統(tǒng)計(jì)運(yùn)用及品管實(shí)務(wù)工具資料數(shù)據(jù)基礎(chǔ)統(tǒng)計(jì)運(yùn)用概念生產(chǎn)製造環(huán)境實(shí)用品質(zhì)統(tǒng)計(jì)工具製程能力分析與SPC統(tǒng)計(jì)製程控制資料及數(shù)據(jù)你想瞭解什麼?資訊源:分組離散型名義型順序型間距型“資料本身並不能提供資訊——必須對資料加以處理以後才能得到資訊,而處理資料的工具就是統(tǒng)計(jì)學(xué)”.衡量連續(xù)型比率型●文字的(AtoZ)●圖示的●口頭的●數(shù)位的(0-9)數(shù)據(jù)FAILPASS計(jì)時(shí)器

NO-GOGO

數(shù)量

單價(jià)

說明

總價(jià) 1 $10.00 $10.00 3 $1.50 $4.50 10 $10.00 $10.00 2 $5.00 $10.00裝貨單

離散型資料和連續(xù)型資料電氣電路溫度溫度計(jì)連續(xù)型離散型卡尺錯誤離散型資料(通常)分組/分類是/否,合格/不合格不能計(jì)算

離散型資料

分級

很少用

很難加以計(jì)算

連續(xù)型資料

最常見的尺規(guī)

計(jì)算時(shí)要很小心

連續(xù)型資料

比例關(guān)係

可應(yīng)用演算法的多數(shù)公式

分類

標(biāo)簽

第一、第二、第三

相對高度

字母順序

1<2<3<4溫度計(jì)

刻度盤

速度=距離/時(shí)間

直尺

衡量工具分類說明例子衡量工具分類名義型:不相關(guān)類,只代表符合條件或不符合條件個體數(shù).順序型:順序類,但沒有各類間隔的資訊.間距型:順序類,兩類之間間隔相等,但沒有絕對零點(diǎn).比例型:順序類,兩

類之間間隔相等,同時(shí)存在絕對零點(diǎn)..離散型連續(xù)型$$連續(xù)資料的優(yōu)勢

連續(xù)的離散的信息量少信息量多基礎(chǔ)統(tǒng)計(jì)運(yùn)用概念變異(Variation)

當(dāng)我們從一過程中收集數(shù)據(jù),會發(fā)現(xiàn)數(shù)據(jù)不會永遠(yuǎn)相同,因?yàn)樽儺?Variation)在過程中隨時(shí)存在

製造流程Step1Step2Step3ProcessOutputOutputofProcessStepEquipmentMaterialsEnvironmentPeopleMethodsInformation變異(Process)=變異(Step1)+變異(Step2)+變異(Step3)+...

變異(ProcessStep)=

變異(Methods)+變異(Materials)+變異(Environment)+變異(People)+變異(Equipment)+變異(Information)變異(Variation)

我們觀察到的變異,是在過程中各種擾動累積起來的.變異(Variation)

