SQE 品質(zhì)工程師 職責(zé)

品質(zhì)控制

(統(tǒng)計製程管制)余德成國立高雄海洋科技大學(xué)運(yùn)籌管理系2007.5.13POM2007國立中山大學(xué)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(zhì)管制方法More前言TQM失敗的原因管理有兩種連續(xù)改善基本的控制模式TQM失敗的原因連續(xù)改善Concepts如何連續(xù)改善?5-Why改善工具Concept-1Concept-2如何連續(xù)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(tǒng)計製程管制(StatisticalProcessControl;SPC)統(tǒng)計思維(StatisticalThinking)品質(zhì)特性(QualityCharacteristics)資料型態(tài)(TypesOfData)變異型態(tài)(TypesofVariations)統(tǒng)計方法(StatisticalMethods)抽樣方法(SamplingMethods)統(tǒng)計思維KeyConcepts主要觀念Processandsystemsthinking製程與系統(tǒng)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(yīng)Characteristicsforwhichyoufocusondefects其特性著重於缺點Classifyproductsaseither‘good’or‘bad’,orcount#defects以產(chǎn)品的好.壞,缺點數(shù)量來看e.g.,radioworksornot如收音機(jī)是否可以播放Categoricalordiscreterandomvariables屬不連續(xù)的雖機(jī)變數(shù)Attributes計數(shù)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(shù)或分?jǐn)?shù)表達(dá)Continuousrandomvariables連續(xù)的隨機(jī)變數(shù)品質(zhì)特性Attributedata計數(shù)資料Productcharacteristicevaluatedwithadiscretechoice產(chǎn)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(chǎn)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(tài)CommonCause共同原因Random隨機(jī)Chronic長期的Small影響小Systemproblems系統(tǒng)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(fā)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(wěn)定性變異型態(tài)Inherenttoprocess固有製程Random隨機(jī)Cannotbecontrolled不可控Cannotbeprevented無法預(yù)防Examples如:Weather氣候accuracyofmeasurements量測精度capabilityofmachine設(shè)備能力Exogenoustoprocess外來因子影響製程N(yùn)otrandom非隨機(jī)Controllable可控Preventable可預(yù)防Examples如toolwear工具磨耗“Monday”effect週一效應(yīng)poormaintenance維護(hù)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(chǎn)品規(guī)格desiredrangeofproductattribute產(chǎn)品屬性之期望範(fàn)圍partofproductdesign產(chǎn)品設(shè)計的一部份length,weight,thickness,color,…長度,重量,厚度,顏色…等nominalspecification(公稱規(guī)格)upperandlowerspecificationlimits(規(guī)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(dá)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(dá)到規(guī)格的要求!產(chǎn)品規(guī)格與品變異Grams(a)LocationAverage(平均值)共同原因(a)LocationGramsAverage特殊原因統(tǒng)計方法統(tǒng)計圖表統(tǒng)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(biāo)準(zhǔn)差TheNormalDistribution常態(tài)分配Mean平均值CentralLimitTheoremStandarddeviation樣本標(biāo)準(zhǔn)差TheoreticalBasisofControlChartsUCL管制規(guī)格上限Nominal中心線LCL管制規(guī)格下限123SamplesControlCharts管制圖123SamplesUCL管制規(guī)格上限管制圖Assignablecauseslikely可能的特殊原因123SamplesUCL管制規(guī)格上限Nominal中心線LCL管制規(guī)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(tài)UniformNormalBetaDistributionofsamplemeans樣本平均值分配Standarddeviationofthesamplemeans(mean)Threepopulationdistributions群體分配群體與樣本間之關(guān)係TargetAtafixedpointintime固定時間TimeTargetOvertime連續(xù)時間Thinkofamanufacturingprocessproducingdistinctpartswithmeasurablecharacteristics.Thesemeasurementsvarybecauseofmaterials,machines,operators,etc.Thesesourcesmakeupchancecausesofvariation.製造各零件之量測特性會因4M等機(jī)遇原因而發(fā)生變異機(jī)遇原因之觀察ProcessControlCharts製程管制圖ControlChartsVariablesChartsAttributesChartsContinuous連續(xù)的NumericalDataCategoricalorDiscrete離散的NumericalData計量計數(shù)管制圖型態(tài)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(guān)聯(lián)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(shù)字資料Showssamplemeansovertime

