統(tǒng)計(jì)過程控制簡介

連接控制圖方法與流程改進(jìn)方法 LinkControlChartmethodstotheProcessImprovementMethodologyTM

討論不同類型的變差

Discussdifferenttypesofvariation介紹各種類型的控制圖

IntroducevarioustypesofControlCharts討論如何解釋控制圖 DiscusstheinterpretationofControlCharts目的

Objectives.2023/12/71.2023/12/72我們是否應(yīng)該采取行動？Shouldwetakeaction?

每天我們都被數(shù)據(jù)淹沒,而且不得不作出決定Everydaywearefloodedbydataandweareforcedtomakedecisions工廠產(chǎn)量下降４％Plant’sOutputDecreasesBy4%美國貿(mào)易赤字增加４００億USTradeDeficitRisesBy$40Billion某公司獲利比上季度降低２．４億CompanyX’sEarningsAreOff$240MillionFromPreviousQuarter我們需要解釋數(shù)據(jù)的方法

WeNeedWaystoInterpretData.2023/12/73今天采集什么樣的數(shù)據(jù)？

WhatTypeOfDataIsCollectedToday?制造業(yè)Manufacturing: _____________________________________非制造業(yè)

Non-Manufacturing

___________________________________如何分析數(shù)據(jù)？

HowIsItAnalyzed?制造業(yè)

Manufacturing

: _____________________________________非制造業(yè)

Non-Manufacturing

___________________________________得知數(shù)據(jù)好壞后該當(dāng)如何？

WhatHappensIfItIsBad/Good?制造業(yè)

Manufacturing

: _____________________________________非制造業(yè)

Non-Manufacturing

___________________________________.2023/12/74客戶需求下限Lower“Customer”Requirement這一方法THISMETHOD告訴你關(guān)于客戶的需求Tellsyouwhereyouareinregardstocustomer’sneeds不告訴你怎么滿足用戶需求及下一步怎么辦

ItwillNOTtellyouhowyougotthereorwhattodonext客戶需求上限Upper“Customer”Requirement我們管理數(shù)據(jù)的方式－過去(歷史來講)的方式

TheWayWeManageData–Historically不用管它,不會壞的LeaveItAlone.ItAin’tBroke痛苦,受累Pain&Suffering痛苦,受累Pain&Suffering.2023/12/75這一方法導(dǎo)致何種管理行為？Thismethodcauseswhattypeofmanagementbehavior?客戶需求下限Lower“Customer”Requirement客戶需求上限Upper“Customer”Requirement我們管理數(shù)據(jù)的方式－歷史來講的方式

TheWayWeManageData–Historically不用管它,不會壞的LeaveItAlone.ItAin’tBroke痛苦,受累Pain&Suffering痛苦,受累Pain&Suffering.2023/12/7623ScrapLevel(%)廢品率11996CelebrationTime工廠廢品率為年度最低的２％ Thefactoryscraplevelisatayearlowof2%經(jīng)理給工廠頒獎(jiǎng) Managerpresentsanawardtotheplant在餐廳進(jìn)行慶祝：每人都可分享免費(fèi)皮薩餅和飲料

Ceremonyinthecafeteria:pizzaandrefreshmentsforall!“每人都應(yīng)為他們的成就驕傲．” “Everyoneshouldbeproudofwhatthey’veaccomplished”.

DerivedfromUnderstandingVariation:TheKeyToManagingChaos,DonaldJ.Wheeler,SPCPress.1993.１９９６年４月

APRIL1996JFMA.2023/12/772311996經(jīng)理希望能將發(fā)出去的獎(jiǎng)收回來Managerwantstotakebackaward廢品率連續(xù)三個(gè)月持續(xù)增長 Threeconsecutivemonthsofscrapincreases.經(jīng)理希望能將發(fā)出去的獎(jiǎng)收回來 Managerwisheshecouldtakebacktheaward經(jīng)理考慮要采取行動了

ManageristhinkingabouttakingactionScrapLevel(%)廢品率１９９６年６月

JUNE1996DerivedfromUnderstandingVariation:TheKeyToManagingChaos,DonaldJ.Wheeler,SPCPress.1993.JFMAMJ.2023/12/782311996Nomore“NiceGuy”不再充好人了廢品率上升到２．６％

Scraprisestoavalueof2.6%

經(jīng)理決定采取行動 Managerdecidestotakeaction召開一個(gè)“特別會議”來尋求一個(gè)永久性的解決方案 A“specialmeeting”iscalledtosolvethisproblemonceandforall.經(jīng)理在長篇大論次品率多么重要后離開了．雇員們不知道該干什么．另外，他們有其他更重要的評估標(biāo)準(zhǔn)．于是，他們什么也沒做．

Afterasoundlectureontheimportanceofscrap,themanagerleaves.Employeesaren’tsurewhattodo.Besides,theyhaveothermetricswhichhavemoreimportance.Sotheydonothing.ScrapLevel(%)廢品率１９９６年１１月NOVEMBER1996DerivedfromUnderstandingVariation:TheKeyToManagingChaos,DonaldJ.Wheeler,SPCPress.1993.JFMAMJJASON.2023/12/79經(jīng)理看到從去年開始廢品率持續(xù)下降

Managerhasseenreducedscraplevelssincetheendoflastyear教訓(xùn)：“嚴(yán)格的管理會出成效！”

TheLearning:“Atoughmanagementstylegetsresults!”

