制程能力分析与SPC统计制程控制

1、統計運用及品管實務工具資料數據基礎統計運用概念生產製造環境實用品質統計工具製程能力分析與SPC統計製程控制資料及數數據你想瞭解解什麽?資訊源:分組離散型名義型順序型間距型“資料本本身並不不能提供供資訊必必須對對資料加加以處理理以後才才能得到到資訊, 而處處理資料料的工具具就是統統計學”.衡量連續型比率型文字的(A to Z)圖示的口頭的數位的(0-9)數據FAILPASS計時器 NO-GOGO數量單價說明總價1$10.00$10.003$1.50$4.5010$10.00$10.002$5.00$10.00裝貨單離散型資資料和連連續型資資料電氣電路路溫度溫度計連續型離散型卡尺錯誤離散型資資料(

2、通常)分組/ 分類類是/否,合格/不合格不能計算算離散型資資料分級 很少用很難加以以計算連續型資資料最常見的的尺規計算時要要很小心心連續型資資料比例關係係可應用演演算法的的多數公公式分類 標簽 第一、第第二、第第三相對高度度字母順序序123 0g1 = 0g1 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準準偏差樣本標準準偏差常用計算公式式母體變異樣本變異Themostimportantand usefuldistributionshapeiscalled theNormaldistribution, which is symmetric(對稱), uni-

3、modal(單峰), andfree of outliers(沒有特異異點):NormalDistribution常態分佈佈“常態” 分佈佈是具有有某些一一致屬性性的資料料的分佈佈這些屬性性對理解解基礎過過程（資資料從該該過程中中收集）的特徵徵非常有有用.大多數自自然現象象和人爲爲過程都都符合常常態分配配，可以以用常態態分配表表示,故大部份份統計都都假設是是常態分分佈。即使在資資料不完完全符合合常態分分配時，分析結結果也很很接近。特別不正正常的分分佈若假假設為常常態而去去分析則則有可能能得到誤誤導結果果。有數學技術可將其轉變成常常態分佈佈來作分析析。A Normalprobabilityplo

4、t is acumulativedistributionplotwheretheverticalscaleischangedinsuch away thatdatafrom aNormal distributionwill formastraightline:HistogramCumulativeDistributionNormalProbabilityPlot常態概率率圖NormalDistribution常態分佈佈第一個屬屬性: 只要要知道下下面兩項項就可以以完全描描述常態態分配:均值標準差常態分配配的好處-簡化化第一個分分佈第二個分分佈第三個分分佈這三個分分佈有什什麽不同同?常態曲線線和

5、其概概率43210-1-2-3-440%30%20%10% 0%99.73%第二個屬屬性: 曲線線下方的的面積可可以用於於估計某某“事件件”發生生的累積積概率95%68%樣本值的的概率距離均值值的標準準偏差數數得到兩值值之間的的值的累累積概率率常態概率率圖130120110100908070603002001000C2常態概率圖頻率1101009080706050403020100500C1常態概率圖頻率807060504030201003002001000C3常態概率圖頻率13012011010090807060.95.01.001平均：70標準偏差：1

6、0資料個數：500Anderson-Darling常態測試A平方:46.447P-值:0.000正偏斜分佈概率正偏斜1069686766656463626.95.01.001常態分配常態概率平均值：70標準偏差:10資料個數：500Anderson-Darling常態測試A平方:0.418P-值:0.328我們可以以用常態態概率圖圖檢驗一一組給定定的資料料是否可可以描述述爲“常常態”如果一個個分佈接接近常態態分配，則常態態概率圖圖將爲一一條直線線。資料收集集時的重重點Howthe dataare collectedaffects thestatistica

7、lappropriatenessand analysis of adataset(資料如何何收集可可影響統統計的適適切性). Conclusions fromproperlycollected datacan be appliedmoregenerallytothe processand output.Inappropriatelycollected dataCANNOT be usedtodrawvalidconclusionsabouta process.Some aspectsofproper datacollectionthat mustbeaccounted forare:Thema

8、nufacturing environment(製程環境境)from which thedata arecollected. Whenproductsare manufacturedinbatches or lots, thedata mustbecollected fromseveralbatches or lots.Randomization(隨機). Whenthe datacollectionisnotrandomized,statisticalanalysismay leadtofaulty conclusions.Continuous Manufacturing(連續)occurs