算出樣本平均值Monitorsprocessaverage

間控製程平均數(shù)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(dāng)製程穩(wěn)定時,利用過去所產(chǎn)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(shè)製程平均值m與樣本平均值相同processstandarddeviationsestimatedby:製程標(biāo)準(zhǔn)差s估算由standarddeviationofallindividualsamples所有個別值樣本之標(biāo)準(zhǔn)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(biāo)準(zhǔn)差估計Rchartsmonitorvariability:Isthevariabilityoftheprocessstableovertime?Dotheitemscomefromonedistribution?R管制圖監(jiān)控變異性,是否整個製程處於安定狀態(tài)?有項目超出此一分配嗎?X-barchartsmonitorcentering(oncetheRchartisincontrol):Isthemeanstableovertime?X-Bar管制圖監(jiān)控中心(一旦R管制圖處於管制狀態(tài)):平均值於爭個製程是否穩(wěn)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(biāo)準(zhǔn)間隔時間取樣,監(jiān)控此管制圖如何建立管制圖AlarmNoAlarmIn-Control管制內(nèi)Out-of-Control失控Type1andType2ErrorOnepointoutsideofeithercontrollimit

一點超出管制界線2outof3pointsbeyondUCL-2sigma3點有2點在2個標(biāo)準(zhǔn)差或以外7successivepointsonsamesideofthecentralline

連續(xù)7點在中心線之同一側(cè)of11successivepoints,atleast10onthesamesideofthecentralline

連續(xù)11點有10點在中心線之同一側(cè)of20successivepoints,atleast16onthesamesideofthecentralline

連續(xù)20點有16點在中心線之同一側(cè)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(shù)表Typeofvariablescontrolchart計量管制圖Intervalorratioscalednumericaldata間距或比率量測數(shù)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(shù)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(shù)除以椅子總檢驗數(shù),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?dāng)?shù)統(tǒng)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(shù)管制圖Takeabout20-25samplesfromtheprocess.Eachsamplecontains1unit.Foreachunitcountthenumberofoccurrencesfortheobservationofinterest.Calculatetheaveragenumberofoccurrencesperunit.ThisisC-BAR.Calculatetheupper&lowercontrollimitfortheC-BARchartusingthefollowingformulas:建立缺點數(shù)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(shè)製程為穩(wěn)定且為常態(tài)分配Cpk=min(Cpu,Cpl)Cpu=(USL-μ)/3Cpl=(μ-LSL)/3Precision精密度Capability準(zhǔn)確度製程能力指數(shù)Cpk=negativenumberCpk=zeroCpk=between0and1Cpk=1Cpk>1Cpk

量測之意義LowerspecificationlimitUpperspecificationlimit(a)Acceptancesampling(b)Statisticalprocesscontrol(c)cpk>1確認(rèn)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(jī)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(jī)率,心不在焉的錯誤生產(chǎn)者與消費(fèi)者冒險率Acceptancequalitylevel(AQL)

允收水準(zhǔn)

Acceptablefractiondefectiveinalot

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

拒收水準(zhǔn),批容許不良率Maximumfractiondefectiveacceptedinalot

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

顯示批允收的機(jī)率Basedon是基於:samplingplan抽樣計劃qualityleveloflot批品質(zhì)的等級Indicatesdiscriminatingpowerofplan

顯示不同計劃的差異性作業(yè)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(shù)允收機(jī)率OperatingCharacteristicCurveOC曲線AverageOutgoingQuality(AOQ)Expectednumberofdefectiveitemspassedtocustomer

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

maximumpointonAOQcurve

平均出廠品質(zhì)界限是AOQ曲線的最大值平均出廠品質(zhì)0.0150.0100.0050.010.020.030.040.050.060.070.080.090.10AOQLAverageOutgoingQuality(Incoming)PercentDefectiveAQLLTPDAOQCurve平均出廠品質(zhì)曲線Process製程Variation變異Data資料StatisticalTools統(tǒng)計方法StatisticalThinking統(tǒng)計思維StatisticalMethods統(tǒng)計方法從統(tǒng)計思維到統(tǒng)計方法統(tǒng)計訓(xùn)練訓(xùn)練課程認(rèn)證體系薪資調(diào)整抽樣方法雙次抽樣計劃多重(連續(xù))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(shù)<下界限,允收若不良數(shù)>上界限,拒收若不良數(shù)界於界限內(nèi),第二次抽樣Acceptorrejectba