Managerconcludes:

“ToughLoveMakesThingsHappen”23119961997ScrapLevel(%)廢品率1997年6月

JUNE1997DerivedfromUnderstandingVariation:TheKeyToManagingChaos,DonaldJ.Wheeler,SPCPress.1993.JFMAMJJASONDJFMAMJ.2023/12/710DerivedfromUnderstandingVariation:TheKeyToManagingChaos,DonaldJ.Wheeler,SPCPress.1993.將數(shù)據(jù)置于統(tǒng)計(jì)流程控制圖中

PuttingTheDataInASPCChart23119961997ScrapLevel(%)廢品率JFMAMJJASONDJFMAMJUCLLCL.2023/12/711統(tǒng)計(jì)流程控制圖顯示不同的解釋,可為什么呢?

SPCTellsADifferentStory.ButWhy?23119961997ScrapLevel(%)廢品率JFMAMJJASONDJFMAMJUCLLCL.2023/12/712“人們已知的最佳方式之一是如不能使用控制圖分析數(shù)據(jù)會：增加成本,浪費(fèi)的努力和降低士氣;"-DonaldJ.Wheeler

博士“Failuretousecontrolchartstoanalyzedataisoneofthebestwaysknowntomankindto:increasecostswasteeffortandlowermorale.”

-Dr.DonaldJ.Wheeler統(tǒng)計(jì)流程控制圖顯示不同的解釋,可為什么呢?

SPCTellsADifferentStory,ButWhy?.2023/12/713S=

統(tǒng)計(jì)技術(shù):檢查偏差StatisticaltechniquesusedtoexamineprocessvariationC=

控制過程通過積極管理ControllingtheprocessthroughactivemanagementP=

過程,任何過程Process,ANYProcess現(xiàn)在我們管理數(shù)據(jù)的方法-SPC

TheWayWeManageData-Today

SPC顯示過程偏差隨時(shí)間變化的圖形.2023/12/714控制圖方法 ControlChartsMethod

它從哪里來的? WhereDidItComeFrom?19世紀(jì)20年代-西部電器的WalterShewhart博士: 1920’s-WesternElectric/Dr.WalterShewhart慣于確認(rèn)受控的&未受控的偏差UsedtoidentifyControlled&UncontrolledVariation

受控制的:普通原因或固有偏差

Controlled:CommonCauseorInherentVariation未控制的:特殊起因或可指定的偏差

Uncontrolled:SpecialCauseorAssignableVariation在背景噪聲中試圖發(fā)現(xiàn)由特殊原因造成的偏差

Triestofindthespecialcausevariationinallofthebackgroundnoise使用控制圖作為主要工具 UsesControlChartsasmaintool.2023/12/715FiveMainUsesofControlCharts

控制圖的5個(gè)主要用途Toreducescrapandreworkandforimprovingproductivity.為了減少廢品和返工及提高生產(chǎn)力Defectprevention.Incontrolmeanslesschanceofnonconformingunitsproduced.預(yù)防缺陷Preventsunnecessaryprocessadjustmentsbydistinguishingbetweencommoncausevariationandspecialorassignablecausevariation.預(yù)防不必要的過程調(diào)整Providesdiagnosticinformationsothatanexperiencedoperatorcandeterminethestateoftheprocessbylookingatpatternswithinthedata.Theoperatorcanthenmakethenecessarychangestoimprovetheprocessperformance.提供過程診斷信息Providesinformationaboutimportantprocessparametersovertime.

提供過程重要參數(shù)隨時(shí)間推移的信息.2023/12/716

差異類型-“普遍VS特別”

TypesofVariation“Commonvs.Special”普遍原因 COMMONCAUSE呈現(xiàn)在每個(gè)過程中Ispresentineveryprocess

自然的

Natural隨機(jī)的Random可能被去除和或變小,但在過程上要求一個(gè)根本變化 Canberemovedand/orlessenedbutrequiresafundamentalchangeintheprocess穩(wěn)定的,可重復(fù)的過程偏差來源.存在于每一個(gè)操作/過程由過程本身造成的(由我們做事的方式?jīng)Q定的)一般來說,通過管理可以控制.2023/12/717特殊原因 SPECIALCAUSE不可預(yù)見的 Unpredictable與普通偏差比較大TypicallylargeincomparisontoCommonCausevariation可以由基本的過程控制和監(jiān)視去除或變小Canberemoved/lessenedbybasicprocesscontrolandmonitoring

偏差類型“普遍VS特別"

TypesofVariation“Commonvs.Special”時(shí)不時(shí)地存在于大多數(shù)操作/過程,并且持續(xù)地存在于某些過程.由一個(gè)或一系列的干擾造成的.一般來說,通過操作者可以控制(至少可以發(fā)覺).我們認(rèn)為如果過程中有特別原因偏差,它們就是失控和不穩(wěn)定的.