參數(shù)XXXXXXXXX量測值分佈多數(shù)在此少數(shù)在此Center均值Spread散佈雖然變異是隨機(jī)的,但他們的隨機(jī)性通常有模式存在,這種模式可用統(tǒng)計(jì)上的分佈(Distribution)來形容.如此變異加以統(tǒng)計(jì)分析,便可有某種程度的預(yù)測性存在並易於被理解或控制.變異(Variation)中心Center:數(shù)據(jù)最最集中中在何何處?散佈Spread:數(shù)據(jù)變變異程程度及及分散散狀況況如何何?形狀Shape:分佈是是否對對稱?扁平平?凹凹凸?是否有有異常常區(qū)描述分佈(Distribution)Shape形狀Center中心Spread散佈變異(Variation)變異可可以是是穩(wěn)定定(Stable)或不穩(wěn)定(Unstable)的.-穩(wěn)穩(wěn)定變變異:變化化的分分佈較較具預(yù)預(yù)測性性及一一致性性,對時(shí)間間而言言具可可預(yù)測測性-不不穩(wěn)定定變異異:對對時(shí)間間而言言不具具可預(yù)預(yù)測性性PROCESS#1-StableVariation穩(wěn)定定PartThicknessPROCESS#2-UnstableVariation不穩(wěn)定定PartDistributionDistributionThickness變異異(Variation)在製製造造過過程程中中,有有變變異異都都是是不不好好.問問題題是是我我們們能能容容忍忍到到何何種種範(fàn)範(fàn)圍圍.我我們們能能容容忍忍的的變變異異是是具具有有以以下下兩兩項(xiàng)項(xiàng)特特徵徵:TimeParameterSTABLE(i.e.,consistentandpredictableovertime).CAPABLE(i.e.,smallvariationcomparedtotheproductspecifications.)ProductSpecificationsParameterDistribution穩(wěn)定散佈小控制變異(Variation)1.Characterize2.Improve3.Control瞭解過程:使制程更好好:保持穩(wěn)定並並維持高制制程能力過程由時(shí)間間來看是否否穩(wěn)?制程能力是是否能滿足足目標(biāo)規(guī)格格?確認(rèn)並除去去不穩(wěn)定原原因確認(rèn)並降低低變異程度度使?jié)M足規(guī)規(guī)格持續(xù)監(jiān)視及及控制過程程的變異源源特徵化改善控制因?yàn)橛贸闃訕咏y(tǒng)計(jì),其其結(jié)果只是是估計(jì),和真實(shí)可能能有差異.適當(dāng)?shù)某闃訕涌墒菇y(tǒng)計(jì)計(jì)分析更準(zhǔn)準(zhǔn)確.Statistics分佈的數(shù)學(xué)學(xué)描述與定定義中心Center:數(shù)據(jù)最集中中在何處?散佈Spread:數(shù)據(jù)變異程程度及分散散狀況如何何?形狀Shape:分佈是否對對稱?扁平平?凹凸?是否有異常常區(qū)樣本均值=X樣本本抽樣樣概概念念-母母體體參參數(shù)數(shù)和和樣樣本本統(tǒng)統(tǒng)計(jì)計(jì)量量母體體:包含含所所關(guān)關(guān)心心特特性性的的已已經(jīng)經(jīng)製製造造或或?qū)⒁u製造造的的物物件件的全體樣本:在統(tǒng)計(jì)研究中中實(shí)際測量的的物件組。樣本通常爲(wèi)所所關(guān)心母體的的子集“母體參數(shù)””“樣本統(tǒng)計(jì)量量”m=母體均值s=樣本標(biāo)準(zhǔn)偏差差母體s=母體標(biāo)準(zhǔn)偏差差~抽樣方法抽樣方法上面介紹了幾幾種從母體中中抽樣的方式式隨機(jī)性從母體中中抽取的樣本本設(shè)計(jì)應(yīng)使母母體中每一個個都有同等機(jī)機(jī)會抽中.代表性作為同一一母體中其他他樣本的實(shí)例例.系統(tǒng)隨機(jī)抽樣樣分組抽樣每一小時(shí)在該該點(diǎn)抽3個樣本隨機(jī)抽樣每個均有被選選上的相等機(jī)機(jī)會層別式抽樣母體被“層別別”成幾個組組,在每個組組內(nèi)隨機(jī)選擇擇.行進(jìn)中的過程程每隔n個柚樣一般準(zhǔn)則計(jì)數(shù)數(shù)據(jù):50-100計(jì)量數(shù)據(jù):每每個分組最少少是30均值:一一組值的算術(shù)平均均值:-反映所有有值的影響-受極值影影響嚴(yán)重中位數(shù):反應(yīng)50%的序一組數(shù)排排序後居中的的數(shù)-在計(jì)算中不必必包含所有值值-相相對於於極值值具有有“可靠靠性”眾數(shù)值值:-在一組組資料料中最最常發(fā)發(fā)生的的值Median(Mean平均)(Median中數(shù))眾數(shù)Center(中心)50%50%全距:在一組資料料中，最高高值和最低低值間的數(shù)值距距離變異(s2):每個資料點(diǎn)點(diǎn)與均值的的平均平方方偏差標(biāo)準(zhǔn)偏差(s):變異數(shù)的平平方根.量化變動最最常用的量量全距＝最大大值－最小小值Spread(散佈)6sThe"Rule"stateshowandcanbeusedtodescribetheentiredistribution:·Roughly60-75%ofthedataarewithin1of.·Roughly90-98%ofthedataarewithin2of.·Roughly99-100%ofthedataarewithin3of.60-75%90-98%99-100%mm-sm-2sm+sm+2sm+3sm-3sSpread(散佈)Theshapeofadistributioncanbedescribedbyskewness歪斜(denotedby1)andbykurtosis凹凸平坦坦(denotedby2).g1

