve平均出廠品質曲線Process製程Variation變異Data資料StatisticalTools統計方法StatisticalThinking統計思維StatisticalMethods統計方法從統計思維到統計方法統計訓練訓練課程認證體系薪資調整抽樣方法雙次抽樣計劃多重(連續)抽樣計劃如何選擇抽樣之方法DoubleSamplingPlans

雙次抽樣計劃Takesmallinitialsample

抽取少量之原始樣本If#defective<lowerlimit,acceptIf#defective>upperlimit,rejectIf#defectivebetweenlimits,takesecondsample若不良數<下界限,允收若不良數>上界限,拒收若不良數界於界限內,第二次抽樣Acceptorrejectba