AprocessexhibitingSpecialCausevariationissaidtobeOut-of-ControlandUnstable.2023/12/718練習(xí)

Exercise當(dāng)它與你的項(xiàng)目有關(guān)系時(shí),確認(rèn)某種“普通原因”和“特別原因”偏差可能的形式 Asitrelatestoyourproject,identifysomepossibleformsof“commoncause”and“specialcause”variation普遍原因 CommonCause特殊原因 SpecialCause

.2023/12/719Minitab–控制圖

ControlCharts.2023/12/720Minitab–控制圖練習(xí)

ControlChartsExercise我們用一些隨機(jī)的數(shù)據(jù) Let’susesomeRandomdata從您的生意中，

我們使用一些代表性的數(shù)值和正態(tài)偏差創(chuàng)造25行任意正常數(shù)據(jù)，

Create25rowsofrandomnormaldatausingsomerepresentativevaluesforMeanandStdDevfromyourbusiness繪制單獨(dú)圖PlotanIndividualschart注意監(jiān)視時(shí)間和價(jià)值被繪制在Y軸 NotethatmonitoringovertimeandthevalueisplottedintheYaxis.2023/12/721隨時(shí)間變化的數(shù)據(jù)DATAPLOTTEDOVERTIMEMONITOREDCHARACTERISTICUCLCenterLineLCLUCL=UpperControlLimit/LCL=LowerControlLimitPlottedData主要部分-控制圖

KeyComponent-ControlCharts

.2023/12/722Definitions定義InControl受控Nospecialcausevariationpresent在波動中沒有特殊原因引入Allvariationisrandom所有的波動都是隨機(jī)的OutofControl失控Atleastonespecialcauseispresent至少有一個(gè)特殊原因引入Somevariationisnon-random一些波動不是隨機(jī)的關(guān)于測試我們建議Thetestswesuggest:MINITAB測試Minitabtests:全部測試 AllTests(測試1-8Test01through08)樣品規(guī)則Patternrule:如果你看到一個(gè)樣品，過程已經(jīng)失控Ifyouseeapattern,theprocessisoutofcontrol.2023/12/723

1Sigma2Sigma3Sigma1Sigma2Sigma3Sigma60-75%90-98%99-99.9%%ofDataPointsUCLLCL時(shí)間TIME我們測量的項(xiàng)目

TheItemWeAreMeasuring標(biāo)準(zhǔn)偏差的規(guī)則 RulesofStandardDeviation

數(shù)據(jù)應(yīng)該在哪? “Whereshouldthedatalie?”.2023/12/724Minitab測試TestsTest#1Test#2.2023/12/725過程控制測試標(biāo)準(zhǔn)

ProcessControlTests我們建議使用。。。全部測試 Wesuggestusingalltests..2023/12/726在控制下還是失控？InControlorOutofControl?

如果在控制以外,打破了什么規(guī)則或表現(xiàn)出什么條件?

IfoutofControl,whichrule(s)isbrokenorcondition(s)ispresent?.2023/12/727在控制下還是失控？InControlorOutofControl?

如果在控制以外,打破了什么規(guī)則或表現(xiàn)出什么條件?

IfoutofControl,whichrule(s)isbrokenorcondition(s)ispresent?.2023/12/728在控制下還是失控？InControlorOutofControl?

如果在控制以外,打破了什么規(guī)則或表現(xiàn)出什么條件?

IfoutofControl,whichrule(s)isbrokenorcondition(s)ispresent?.2023/12/729.2023/12/730失控意味什么?WhatdoesOut-of-Controlmean?查出控制的缺陷

DetectingLackofControl.2023/12/731如果您確定您的過程是“失控”你應(yīng)該做什么？Whatshouldyoudoifyoudeterminethatyourprocessis“OutofControl?”查出控制的缺陷

DetectingLackofControl.2023/12/732因此,根據(jù)現(xiàn)在你所知道的,如果你的過程在控制下，在控制上限和下限之間百分之多少數(shù)據(jù)點(diǎn)將會下降?Therefore,basedonwhatyouknowsofar,whatpercentofdatapointsshouldfallbetweentheuppercontrollimit(UCL)andlowercontrollimit(LCL)ifyourprocessisin-control?

UCLLCLTIME控制極限VS規(guī)格限制

ControlLimitsvs.SpecificationLimits.2023/12/733如果點(diǎn)落在上限之外或控制下限之下，是否意味著我們?yōu)轭櫩妥隽艘粋€(gè)缺陷產(chǎn)品?

Ifapointfallsbeyondtheupperorlowercontrollimitdoesthismeanwearemakingadefectforthecustomer?控制極限VS規(guī)格限制

ControlLimitsvs.SpecificationLimits

UCLLCLTIME.2023/12/734控制極限對規(guī)格限制

ControlLimitsvs.SpecificationLimits過程控制極限是由過程能力決定的

ProcessControlLimitsarecalculatedbasedondatafromtheprocessitself他們根據(jù)+/-3s(99.73%我們期望過程偏差落在這些極限之間) Theyarebasedon+/-3s(99.73%oftheprocessvariationisexpectedtofallbetweentheselimits)產(chǎn)品規(guī)格極限規(guī)范極限是由客戶的要求決定的,

不是在控制圖上發(fā)現(xiàn)的

ProductSpecificationLimitsARENOTfoundonthecontrolchart很重要一點(diǎn)是要了解程序控制與顧客要求如何吻合.