>0g1

=0g1

<0g2

>0g2

=0g2

<0歪斜凹凸平坦坦Shape(形狀)母體均值值樣本均值值母體標(biāo)準(zhǔn)偏差差樣本標(biāo)準(zhǔn)偏差差常用計(jì)算公式~母體變異樣本變異~ThemostimportantandusefuldistributionshapeiscalledtheNormaldistribution,whichissymmetric(對稱),uni-modal(單峰),andfreeofoutliers(沒有特異點(diǎn)):NormalDistribution常態(tài)分佈“常態(tài)”分分佈是具有某某些一致屬性性的資料的分分佈這些屬性對理理解基礎(chǔ)過程程（資料從該該過程中收集集）的特徵非非常有用.大多數(shù)自然現(xiàn)現(xiàn)象和人爲(wèi)過過程都符合常常態(tài)分配，可可以用常態(tài)分分配表示,故大大部部份份統(tǒng)統(tǒng)計(jì)計(jì)都都假假設(shè)設(shè)是是常常態(tài)態(tài)分分佈佈。即使使在在資資料料不不完完全全符符合合常常態(tài)態(tài)分分配配時(shí)時(shí)，，分分析析結(jié)結(jié)果果也也很很接接近近。。特別別不不正正常常的的分分佈佈若若假假設(shè)設(shè)為為常常態(tài)態(tài)而而去去分分析析則則有有可可能能得得到到誤誤導(dǎo)導(dǎo)結(jié)結(jié)果果。有數(shù)學(xué)學(xué)技術(shù)術(shù)可可將其轉(zhuǎn)變變成成常常態(tài)態(tài)分分佈佈來作作分分析析。ANormalprobabilityplotisacumulativedistributionplotwheretheverticalscaleischangedinsuchawaythatdatafromaNormaldistributionwillformastraightline:HistogramCumulativeDistributionNormalProbabilityPlot常態(tài)態(tài)概概率率圖圖NormalDistribution常態(tài)態(tài)分分佈佈第一一個個屬屬性性:只只要要知知道道下下面面兩兩項(xiàng)項(xiàng)就就可可以以完完全全描描述述常常態(tài)態(tài)分分配配:均值值標(biāo)準(zhǔn)準(zhǔn)差差常態(tài)態(tài)分分配配的好處處-簡化化第一個個分佈佈第二個個分佈佈第三個個分佈佈這三個個分佈佈有什什麼不不同?常態(tài)曲曲線和和其概概率43210-1-2-3-440%30%20%10%0%99.73%第二個個屬性性:曲曲線下下方的的面積積可以以用於於估計(jì)計(jì)某““事件件”發(fā)發(fā)生的的累積積概率率95%68%樣本值值的概概率距離均均值的的標(biāo)準(zhǔn)準(zhǔn)偏差差數(shù)得到兩兩值之之間的的值的的累積積概率率常態(tài)概概率圖圖130120110100908070603002001000C2常態(tài)概率圖頻率1101009080706050403020100500C1常態(tài)概率圖頻率807060504030201003002001000C3常態(tài)概率圖頻率13012011010090807060.95.01.001平均：70標(biāo)準(zhǔn)偏差：10資料個數(shù)：500Anderson-Darling常態(tài)測試A平方:46.447P-值:0.000正偏斜分佈概率正偏斜1069686766656463626.95.01.001常態(tài)分配常態(tài)概率平均值：70標(biāo)準(zhǔn)偏差:10資料個數(shù)：500Anderson-Darling常態(tài)測試A平方:0.418P-值:0.328我們可可以用用常態(tài)態(tài)概率率圖檢檢驗(yàn)一一組給給定的的資料料是否否可以以描述述爲(wèi)““常態(tài)態(tài)”如果一一個分分佈接接近常常態(tài)分分配，，則常常態(tài)概概率圖圖將爲(wèi)爲(wèi)一條條直線線。資料收收集時(shí)時(shí)的重重點(diǎn)Howthedataarecollectedaffectsthestatisticalappropriatenessandanalysisofadataset(資料如如何收收集可可影響響統(tǒng)計(jì)計(jì)的適適切性性).Conclusionsfromproperlycollecteddatacanbeappliedmoregenerallytotheprocessandoutput.InappropriatelycollecteddataCANNOTbeusedtodrawvalidconclusionsaboutaprocess.Someaspectsofproperdatacollectionthatmustbeaccountedforare:Themanufacturingenvironment(製程環(huán)環(huán)境)fromwhichthedataarecollected.Whenproductsaremanufacturedinbatchesorlots,thedatamustbecollectedfromseveralbatchesorlots.Randomization(隨機(jī)).Whenthedatacollectionisnotrandomized,statisticalanalysismayleadtofaultyconclusions.ContinuousManufacturing(連續(xù))occurswhenanoperationisperformedononeunitofproductatatime.Anassemblylineistypicalofacontinuousmanufacturingenvironment,whereeachunitofproductisworkedonindividuallyandacontinuousstreamoffinishedproductsrollofftheline.TheautomotiveindustryisoneexampleofContinuousManufacturing.Otherexamplesofcontinuouslymanufacturedproductare:·televisionsets,·fastfoodhamburgers,·computers.Lot/BatchManufacturing(批次)occursoccurswhenoperationsareperformedonproductsinbatches,groups,orlots.Thefinalproductcomesoffthelineinlots,insteadofastreamofindividualparts.Productwithinthesamelotareprocessedtogether,andreceivethesametreatmentwhilein-process.Lot/BatchManufacturingistypicalofthesemiconductorindustryandmanyofitssuppliers.Otherexamplesoflot/batchmanufacturedproductinclude:·chemicals,·semiconductorpackages,·cookies.生產(chǎn)製造環(huán)境境InContinuousManufacturingthemostimportantvariationisbetweenpartsInLot/BatchManufacturing,thevariationcanoccurbetweenthepartsinalotandbetweenthelots:·Productwithinthesamelotismanufacturedtogether.·Productfromdifferentlotsaremanufacturedseparately.Becauseofthis,eachlothasadifferentdistribution.ThisisimportantbecauseContinuousManufacturingisabasicassumptionformanyofthestandardstatisticalmethodsfoundinmosttextbooksorQChandbooks.ThesemethodsarenotappropriateforLot/BatchManufacturing.DifferentstatisticalmethodsneedtobeusedtotakeintoaccounttheseveralsourcesofvariationinLot/BatchManufacturing.要注意:連連續(xù)和批量生生產(chǎn)所用的統(tǒng)統(tǒng)計(jì)方法有些些不同WithLot/BatchManufacturing,eachlothasadifferentmean.Duetorandomprocessingfluctuations,theselotswillvaryeventhoughtheprocessmaybestable.Thisresultsinseveral“l(fā)evels”ofdistributions,eachlevelwithitsownvarianceandmean:·Adistributionofunitsofproductwithinthesamelot.·Adistributionofthemeansofdifferentlots.·Thetotaldistributionofallunitsofproductacrossalllots.LotX12345**********DistributionofIndividualLotDistributionofLotMeansOverallDistributionofCombinedLotsVariationWithinEachLotVariationBetweenLotsTotalVariation2222222X12X2212121,,;X;X;XXXX+=+====總總總6原則變異數(shù)可可相加,標(biāo)準(zhǔn)準(zhǔn)差則不不能相加加輸入變數(shù)數(shù)變異數(shù)數(shù)相加計(jì)計(jì)算輸出出中的總總變異數(shù)數(shù)所以那麼引起的變變異數(shù)輸入變數(shù)數(shù)引起的變變異數(shù)輸入變數(shù)數(shù)過程輸出出的變異異數(shù)如果123456LotsWithinissmallsLotislargeprocesshassmallwithin-lotvariationandlargelot-to-lotvariation(whichisverycommon),datavaluesfromthesamelotwillbehighlycorrelated,whiledatafromdifferentlotswillbeindependent:實(shí)用品質(zhì)質(zhì)統(tǒng)計(jì)工工具直方圖(Histograms)柏拉圖(ParetoDiagrams)散佈圖(Scatterplots)趨勢圖(TrendCharts)品質(zhì)統(tǒng)計(jì)計(jì)圖表-直方圖(Histograms)Histogramsprovideavisualdescriptionofthedistributionofasetofdata.Ahistogramshouldbeusedinconjunctionwithsummarystatisticssuchasands.Ahistogramcanbeusedto:·Displaythedistributionofthedata(現(xiàn)示數(shù)數(shù)據(jù)的的分佈佈).·Provideagraphicalindicationofthecenter,spread,andshapeofthedatadistribution(較定性性地顯顯示數(shù)數(shù)據(jù)的的均值值,散散佈及及形狀狀).·Clarifyanynumericalsummarystatistics(whichsometimesobscureinformation).