spc统计制程管制培训教案

本资料来源2

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11

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12

Dependsonlevelsofactivityandjobresponsibility.依據活動的層級與工作執掌Wherewe'reheaded我們朝何方Managerialprocessestoguideus用管理的程序來指導我們WheretheworkgetsDone讓所需的工作被執行完成

Strategic策略上的Managerial管理上的Operational作業性的Executives高階決策層Managers經理階層Workers現場員工UseofStatisticalThinking

運用統計思維13

Executivesusesystemsapproach.

決策者運用系統導向策略Coreprocesseshavebeenflowcharted

主要程序已被流程圖表化Strategicdirectiondefinedanddeployed.

策略方向的訂定與展開Measurementsystemsinplace.

適當的量測系統Employee,customer,andbenchmarkingstudiesareusedtodriveimprovement.

是以員工,客戶與benchmarking的研究被用來主導改善Experimentationisencouraged.鼓勵實驗StatisticalThinkingattheStrategicLevel

決策者之統計思維14

.Managersusemeetingmanagementtechniques經理利用會議管理技巧Standardizedprojectmanagementsystemsareinplace.適當的標準化專案管理系統Bothprojectprocessandresultsarereviewed.此專案的流程與結果已被審核Processvariationisconsideredwhensettinggoals.當設定目標時,流程的變異已被考慮Measurementisviewedasaprocess.量測點被視為一個流程Thenumberofsuppliersisreduced供應者數目減少Avarietyofcommunicationmediaareused.廣泛的傳訊媒體被採用StatisticalThinkingattheManagerialLevel

經理階層統計思維15

Workprocessesareflowcharted&documented工作程序已被流程圖表化與書面化Keymeasurementsareidentified.主要量測點已被確認

Timeplotsdisplayed時間的圖示被展現Processmanagementandimprovementutilize:製程管理與改善採用Knowledgeofvariation,and變異觀念的知識及Dataanalysis資料分析Improvementactivitiesfocusontheprocess,notblamingemployees.改善工具著重於製程,而非責備員工StatisticalThinkingattheOperationalLevel

現場員工的統計思維範例16

StatisticalThinkingattheOperationalLevel

現場員工的統計思維範例ARecentExperience最近的經驗

Hugequantitiesofdata大量的資料Limitedunderstandingofstructure在有限度理解的結構上Consultantsappliedartificialneuralnets顧問群運用人工神經網狀系統Didn’twork但不成功17

StatisticalThinkingattheOperationalLevel

現場員工的統計思維範例ARecentExperience最近的經驗ArtificialNeuralNetsapplynicelyinmanysituations(NISTExamples):人工神經網狀系統出色地運用於許多領域:OpticalCharacterRecognition光學文字辨識系統FingerPrinting指紋辨識FacePrintingfortheFBI相貌辨識Example等案例上18

….But,但Unlessyousampletheprocesstakingtherightamountoftherightkindofdata(rationalsubgroups)youwillneverapproachprocessunderstanding.在抽驗的流(製)程裡若你無法取得正確的數量與資料(合理的樣組),你將無法深入了解此一流(製)程Withoutprocessunderstanding,thereisnoprocesscontrol.流(製)程若不了解,就無所謂的流(製)程管制19

KeyLearningsfrom

StatisticalThinkingEfforts

由統計思維的努力中,吾人學到的要點Statisticiansdon’tunderstandStatisticalThinkingaswellastheythinktheydo.統計的思維不僅要懂而且也要會做Thosewhodounderstandithavelimitedaccesstomanagerialandstrategiclevels.真正了解統計思維的人,在管理與決策上之能力較少受限制There’smuchmoreworktobedone.較多的事能被完成Spreadtheword口令的展開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Attributes計數值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21

TypesOfData

資料型態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StatisticalProcessControl

統計製程管制Statisticaltechniqueusedtoensureprocessismakingproducttostandard統計技術用於確保製程所製出的產品合乎標準Allprocessaresubjecttovariability所有製程受變異性所支配

NaturalorCommoncauses自然或共同原因:Randomvariations隨機變異如設備損耗Assignablecauses特殊原因:Correctableproblems可改善的問題Machinewear,unskilledworkers,poormaterial

如生手,材料不良…Objective:Identifyassignablecauses目標:確認特殊原因Usesprocesscontrolcharts利用管制圖表24

CausesofVariation變異的原因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…ProductSpecificationandProcessVariation

產品規格與品變異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!26

Grams(a)LocationAverage(平均值)CommonCauses

共同原因27

(a)LocationGramsAverageAssignableCauses

特殊原因28

-3s-2s-1s+1s+2s+3sMean平均值68.26%95.44%99.74%=Standarddeviation=標準差TheNormalDistribution

常態分配29

Mean平均值CentralLimitTheoremStandarddeviation樣本標準差TheoreticalBasisofControlCharts30