UnderstandinghowtheprocessmatchesupagainstcustomerrequirementsIS

importanttoknow確定過程執(zhí)行如何滿足顧客期望,需要進(jìn)行過程能力研究。TodeterminehowtheprocessperformstoCustomerExpectations,aProcessCapabilityStudyisrequired..2023/12/735把規(guī)格限制放在在控制圖上

PuttingspecificationlimitsonaControlChart把控制上限和控制下限當(dāng)做規(guī)格限制 TreatingUCLandasaspecificationlimit2個(gè)控制圖的大錯(cuò)誤TWOBIGCONTROLCHARTERRORS控制極限對規(guī)格限制

ControlLimitsvs.SpecificationLimits當(dāng)你把任意上下限作為監(jiān)視工具時(shí)，他就不再是個(gè)控制圖.LCLWhenyoudoeitherofthesethecontrolchartbecomesjustaninspectiontool-it’snolongeracontrolchart.控制上限和控制下限并不直接與客戶缺陷有聯(lián)系!

UCL/LCLarenotdirectlytiedtocustomerdefects!.2023/12/736如何收集數(shù)據(jù)HowtoCollectData合理分組

Rationalsubgroups

通過合理分組，使各組只包括普遍原因collectdatasothatsubgroupscontainonlycommoncausevariation.Thesameasincapabilityanalysis.通過合理分組，使各組盡可能包括更多信息Chooserationalsubgroupstogainasmuchinformationaspossibleabouttheprocess.過程偏移

Todetectprocessshifts:每組盡可能在相同時(shí)間獲取測量結(jié)果eachsubgroupshouldconsistofmeasurementstakenatapproximatelythesametime.

選擇樣本時(shí)盡可能獲取組內(nèi)各樣本間最大的波動可能性Chooseasamplesothatitmaximizesthelikelihoodofdetectingvariabilitybetweenthesamples.2023/12/737抽樣Sampling樣本大小Samplesize

過程容量越大，對于關(guān)鍵CTQ特性的測量就越容易越簡單。ThehighertheprocessvolumeandtheeasierandcheaperthemeasurementsoftheCTQcharacteristic,themorelikelyyouaretoselectanXandRchart(typically3-5datapointspersample)overanIndividualandMovingRangechart(IandMR).抽樣頻率

Frequencyofsampling 考慮到每時(shí)、每天、每班、每月、每年、每批次等等。過程質(zhì)量水平越高，所需樣本越小。

Considerhourly,daily,shifts,monthly,annually,lots,andsoon.Thebetteryourprocessisperforming,thelessfrequentlyyouwillneedtosample. 當(dāng)前產(chǎn)業(yè)標(biāo)準(zhǔn)趨向于小批量多頻率的抽樣。Currentindustrystandardtendstofavorsmaller,morefrequentsamples.如果采取消除特別起因行動(穩(wěn)定過程)并且能力被證明,100%監(jiān)視可能被取消(但是要知道客戶的特殊檢查計(jì)劃).2023/12/738

建立和維護(hù)控制限SettingUpandMaintainingControlLimits用20-25個(gè)樣本計(jì)算控制限,每個(gè)樣本大小為3-5。 Calculatethecontrollimitswith20-25samples(e.g.,fortheXandRchartthatwouldmean20-25samplesofsize3-5).如果受控進(jìn)入最后一步。Ifprocessisincontrol,gotothelaststep.

如果不受控，找出特殊原因Ifprocessisnotincontrol,trytoidentifyspecialcause.消除特殊原因，重新收集數(shù)據(jù)，重新計(jì)算控制限，直到過程受控Removespecialcause,recollectdata,recalculatecontrollimits,…untilyoufindtheprocessisincontrol.在未來的監(jiān)測中不要隨意的改變控制限，除非過程有永久和渴望的改變。Forfuturemonitoring,donotchangethelimitsunlessapermanent,desiredchangehasbeenmadetotheprocess..2023/12/739兩種數(shù)據(jù)類型控制圖

TwoGeneralKindsofData屬性控制圖ATTRIBUTE

使用離散,可計(jì)的數(shù)據(jù) Pass/Fail,Good/Bad,Go/No-GoInformation合格/不合格,好/壞,通過/不通過等信息CanBeManyCharacteristicsPerChart一張圖可以同時(shí)描述許多特性

LessExpensive,ButLessInformation需要較少的資源，所含信息量亦較少

Ex: 1,2,3,4etc… Good/Bad Machine1,2,3...變量控制圖VARIABLES

使用連續(xù),可測量的數(shù)據(jù) Continuous,MeasuredDataCycleTime,Lengths,Diameters,Drops,etc周期,長度,直徑,體積,等等GenerallyOneCharacteristicPerChart通常每張圖描述一種特性