(顯示較較模糊糊的統(tǒng)統(tǒng)計(jì)結(jié)結(jié)果).·Lookforoutliers-datapointsthatdonotfitthedistributionoftherestofthedata.(顯示異異常點(diǎn)點(diǎn))::...:..::::::.::::.::.:...:.:.:::::::::::::::.::.::::..::.+++++加侖/分鐘鐘49.0049.5050.0050.5051.00點(diǎn)圖分佈設(shè)想有一個個泵流量爲(wèi)爲(wèi)50加侖侖/分鐘的的計(jì)量泵。。按照節(jié)拍對對泵的實(shí)際際流量進(jìn)行行了100次獨(dú)立測量量。畫出各個點(diǎn)點(diǎn)，每點(diǎn)代代表一個給給定值的輸輸出“事件”。當(dāng)點(diǎn)聚集集起來時(shí)，，泵的實(shí)際際性能狀況況可以看作作泵流量的的“分佈””。51.350.850.349.849.348.8403020100直方圖分佈還是這些資料料，現(xiàn)在設(shè)想想將其分組後後歸入“區(qū)間間”。泵流量量點(diǎn)落入指定定區(qū)間的次數(shù)數(shù)決定區(qū)間條條的高度。頻率加侖/分鐘品質(zhì)統(tǒng)計(jì)圖表表-直方圖(Histograms)150.7149.7154.5149.6155.3149.0160.5149.0155.3149.3149.2153.5145.5161.0151.5154.3150.9152.4150.5152.3144.5151.6151.1151.0147.5150.6147.4150.8148.3146.8148.7147.6153.0139.0153.4146.5151.4143.5149.4150.4153.1150.7149.1150.6149.6152.5145.2150.5146.4151.3151.7145.6147.1152.6147.0148.5155.0148.4151.3148.8146.7152.7155.3146.6144.8150.9149.5151.4147.3154.9151.2148.6142.5151.6151.0152.9146.9145.3150.8150.3153.6154.6150.6148.6155.1145.4148.5157.0148.9145.0147.7151.1149.7154.4149.1151.5153.3149.5152.8150.8品質(zhì)統(tǒng)計(jì)圖表表-直方圖(Histograms)·Multi-ModalShape(雙峰):·SkewedShape(偏一邊):Datacanberight-skewedorleft-skewed.Thisdataisright-skewed–therighttailislongerthanthelefttail.Outliers:特異點(diǎn)品質(zhì)統(tǒng)計(jì)圖表表-柏拉圖(ParetoDiagrams)Whilehistogramsareusedtodisplaythedistributionofasetofcontinuous(measured)data,Paretodiagramsareusedtodisplaythedistributionofdiscrete(counted)data,suchasdifferenttypesofdefects.Paretodiagramscanalsobeusedwithcontinuous(measured)data,particularlyindisplayingvariancecomponentsanalysisresults,aswewillseelaterinthiscourse.Paretodiagramsareausefultoolfordeterminingwhichproblemsortypesofproblemsaremostsevereoroccurmostfrequently,henceshouldbegivenhighpriorityforprocessimprovementefforts.Paretodiagramsseparatethesignificant"vitalfew"problemsfromthe"trivialmany"tohelpdeterminewhichproblemstoaddressfirst(andwhichtoaddresslater).重點(diǎn)中中找重重點(diǎn)!Pareto圖分析析Pareto圖根據(jù)frequency欄的內(nèi)內(nèi)容判判斷各各個缺缺陷影影響的的大小小，並並按從從大到到小的的次序序排列列。最後一一組總總是標(biāo)標(biāo)有““其其他””，，並以以默認(rèn)認(rèn)方式式包括括所有有缺陷陷的分分類計(jì)計(jì)算，，這幾幾類缺缺陷非非常少少，它它們們占總總?cè)毕菹莸?%以以下。。該圖右右側(cè)Y軸表示示占總總?cè)毕菹莸陌侔俜直缺?，左左?cè)Y軸表示示缺陷陷數(shù)。。紅線(在在螢?zāi)荒簧峡煽梢钥纯吹?表表示累累積百百分比比，而而直方方圖表表示每每類缺缺陷的的頻率率(占總總量的的百分分比)。。在圖圖的下下方列列出所所有的的值百分分比比缺陷陷的的Pareto圖計(jì)數(shù)數(shù)缺陷陷計(jì)數(shù)數(shù)2745943191018百分分比比64.813.94.3累積積百百分分比比％％64.878.788.993.493.4100.0螺釘釘丟丟失失夾子子丟丟失失襯墊墊泄泄漏漏外殼殼有有缺缺陷陷零件件不不完完整整其他他4003002001000100806040200百分分比比（（%））品質(zhì)質(zhì)統(tǒng)統(tǒng)計(jì)計(jì)圖圖表表-柏拉拉圖圖(ParetoDiagrams)層別別Pareto圖:解解釋釋分分組組資資料料上圖圖使使用用了了一一個個ByVariable（（從屬屬變變數(shù)數(shù)）），，所有有的的圖圖都都在在一一頁頁上上。。下下圖圖使使用用同同樣樣的的命命令令，，沒沒有有從從屬屬變變數(shù)數(shù)。。當(dāng)選選擇擇每每頁頁一一張張圖圖時(shí)時(shí)，，所所有有的的圖圖的的計(jì)計(jì)數(shù)數(shù)(左左軸軸)刻刻度度相相同同。。