UCL管制規格上限Nominal中心線LCL管制規格下限123SamplesControlCharts管制圖31

123SamplesControlCharts管制圖UCL管制規格上限Nominal中心線LCL管制規格下限32

Assignablecauseslikely可能的特殊原因123SamplesControlCharts管制圖UCL管制規格上限Nominal中心線LCL管制規格下限33

ProcessControl:

ThreeTypesofProcessOutputs

製程管制的三種顯示型態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34

TheRelationshipBetween

PopulationandSamplingDistributions

群體與樣本間之關係UniformNormalBetaDistributionofsamplemeans樣本平均值分配Standarddeviationofthesamplemeans(mean)Threepopulationdistributions群體分配35

VisualizingChanceCauses

機遇原因之觀察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36

ProcessControlCharts

製程管制圖37

Control

Charts

Variables

Charts

Attributes

Charts

Continuous連續的NumericalDataCategoricalorDiscrete離散的NumericalDataControlChartTypes

管制圖型態計量計數38

ControlChartSelection

管制圖的選定QualityCharacteristicvariableattributen>1?n>=10orcomputer?xandMRnoyesxandsxandRnoyesdefectivedefectconstantsamplesize?p-chartwithvariablesamplesizenopornpyesconstantsamplingunit?cuyesno39

ProduceGood

ProvideService

StopProcess

Yes

No

Assign.

Causes?

TakeSample

InspectSample

FindOutWhy

Create

ControlChart

Start

StatisticalProcessControlSteps

統計製程管制控制步驟40

StatisticalThinkingisaphilosophyoflearningandActionbasedonthefollowingfundamentalprinciples:

統計思維哲學之學習與行動基於以下原則Allworkoccursinasystemofinterconnectedprocesses,Variationexistsinallprocesses,andUnderstandingandreducingvariationarekeystosuccess.所有工作的產生源於系統互相連結之製程,而變異存在於所有製程,了解並降低製程的變異是成功的關鍵41

UsingControlCharts

如何使用管制圖1)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`XChart平均值管制圖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43

BasicProbabilitiesConcerningtheDistributionofSampleMeans

有關樣本平均數之機率分佈Std.dev.ofthesamplemeans樣本平均數標準差:44

EstimationofMeanandStd.Dev.

oftheUnderlyingProcess

在製程控制之下之平均值與標準差估計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/d2

samplerangeR=(Rmax-Rmin),d2=valuefromlook-uptable,全距為R,d2可由查表得知,45

X-barvs.Rcharts

平均值VS全距管制圖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)46

HowtoConstructaControlChart

如何建立管制圖1.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47

Type1andType2Error

第一種與第二種錯誤AlarmNoAlarmIn-Control管制內Out-of-Control失控48

CommonTeststoDetermineifthe

ProcessisOutofControl

管制圖異常之判定

Onepointoutsideofeithercontrollimit

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49

Type1ErrorsfortheseTests第一種錯誤Test ProbabilityType1Error2/37/710/1116/201/12(0.00135)0.00270.0052(0.5)7

0.00780.005860.005950

Type2Error

第二種錯誤Supposem1>m

Type2Error=

whereF(z)denotesthethecumulativeprobabilityofastandardnormalvariateatzPower=1-Type2Error.Powerincreasesas…nincreases,as(m1-m)increases,andassdecreases.Extensiontom1<misstraightforward51

`XChartControlLimitsSampleRangeatTimei#SamplesSampleMeanatTimeiFrom

Table52

FactorsforComputingControlChartLimits

管制圖之係數表TableRChart全距管制圖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54

SampleRangeatTimei某時間間隔之全距Samplessize樣本大小FromTable查表RChartControlLimits

R管制圖管制界限公式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

利用標準差圖取代R管制圖S-Chartsareusedwhen:Tightcontrolofprocessvariationisessential.Samplesizeequals10ormore.acomputercanbeusedtosimplify&speedupcalculations.Formulas:ControlLimitsfors-ChartControlLimitsforX-barChart57

Example:Thefirst20dayssamplesareasfollows:58

UCLLCLX-barChartIstheprocessincontrol?Arethespecificationsbeingmet?Howcanwetellifthevariabilityisincontrol?59

R-ChartTheRchartmeasuresthechangeinthespreadovertime.PlotR,therangeforeachsample.LowerControlLimit=UpperControlLimit=UCLLCL60

Ex: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=061

Control“Commutingtimes”(cont.)step4Commutingtimes-A.M.UCL=95.48Xbarbar=74.6LCL=53.72XbarChart110234567895010075RChartUCL=75.96Rbar=36.0LCL=0110234567897553562

FigurepChart

不良率管制圖Typeofattributescontrolchart

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SettingupapChart

建立p管制圖Takeabout20-25samplesoftheprocessresult.EachsampleshouldbelargeenoughtocontainATLEAST1badobservation.OftenforP-Chartssamplessizesareinexcessof100.Foreachsamplecalculatethepercentageofbadunits.Averageallthesamplepercentagestogether,thisisP-BAR.Calculatetheupper&lowercontrollimitfortheP-BARchartusingthefollowingformulas:65

pChartControlLimits

不良率管制圖管制界限#DefectiveItemsinSampleiSizeofsampleiIfindividualsamplesarewithin25%oftheaveragesamplesizethencontrollimitscanbecalculatedusingtheaveragesamplesize:z=2for95.5%limits;z=3for99.7%limitsIfsamplesizesvarybymorethan25%oftheaveragesamplesizethencontrollimitsshouldbecomputedforeachsample.66

Example:p-ChartM&MMarswantstoinstituteastatisticalprocesscontrolonanewcandybar.Inordertodoso,everyshifttheysample50barsanddeterminethenumberofdefectiveones.Theyobtainthefollowingdata:67

20groupsof50=1000samplesTotaldefective=170p-bar=0.17

UCL=0.17+3x0.053=0.329LCL=0.17-3x0.053=0.010Plottingthe%defectiveshows:68

IdentifyingSpecialCauses

確認特殊要因Itappearsthatshifts4,7and12wereoutofcontrol.Uponfurtherinspectionitappearsthattoomuchwaterwasaddedtotheprocessinshifts4and7andthatinshift12anewoperatorstarted.Sinceeachoftheoutofcontrolpointshaveassignablecauses,weeliminatethemfromthedata.Thenewcontrolchartisthen:69

Nowitappearsthatshift15isout-of-control.Furthercheckingshowsthatthetemperaturewassettoohighduringthisshift.Therefore,wewanttoeliminatethispointsothatinsubsequenttestswecanidentifywhenthisoccurs.Ifweeliminatethispointthenewcontrolchartis:IdentifyingSpecialCauses70

FinalpChartUCL=0.122+3x0.046=0.260LCL=0.122-3x0.046=-0.016=0.0(negativecontrollimitsshouldbesetto0)Nowtheyshouldusethischartforallsubsequentsamplinguntiltheprocesschanges71

DeterminingifYourProcessis

“OutofControl”

決定你的製程是否在穩定狀態EstablishregionsA,B,andCasone,two,andthreesOneormorepointsfalloutsidethecontrollimits.2outof3consecutivepointsfallinthesameregionA4outof5consecutivepointsfallinthesameregionAorB6consecutivepointsincreasingordecreasing9consecutivepointsonthesamesideoftheaverage.14consecutivepointsalternatingupanddown15consecutivepointswithinregionC.ABCABCUsingannpChart

建立不良數管制圖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:Settingupacchart

建立缺點數管制圖Takeabout20-25samplesfromtheprocess.Eachsamplecontains1unit.Foreachunitcountthenumberofoccurrencesfortheobservationofinterest.Calculatetheaveragenumberofoccurrencesperunit.ThisisC-BAR.Calculatetheupper&lowercontrollimitfortheC-BARchartusingthefollowingformulas:

UsinganuChart

建立單位缺點數管制圖

Auchartisusedwhentheunitsizeinspectedfordefectsisnotconstant.Inthesecasestheunitisoftenreferredtoasanareaofopportunity(ni).Theaverageoccurrenceperareaofopportunity(i.e.thecenterline)iscalculatedas:Thesame25%variationrulediscussedforp-chartsapplieshereaswell.Controllimitsarecalculatedas:75

Figure76

425GramsMean平均值ProcessDistribution製程分配Distributionofsamplemeans樣本平均值分配SampleMeansandthe

ProcessDistribution

樣本平均值與製程分配77

ProcessCapability製程能力µ,Nominalvalue80010001200HoursUpperspecificationLowerspecificationProcessdistribution(a)Processiscapable78

ProcessCapability製程能力

LowerspecificationMeanUpperspecificationTwosigmaµ,Nominalvalue79

ProcessCapability製程能力

LowerspecificationMeanUpperspecificationFoursigmaTwosigmaµ,Nominalvalue80

ProcessCapability製程能力

LowerspecificationMeanUpperspecificationSixsigmaFoursigmaTwosigmaµ,Nominalvalue81

ProcessCapability製程能力Capable

Verycapable

NotcapableLSLUSLSpecProcessvariation82

ProcessCapabilityCpk

製程能力指數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83

MeaningsofCpkMeasures

Cpk

量測之意義Cpk=negativenumberCpk=zeroCpk=between0and1Cpk=1Cpk>184

StatisticalProcessControl–

IdentifyandReduceProcessVariability

統計製程管制-確認並降低製程變異LowerspecificationlimitUpperspecificationlimit(a)Acceptancesampling(b)Statisticalprocesscontrol(c)cpk>185

QualityControlApproaches

品質管制方法Statisticalprocesscontrol(SPC)統計製程管制Monitorsproductionprocesstopreventpoorquality監控產品製程以預防不良品質Acceptancesampling允收抽樣Inspectsrandomsampleofproductormaterialstodetermineifalotisacceptable隨機抽樣檢驗產品或物料以決定此批是否允收86

Samplingvs.Screening

抽樣與篩選Sampling抽樣Whenyouinspectasubsetofthepopulation群體批中檢查小批ScreeningWhenyouinspectthewholepopulation群體