MoreExpensive,ButMoreInformation需要更多的資源,但所含信息量更多

Ex: Weight=10.2Lbs Thickness=11.211inches.2023/12/740螺釘扭矩在每個(gè)裝配線傳輸?shù)淖笄敖请x開

Bolttorqueonthefrontleftcornerofeverytransmissioncomingofftheassemblyline每個(gè)螺釘離開裝配線傳輸?shù)钠骄ぞ?Averagebolttorqueofeveryboltforeachtransmissioncomingofftheassemblyline(3) 每個(gè)發(fā)動機(jī)所缺的螺釘數(shù) #ofmissingboltsperengine(4) 每個(gè)銷售合同的排字?jǐn)?shù) #oftypospersalescontract每月生產(chǎn)缺陷發(fā)動機(jī)的數(shù)目

Numberofengineswithdefectsinmonthlyproduction每月生產(chǎn)缺陷發(fā)動機(jī)的的百分比數(shù) %ofdefectiveenginesinmonthlyproduction根據(jù)應(yīng)收帳款,收回它的時(shí)間 Peraccountsreceivable,amountoftimeittakestocloseit每100個(gè)發(fā)動機(jī)的缺陷數(shù) Numberofengineswithdefectsper100built練習(xí)：什么類型的數(shù)據(jù)？

Exercise:WhatTypeofData?.2023/12/741屬性型變量連續(xù)型變量數(shù)據(jù)類型？連續(xù)變量VS屬性變量數(shù)據(jù)分組還是單個(gè)數(shù)據(jù)?缺陷數(shù)VS缺陷比例?GROUPS(Averages)(n>1)INDIVIDUALVALUES(n=1)X-BarRX-BarSIndividualsMovingRange缺陷數(shù)缺陷比例IsTheProbabilityOfADefectLow?IfYouKnowHowManyAreBad,DoYouKnowHowManyAreGood?PoissonDistributionBinomialDistributionIndividualsMovingRangeNOYESYES樣本大小一定？YESNOcChartuChart樣本大小一定？npChartNOYESpChart如何選擇控制圖

ChoosingtheCorrectControlChart

NOTE:X-BarSisappropriateforsubgroupsizes(n)of>10.2023/12/742控制圖的主要類型

MajorTypesofControlCharts變量圖 VariablesChartsI-MR(個(gè)體 individuals)X-Bar(平均 average)特性圖 AttributeChartsNP (有缺陷的數(shù)字 Numberdefective)P (有缺陷的比率 Proportiondefective)C (過失數(shù)量 Numberofdefects)U (每個(gè)單位的過失數(shù)量Numberofdefects/unit).2023/12/743練習(xí):選擇什么類型的控制圖?

Exercise:WhatTypeofControlChart?螺釘扭矩在每個(gè)裝配線傳輸?shù)淖笄敖请x開

Bolttorqueonthefrontleftcornerofeverytransmissioncomingofftheassemblyline每個(gè)螺釘離開裝配線傳輸?shù)钠骄ぞ?Averagebolttorqueofeveryboltforeachtransmissioncomingofftheassemblyline(3) 每個(gè)發(fā)動機(jī)所缺的螺釘數(shù) #ofmissingboltsperengine(4) 每個(gè)銷售合同的排字?jǐn)?shù) #oftypospersalescontract每月生產(chǎn)缺陷發(fā)動機(jī)的數(shù)目

Numberofengineswithdefectsinmonthlyproduction每月生產(chǎn)缺陷發(fā)動機(jī)的的百分比數(shù) %ofdefectiveenginesinmonthlyproduction根據(jù)應(yīng)收帳款,收回它的時(shí)間 Peraccountsreceivable,amountoftimeittakestocloseit每100個(gè)發(fā)動機(jī)的缺陷數(shù) Numberofengineswithdefectsper100built.2023/12/744VariableControlCharts連續(xù)數(shù)據(jù)控制圖

X-barRChart平均值和極差圖

(Xbar-R圖).2023/12/745屬性型變量連續(xù)型變量數(shù)據(jù)類型？連續(xù)變量VS屬性變量數(shù)據(jù)分組還是單個(gè)數(shù)據(jù)?缺陷數(shù)VS缺陷比例?GROUPS(Averages)(n>1)INDIVIDUALVALUES(n=1)X-BarRX-BarSIndividualsMovingRange缺陷數(shù)缺陷比例IsTheProbabilityOfADefectLow?IfYouKnowHowManyAreBad,DoYouKnowHowManyAreGood?PoissonDistributionBinomialDistributionIndividualsMovingRangeNOYESYES樣本大小一定？YESNOcChartuChart樣本大小一定？npChartNOYESpChart如何選擇控制圖

ChoosingtheCorrectControlChart

NOTE:X-BarSisappropriateforsubgroupsizes(n)of>10.2023/12/746有效的連續(xù)數(shù)據(jù)控制圖包括...

AValidVariableControlChartHas…

Dataintimeorproductionsequence以時(shí)間或生產(chǎn)順序排序的數(shù)據(jù)toshowstability,time-to-timevariation表示穩(wěn)定性，隨時(shí)間的波動Ameasureofcentraltendency對居中趨勢的測量toportraybehaviorofprocesscenter描述過程的居中Ameasureofvariability對離散程度的測量Controllimits控制極限toallowseparatingcommoncausefromassignablecause可用來區(qū)分通常原因和特殊原因(可歸因原因)

X-Bar-Rcharts(Xbar-R圖)XBarChart:aplotofthesamplemeansovertime.