右右側(cè)側(cè)的的百百分分比比只只反反映映該該圖圖占占總總體體的的百百分分比比。。這些些圖圖表表明明，，70%的的記記錄錄缺缺陷陷是是刮刮傷傷和和剝剝落落的的(下下部部)，，約約有有一一半半的的缺缺陷陷是是夜夜班班人人員員記記錄錄的的(上上右右圖圖)。。此外，記記錄缺陷陷是刮傷傷和剝落落的比例例，對白白班和夜夜班的來來說似似乎也差差不多。。然而，，晚班和和周末班班出現(xiàn)的的缺陷樣樣式是不不同的。。裂紋Pareto圖白班晚班夜班周末班刮傷剝落其他污點(diǎn)151050151050151050151050裂紋Pareto圖403020100100806040200缺陷計(jì)數(shù)151366百分比37.532.515.015.0累積百分分比％35.570.085.0100.0刮傷撥落其他污點(diǎn)計(jì)數(shù)計(jì)數(shù)計(jì)數(shù)計(jì)數(shù)計(jì)數(shù)百分比（%））品質(zhì)統(tǒng)計(jì)圖表表-柏拉圖(ParetoDiagrams)品質(zhì)統(tǒng)計(jì)圖表表-散佈圖(Scatterplots)Untilnow,allthegraphicaltoolswe'vediscussedhavebeenforexaminingthedistributionofasingleprocesscharacteristic.Thescatterplotisagraphicaltoolforexaminingtherelationshipbetweentwoprocesscharacteristics.AscatterplotisanX-Yplotofonevariableversusanother.Eachunitofproductusuallyhasmanycharacteristics,processinputvariables,etc.Oneobjectivemightbetoseewhethertwovariablesorcharacteristicsarerelatedtoeachother(i.e.,toseewhathappenstooneofthevariableswhentheothervariablechanges).Thisrelationshipbetweentwovariablesiscalledcorrelation.Scatterplotscanhelpusanswerthistypeofquestion.品質(zhì)統(tǒng)計(jì)圖表表-散佈圖(Scatterplots)AcidAgeEtchRateAcidAgeEtchRateAcidAgeEtchRate4.0134.5134.0154.5181.5302.5233.0183.5191.0313.5195.575.044.0122.0253.5212.0241.0292.0261.0283.0205.593.0195.064.5145.095.592.5272.5251.5301.531品質(zhì)統(tǒng)計(jì)圖表表-散佈圖(Scatterplots)Inadditiontotellinguswhetherornottwovariablesarerelated,scatterplotscantellushowtheyarerelated,andthestrengthoftherelationship:StrongPositiveCorrelation強(qiáng)正相關(guān)NoCorrelation無關(guān)WeakNegativeCorrelation弱負(fù)相關(guān)WeakPositiveCorrelation弱正相關(guān)StrongNegativeCorrelation強(qiáng)負(fù)相關(guān)品質(zhì)統(tǒng)計(jì)圖圖表-散佈圖(Scatterplots)Inaddition,scatterplotsareanexcellenttoolfordeterminingthetypeofrelationshipbetweenthetwovariables,aswellaslookingforoutliers:LinearRelationship線性相關(guān)Outliers特異Non-LinearRelationship非線性相關(guān)關(guān)品質(zhì)統(tǒng)計(jì)圖圖表-散佈圖(Scatterplots)CorrelationandCausationWemustalwaystakecarenottoconfusecorrelationwithcausation.Thefactthattwocharacteristicsarecorrelateddoesnotprovethatonecausestheother.Bothmayberelatedtosomeotherfactorwhichisthetruerootcause.NumberofTelevisionsNumberofTrafficAccidents19701990Butisthereacause-effectrelationshipbetweenthetwo?·DidtheincreaseinTV’scausethenumberofaccidentstogoup?(Notlikely.)·DidtheincreaseintrafficaccidentscausepeopletobuymoreTV’s?(Notlikely,either.)品質(zhì)統(tǒng)計(jì)圖圖表-趨勢圖(TrendCharts)TrendChartsStability:Aprocessisstableifitsmeanandstandarddeviationareconstantandpredictableovertime.Adisadvantageofhistogramsandnormalprobabilityplotsisthattheycannotbeusedtodeterminewhethertheprocessisstableovertime.Aplotofthedataintimeorderwillallowustodothat.Thesetime-orderedplots,calledTrendchartsandControlchartsareessentialwhenexaminingthestabilityofadistributionovertime.Atrendchartoracontrolchartcandetectinstabilityifitexists.Controlcharts,whichareaspecialkindoftrendchart,arediscussedindetailseparatelyinalatercoursemodule.可看出穩(wěn)定定性及預(yù)測測性品質(zhì)統(tǒng)計(jì)圖圖表-趨勢圖(TrendCharts)Thetablebelowcontainsaverageplatingthicknessmeasurementstakenfrom21lotsofproduct.Belowthatisatrendchartofthedata.Lot#PlatingThicknessLot#PlatingThicknessLot#PlatingThickness1151.98143.815149.22147.49152.716147.53155.810147.417151.94151.711152.718141.95149.212143.819152.76153.813137.120147.47159.914142.521157.3品質(zhì)統(tǒng)計(jì)圖圖表-NoisyTheresultsofastatisticalanalysiscanbeseriouslyaffectedbythefailureofthedatatomeetcertainrequiredassumptions.OneofthemostcommonassumptionsisthatthedatavaluesareindependentandthattheycomefromaNormaldistribution.Thisassumptioncanbeviolatedinseveralways:·Outliers(pointsthatdonotfittherestofthedistribution)inthedata,·Non-Normal-shapeddistributions(multi-modalorskeweddistributions),Datathatexhibitthesecharacteristicscanbethoughtofasnoisydata.Theproceduresinthissectionprovidetechniquesforeffectivedetectionandanalysisofnoisydata.雜訊品質(zhì)統(tǒng)計(jì)圖圖表-NoisyBoxplotsTrendChartHistogramScatterplotNormalProb.Plot品質(zhì)統(tǒng)計(jì)圖圖表-NoisyRecommendedstrategyforhandlingoutliers:1.Identifytheoutliersusingthemethodsdescribedinthefollowingpages.Ifpossible,findthecausesoftheoutliers.Removetheoutlierswithidentifiedcausesfromthedataset(找原因).2.Ifalltheoutlierscanbeexplained,thenanalyzethedataasusual.3.However,ifthereareanyoutliersthatdonothaveexplanations,analyzethedatatwice:·includingtheoutliers,·excludingtheoutliers.Seeifandhowtheanalysisresultsdiffer.製程程能能力力分分析析與SPC統(tǒng)計(jì)計(jì)製程程控制制當(dāng)製製程程開開始始產(chǎn)產(chǎn)生生變變異異時(shí)時(shí),其其統(tǒng)統(tǒng)計(jì)計(jì)分分佈佈圖圖的的形形狀狀也也開開始始變變化化。。通通常常變變化化不不外外下下面面三三種種基基本本狀狀況況的的組組合合:整體製程數(shù)據(jù)漂移散佈變寬中心值漂移若將將每每日日之之統(tǒng)統(tǒng)計(jì)計(jì)分分佈佈串串起起來來一一起起看看,則又又可可看看到到更更多多變變異異現(xiàn)現(xiàn)象象,一般般可可分分為為兩兩種種如如下下:時(shí)間間時(shí)間間1.突突發(fā)發(fā)變變異異:製製程程中中有有特特殊殊或或突突發(fā)發(fā)原原因因而而產(chǎn)產(chǎn)生生變變異異,造成成不不穩(wěn)穩(wěn)定定。。例例:每每日日生生產(chǎn)產(chǎn)參參數(shù)數(shù)設(shè)設(shè)定定漂漂移移。。2.共共同同變變異異:製製程程中中只只有有共共同同原原因因的的變變異異此種現(xiàn)象是穩(wěn)穩(wěn)定的”不良良”。例:模模具尺寸超差差。瞭解以上基本本觀念後便開開始加入管制制的觀念。作作管制時(shí)加入入規(guī)格上下線線,超出規(guī)規(guī)格則視為不不良如下圖:製程能力好,中心值在目標(biāo)上且分佈均在規(guī)格內(nèi)製程能力尚可,中心值在目標(biāo)上,分佈均在規(guī)格內(nèi)但稍微太分散製程能力尚可,中心值有漂移,但分佈尚在規(guī)格內(nèi)製程能力不好,中心值雖在目標(biāo),但分佈超出規(guī)格外製程能力不好好,中心值不不在目標(biāo),分分佈雖集中但但超出規(guī)格外外製程能力最差差,中心值不不在目標(biāo),分分佈不集中且且超出規(guī)格外外計(jì)算Ca,Cp,Cpk公式規(guī)格中心mLSL+3-3製程寬度6規(guī)格寬度TUSLSuSLCa:CapabilityofAccuracy準(zhǔn)確確度度:實(shí)際際中中心心Ca-=Xm(T/2)-XmXCa只對對雙雙邊邊規(guī)規(guī)格格適適用用.分級級標(biāo)標(biāo)準(zhǔn)準(zhǔn)如如下下:等級