Xbar圖：反映樣本平均值隨時(shí)間的變化RChart:aplotoftherange(differencebetweenhighestandlowestvalues)ofasampleovertime.R圖：反映樣本的極差(樣本中最大值和最小值的差)隨時(shí)間的變化.2023/12/747Xbar-R圖實(shí)例

MinitabFile:Xbar_r.mtwcontainsmeasureddataforamainshaftO.D.—seecolumn1(C1)=NC_Lathe.Thedataisinsubgroupsofsize3.Minitab文件:Xbar_r.mtw包含主軸的測量數(shù)據(jù)，數(shù)據(jù)見C1欄(NC_Lathe).數(shù)據(jù)子樣為3.TheO.D.specificationsare.060+/-.003.產(chǎn)品的規(guī)范是.060+/-.003.=============1.Checkstabilitywitharunchart.用趨勢圖檢驗(yàn)過程的穩(wěn)定性2.Checkfornormality.檢驗(yàn)過程是否是正態(tài)分布3.UsingMinitab,createanXbarandRChart—whatareyourobservations?

用Minitab畫出Xbar-R圖，你得出什么觀察結(jié)論?4.Dothegivenspecifications(specs)“relate”totheControlLimitsontheXbarChart?Ifso,how?

給出的產(chǎn)品規(guī)范與Xbar圖的控制極限相關(guān)嗎？如果是的話，如何相關(guān)？5.HowdoesProcessControl“relate”toProcessCapability?

過程控制如何與過程能力相關(guān)？.2023/12/748MINITABFILE:Xbar_r.mtwMINITAB文件:Xbar_r.mtwXbar-R圖實(shí)例.2023/12/7491.DoubleClick“C1.”雙擊“C1.”2.Typeina3forSubgroupsize.子樣大小為3.3.Click“OK.”

點(diǎn)擊“OK.”Notethat3.0SLdenotesa3sigmalimit=ControlLimit注意3.0SL表示控制極限=3sigma水平Donotconfusethiswithspecificationlimits.不要將控制極限與規(guī)范極限混淆Xbar-R圖實(shí)例.2023/12/750Thecontrollimitsareforaverages,notindividualvalues.控制極限是根據(jù)平均值計(jì)算得出的Mostspecificationsareforindividualvalues.大多數(shù)規(guī)范是關(guān)于個(gè)體數(shù)值的USLUCLLCLLSLXbar-R圖實(shí)例.2023/12/751VariableControlCharts：I&MRChart

連續(xù)數(shù)據(jù)控制圖：I-MR圖.2023/12/752離散型變量連續(xù)型變量數(shù)據(jù)類型？連續(xù)變量VS屬性變量數(shù)據(jù)分組還是單個(gè)數(shù)據(jù)?缺陷數(shù)VS缺陷比例?GROUPS(Averages)(n>1)INDIVIDUALVALUES(n=1)X-BarRX-BarSIndividualsMovingRange缺陷數(shù)缺陷比例IsTheProbabilityOfADefectLow?IfYouKnowHowManyAreBad,DoYouKnowHowManyAreGood?PoissonDistributionBinomialDistributionIndividualsMovingRangeNOYESYES樣本大小一定？YESNOcChartuChart樣本大小一定？npChartNOYESpChart如何選擇控制圖

ChoosingtheCorrectControlChart

NOTE:X-BarSisappropriateforsubgroupsizes(n)of>10.2023/12/753I-MR圖Moreusefulinlowvolume,intermittentoperations

在數(shù)據(jù)量較少，間歇性操作時(shí)更有用SimilartoXbar&RCharts,Except…除以下幾點(diǎn)外，與Xbar-R圖相似SingleValues,NotSubgroups單個(gè)數(shù)值，不是子樣平均值RangeValuesMustBeArtificiallyConstructed極差值需要人工計(jì)算Somewhat“Noisier”BecauseOfLossOf“Damping”由于使用個(gè)體數(shù)值，與Xbar-R圖比較更易受干擾

IMChartsIM圖IndividualsChart:aplotoftheindividualvaluesovertime.

個(gè)體圖(I圖)：反映個(gè)體數(shù)值隨時(shí)間的變化MovingRangeChart:aplotofthemovingrange(fortwosamples|Xi-Xi-1|)overtime.

移動極差圖(MR圖)：反映兩個(gè)連續(xù)樣本的移動極差隨時(shí)間的變化

.2023/12/754IndividualData個(gè)體數(shù)據(jù)

MovingRange移動極差55 N/A56 ABS(55-56)=159 ABS(56-59)=355 ABS(59-55)=4605958575655Individuals個(gè)體43210MovingRange移動極差建立I-MR圖.2023/12/7552023/12/756Datafromashaftdiameterturningoperationareenteredonthecontrolchartformonthenextpagefor25consecutivepiecesofproduct,inproductionsequence.

數(shù)據(jù)是按照生產(chǎn)次序排列的25個(gè)連續(xù)的轉(zhuǎn)軸產(chǎn)品的直徑ThedataisinMinitabFile:Imr.mtw,columnshaft_OD.UsingMinitab,createtheI-MRchart.數(shù)據(jù)在Minitab文件:Imr.mtw的shaft_OD.欄中，用Minitab畫I-MR圖Analyzeyourresults.Arethereout-of-controlindications?Listtheindications,ifany,bytypeandbyplotpointnumbers.分析結(jié)果，過程是否有失控的征兆?根據(jù)征兆類型及其編號，列出失控征兆

Whatishappeningintheprocess?過程出現(xiàn)了什么情況?I-MR圖實(shí)例.2023/12/757MINITABFILE:Imr.mtwMINITAB文件:Imr.mtwI-MR圖實(shí)例.2023/12/7581.Doubleclickon“Shaft_OD.”

雙擊“Shaft_OD.”2.Click“Tests.”

點(diǎn)擊“Tests.”3.Clickon“Performalleighttests.”

點(diǎn)擊“Performalleighttests.”I-MR圖實(shí)例.2023/12/759I-MR圖實(shí)例.2023/12/760

連續(xù)數(shù)據(jù)控制圖小結(jié)

TakeAways—VariableControlCharts

Variablecontrolchartscanbeusedwithcontinuousdatatotellwhenaprocessis:連續(xù)數(shù)據(jù)控制圖可以用來區(qū)分過程狀態(tài):experiencingonlycommoncausevariationandworkingatitsintendedbest過程只包含通常原因引起的偏差，處于受控狀態(tài)

whentheprocessisdisturbedandneedscorrectiveaction過程受到干擾，需要采取糾正行動控制圖:timeorderedplotofdata描繪數(shù)據(jù)隨時(shí)間的變化reflecttheexpectedrangeofvariationofthedata反映所期望的數(shù)據(jù)波動的范圍

identifieswhenaspecialcauseappearstobeinfluencingthedata識別何時(shí)特殊原因出現(xiàn)，影響數(shù)據(jù)分布

X-Bar&Rchartsareusedforplottingmeansandrangesofsubgroupsovertime.Xbar-R圖用來描述子樣的平均值和極差隨時(shí)間的變化

I&MRchartsareusedforplottingindividualvaluesandmovingrangesovertime.I-MR圖用來描述個(gè)體的數(shù)值和移動極差隨時(shí)間的變化

.2023/12/761Controllimitsaretypicallycalculatedas3standarddeviationsawayfromthemeanoftheprocess.

控制極限一般是按過程中心值+/-3個(gè)標(biāo)準(zhǔn)偏差計(jì)算出來的Controllimitsandspecificationlimitsarenotthesame.控制極限和規(guī)范極限是不一樣的

Controllimitsarecalculatedfromthesampledata;theyareinternaltotheprocess控制極限是根據(jù)樣本數(shù)據(jù)計(jì)算得出的;是過程的內(nèi)部特征

Specificationlimitsaredeterminedbyyourperformancestandard;theyareexternaltotheprocess規(guī)范極限是由執(zhí)行的標(biāo)準(zhǔn)決定的;是過程的外部特征

Knowwhenaprocessisoutofcontrol:WesternElectricRules.知道過程何時(shí)失控:WesternElectric規(guī)則Controlchartsareonlyasgoodastheactionsthatyoutaketokeeptheprocessundercontrol.控制圖和采取的糾正行動共同使過程保持受控

連續(xù)數(shù)據(jù)控制圖小結(jié)

TakeAways—VariableControlCharts

.2023/12/762AttributeControlCharts

邏輯數(shù)據(jù)控制圖

.2023/12/763屬性型變量連續(xù)型變量數(shù)據(jù)類型？連續(xù)變量VS屬性變量數(shù)據(jù)分組還是單個(gè)數(shù)據(jù)?缺陷數(shù)VS缺陷比例?GROUPS(Averages)(n>1)INDIVIDUALVALUES(n=1)X-BarRX-BarSIndividualsMovingRange缺陷數(shù)缺陷比例IsTheProbabilityOfADefectLow?IfYouKnowHowManyAreBad,DoYouKnowHowManyAreGood?PoissonDistributionBinomialDistributionIndividualsMovingRangeNOYESYES樣本大小一定？YESNOcChartuChart樣本大小一定？npChartNOYESpChart如何選擇控制圖

ChoosingtheCorrectControlChart

NOTE:X-BarSisappropriateforsubgroupsizes(n)of>10.2023/12/764重要定義

ImportantDefinitionsADefect(缺陷)Asinglecharacteristicthatdoesnotmeetrequirements

不滿足要求的單一特性ADefective(缺陷率)AunitthatcontainsoneormoreDEFECTS

包含單個(gè)或多個(gè)缺陷的單位AttributeChartsCanConsiderEitherCaseDependingOnTheChartTypeChosen根據(jù)所選擇的控制圖類型，邏輯數(shù)據(jù)控制圖可以考慮兩者之一的情形.2023/12/765邏輯數(shù)據(jù)控制圖的分類

ClassificationofAttributeChartTypes

cunppConstantLot/UnitSize樣本數(shù)不變VariableLot/UnitSize樣本數(shù)變化Defects缺陷數(shù)Poisson泊松分布Binomial兩項(xiàng)式分布Defective缺陷率.2023/12/766AttributeControlChart