Ca值A(chǔ)│Ca│≦12.25%B12.25%<│Ca│≦25%C25%<│Ca│≦50%D│Ca│>50%主值值計(jì)算算Ca,Cp,Cpk公式式規(guī)格格中中心心mLSL+3-3製程寬寬度度6規(guī)格格寬度度TUSLSuSLCp:CapabilityofPrecision精確確度度:實(shí)際際中中心心-XmX當(dāng)僅僅有有下下限限時(shí)時(shí):Cp=(-SL)/(3σσ)對雙雙邊邊規(guī)規(guī)格格:Cp=T/(6σσ)當(dāng)僅僅有有上上限限時(shí)時(shí):Cp=(Su-)/(3σσ)XX等級Cp值A(chǔ)Cp≧1.33B1.00≦Cp<1.33C0.67≦Cp<1.00DCp<0.67分級級標(biāo)標(biāo)準(zhǔn)準(zhǔn)如如下下:主值計(jì)算算Ca,Cp,Cpk公式式Cpk:指制制程程能能力力參參數(shù)數(shù),是是Cp和Ca的綜綜合合.對雙雙邊邊規(guī)規(guī)格格:Cpk=(1-││Ca││)*Cp=Min[(Su-)/(3σσ),(-SL)/(3σσ)]對單單邊邊規(guī)規(guī)格格,可可以以認(rèn)認(rèn)為為T為∞∞,則則Ca=(-μμ)/(T/2)=0Cpk=(1-││Ca││)*Cp=Cp等級Cpk值評價(jià)ACpk≧1.33理想B1.00≦Cpk<1.33正常CCpk<1.0不足分級級標(biāo)標(biāo)準(zhǔn)準(zhǔn)如如下下:XXXSPC介紹紹SPC是用用於於研研究究變變動動的的一一種種基基本本工工具具,它它使使用用統(tǒng)統(tǒng)計(jì)計(jì)信信號號監(jiān)監(jiān)測測並並改改善善過過程程績績效效。。該該工工具具可可用用於於任任何何領(lǐng)領(lǐng)域域：：製製造造業(yè)業(yè)、、商商業(yè)業(yè)，，銷銷售售業(yè)業(yè)等等等等…SPC是統(tǒng)統(tǒng)計(jì)計(jì)程程式式控控制制（StatisticalProcessControl））的縮縮寫寫。。大大多多數(shù)數(shù)公公司司是是將將SPC用於於最最終終産産品品(Y)上,而而不不是是用用於於過過程程特特徵徵(X)。。第一一步步是是使使用用統(tǒng)統(tǒng)計(jì)計(jì)方方法法控控制制公公司司的的輸輸出出。。然然而而，，只只有有我我們們將將重重點(diǎn)點(diǎn)放放在在控控制制輸輸入入(X),而不是控控制輸出出(Y)時(shí),我我們才能能認(rèn)識到到我們在在提高質(zhì)質(zhì)量、生生産率及及降低成成本上的的努力收收效有多多大。什麼是統(tǒng)計(jì)製程控制（SPC））所有過程程都有固固有變動動（由於於一般原原因）和和非固有有變動（（由於特特殊原因因），我我們使使用SPC來監(jiān)測並並改善過過程。SPC的使用使使我們能能夠通過過失控信信號發(fā)現(xiàn)現(xiàn)特殊原原因。這這些失控控信號無無法說明明過程失失控的原原因，只只能表明明過程處處於失控控狀態(tài)?？刂茍D圖表是是在統(tǒng)統(tǒng)計(jì)上上從時(shí)時(shí)間上上跟蹤蹤過程程和産産品參參數(shù)的的方法法。控控制圖圖表中中包括括反映映過程程隨機(jī)機(jī)變動動固有有限值值的上上下控制限限值。這些限限值不不應(yīng)與與顧客規(guī)規(guī)定限限值相比較較。什麼是是統(tǒng)計(jì)製程控制（續(xù)））基本統(tǒng)統(tǒng)計(jì)原原理，，控制制圖表表能夠夠用於於識別別過程程變數(shù)數(shù)中的的非固固有（（非隨隨機(jī)））型式式。當(dāng)當(dāng)控制制圖表表出現(xiàn)現(xiàn)非隨隨機(jī)型型式信信號時(shí)時(shí)，我我們就就可以以知道道特殊殊原因因引起起的變變動改改變了了過程程。我我們採採用措措施修修正控控制圖圖表中中非隨隨機(jī)型型式，，這是是成功功使用用SPC的關(guān)鍵鍵?？刂葡尴拗凳鞘且誀?wèi)爲(wèi)衡量量的Y或X建立±3σ限值爲(wèi)爲(wèi)基礎(chǔ)礎(chǔ)。過程改改善及及控制制圖過程衡量系系統(tǒng)輸入輸出1.發(fā)現(xiàn)可可指定定的原原因4.驗(yàn)驗(yàn)證證結(jié)果果3.實(shí)實(shí)施修修正措措施2.確定根根本原原因控制圖圖的益益處用於提提高生生産率率的已已證實(shí)實(shí)的技技術(shù)有效防防範(fàn)缺缺陷防止不不必要要的過過程調(diào)調(diào)整提供診診斷資資訊提供關(guān)於過過程能能力的的資訊訊控制圖圖類型型控制圖圖有許許多類類型，，但是是它們們的根根本原原理是是相同同的利用SPC和過程程目標(biāo)標(biāo)方面面的知知識選選擇正正確的的類型型根據(jù)以下幾幾方面選擇擇控制圖類類型：資料類型:屬屬性還是變變數(shù)?採樣容易：：樣本同質(zhì)質(zhì)性資料分佈:正常?；蚍钦３?分組大小:不變變的或變化化的?其他考慮控制圖的組組成KVOP的X均值圖20100615605595585樣本數(shù)X=599.1UCL=6