邏輯數(shù)據(jù)控制圖

C-Chart(C圖).2023/12/767屬性型變量連續(xù)型變量數(shù)據(jù)類型？連續(xù)變量VS屬性變量數(shù)據(jù)分組還是單個(gè)數(shù)據(jù)?缺陷數(shù)VS缺陷比例?GROUPS(Averages)(n>1)INDIVIDUALVALUES(n=1)X-BarRX-BarSIndividualsMovingRange缺陷數(shù)缺陷比例IsTheProbabilityOfADefectLow?IfYouKnowHowManyAreBad,DoYouKnowHowManyAreGood?PoissonDistributionBinomialDistributionIndividualsMovingRangeNOYESYES樣本大小一定？YESNOcChartuChart樣本大小一定？npChartNOYESpChart如何選擇控制圖

ChoosingtheCorrectControlChart

NOTE:X-BarSisappropriateforsubgroupsizes(n)of>10.2023/12/768C-Chart(C圖)Chartfordefectsperunit(subgroup)

描述每單位或子群所包含的缺陷的控制圖BasedonPoissondistribution

根據(jù)泊松分布而來Highprobabilityoffindingdefectofsometype.Largesamplesareneededifdefectprobabilitiesarelow.

發(fā)現(xiàn)某些缺陷的可能性高；如果缺陷概率低的話，需要大樣本。Lowerprobabilityofadefectofagiventype特定類型缺陷發(fā)生的可能性低Worksbestoncomplexunitofproduct

在產(chǎn)品單元復(fù)雜時(shí)效果最佳Constantsubgroup/lotsize

子樣大小為常數(shù).2023/12/769C圖實(shí)例AttributeData邏輯數(shù)據(jù)ManufacturingdataindicatesthatasignificantlossoccursfromweldingnonconformancesonpartAdetectedatNDT.ThedataonthenumberandgeneraltypeofnonconformityforeachparttestedismaintainedbyserialnumberintheNDTlogbooks.生產(chǎn)數(shù)據(jù)表明部件A的焊接不合格造成了可觀的損失，測試的每個(gè)部件不合格的數(shù)目和類型都有相應(yīng)的記錄。

TodeterminethecurrentperformanceoftheweldingprocesswewillplotthenumberofnonconformitiespersubgroupoftwopartsonaC-Chartusingthedatafromthelogbook:

為了確定目前焊接過程的表現(xiàn)，根據(jù)記錄的數(shù)據(jù)用C圖畫出每一子樣(2個(gè)部件)的不合格數(shù)

Date日期 6/1 6/2 6/3 6/4 6/5 6/8 6/9Numberof4 2 5 6 10 5 6Nonconf. 3 2 8 5 7 6per 7 4 9 9 Subgroup每一子樣的不合格數(shù) 7 5 7 4 5 6 6 7ExamplePartI.實(shí)例第一部分：ThefileC_chart,columnweld_I,containsthedatagivenabove.以上數(shù)據(jù)在文件C_chart中的weld_I列1. UsingMinitab,createaC-Chart.用Minitab畫出C圖2. Isthehighlevelofnonconformanceweareexperiencingduetoanassignablecauseorrandomvariation?

目前的高水平的不合格品是由可歸因原因還是隨機(jī)原因引起的偏差3. Whataresomeactionsforconsiderationtoreducethelevelofnonconformancesgeneratedbythisprocess?

為了降低過程的不合格水平，需要考慮采取什么措施？4.WhatistheProcessCapability?過程能力怎樣.2023/12/770MINITABFILE:C

chart.mtwMINITAB文件:C

chart.mtwC圖實(shí)例.2023/12/771C圖實(shí)例.2023/12/772AttributeControlCharts

邏輯數(shù)據(jù)控制圖

U-Chart(U圖).2023/12/773屬性型變量連續(xù)型變量數(shù)據(jù)類型？連續(xù)變量VS屬性變量數(shù)據(jù)分組還是單個(gè)數(shù)據(jù)?缺陷數(shù)VS缺陷比例?GROUPS(Averages)(n>1)INDIVIDUALVALUES(n=1)X-BarRX-BarSIndividualsMovingRange缺陷數(shù)缺陷比例IsTheProbabilityOfADefectLow?IfYouKnowHowManyAreBad,DoYouKnowHowManyAreGood?PoissonDistributionBinomialDistributionIndividualsMovingRangeNOYESYES樣本大小一定？YESNOcChartuChart樣本大小一定？npChartNOYESpChart如何選擇控制圖

ChoosingtheCorrectControlChart

NOTE:X-BarSisappropriateforsubgroupsizes(n)of>10.2023/12/774U-Chart-defectsperunit,variablelot(subgroup)sizeU圖描述子樣數(shù)變化時(shí)每單元的缺陷數(shù)SamelogicasC-Chart,exceptvariablelot(subgroup)size(n)

除了子樣數(shù)n可變外，原理與C圖相同U圖.2023/12/775InfileU_chart.mtw,column“errors”containstimeorderdataofcustomerpartsorderdefectsfoundeachday.Adefectisdefinedtobeinaccurateinformationfoundonapartsorderrequisition.Boththenumberofdefectsandthedailynumbe