9、whenanoperationisperformed on oneunit of productatatime.Anassemblyline is typicalofacontinuous manufacturingenvironment, where eachunitofproduct is workedonindividuallyand acontinuousstreamoffinishedproductsrolloffthe line. Theautomotive industry is oneexample of ContinuousManufacturing.Otherexample

10、sofcontinuously manufacturedproduct are:television sets,fast foodhamburgers,computers.Lot/BatchManufacturing(批次)occursoccurs whenoperationsareperformed on products in batches, groups,orlots.The final productcomesoff theline in lots, insteadofastreamofindividualparts.Productwithinthe samelot areproce

11、ssedtogether, andreceive thesame treatmentwhilein-process.Lot/BatchManufacturingistypical of thesemiconductor industry andmany of itssuppliers. Other examples of lot/batchmanufacturedproductinclude:chemicals,semiconductor packages,cookies.生產製造造環境InContinuous Manufacturingthe mostimportant variationi

12、sbetweenpartsInLot/BatchManufacturing,the variationcanoccurbetweenthepartsinalotandbetweenthelots:Product withinthesamelotismanufactured together.Product fromdifferent lotsare manufacturedseparately.Because of this,each lothasadifferentdistribution. Thisisimportant becauseContinuousManufacturing is

13、abasicassumptionformanyofthestandardstatisticalmethodsfoundinmost textbooksorQChandbooks.Thesemethods arenotappropriatefor Lot/BatchManufacturing.Differentstatisticalmethodsneed to be usedtotakeinto accountthe severalsourcesofvariationinLot/Batch Manufacturing.要注意: 連續續和批量量生產所所用的統統計方法法有些不不同With Lot/B

14、atchManufacturing,each lothasadifferentmean.Due to randomprocessing fluctuations,theselotswill varyeventhoughthe processmay be stable.Thisresults in several“levels”ofdistributions,eachlevelwith itsownvarianceand mean:A distributionofunitsofproduct withinthesamelot.A distributionofthemeansofdifferent

15、 lots.Thetotaldistribution of allunitsofproduct acrossalllots.LotX12345*Distribution ofIndividual LotDistribution ofLot MeansOverall Distributionof Combined LotsVariation WithinEach LotVariation Between LotsTotal Variation22 22222X12X2212121 , ;X;X ; XXXX+=+=總 總 總 6原則變異數可可相加, 標準準差則不不能相加加輸入變數數變異數數相加計

16、計算輸出出中的總總變異數數所以那麽引起的變變異數輸入變數數引起的變變異數輸入變數數過程輸出出的變異異數如果123456LotsWithin is smallsLot is largeprocess hassmallwithin-lot variationandlargelot-to-lotvariation(which is verycommon),datavaluesfromthesamelotwillbehighlycorrelated,whiledatafrom differentlots willbeindependent:實用品質質統計工工具直方圖(Histograms)柏拉圖(Pa

17、retoDiagrams)散佈圖(Scatterplots)趨勢圖(TrendCharts)品質統計計圖表-直方圖(Histograms)Histogramsprovide avisual description of thedistributionofasetofdata.Ahistogramshould be usedinconjunctionwithsummary statisticssuchasand s.A histogramcanbeusedto:Display thedistributionofthe data(現示數據據的分佈佈).Provide agraphical indi

18、cationofthe center,spread,andshapeofthe datadistribution (較定性地地顯示數數據的均均值,散散佈及形形狀).Clarify anynumericalsummarystatistics (whichsometimesobscureinformation). (顯示較模模糊的統統計結果果).Look foroutliers- datapoints thatdonot fitthedistribution of therest of thedata.(顯示異常常點):. .:.: :.:.:. :.:.:.:.:.:.:.-+-+-+-+-+-

19、加侖/分分鐘49.0049.5050.0050.5051.00點圖分佈佈設想有一一個泵流流量爲50加侖侖/分鐘鐘的計量量泵。按照節拍拍對泵的的實際流流量進行行了100次獨立測測量。畫出各個個點，每每點代表表一個給給定值的的輸出“事件”。當點聚聚集起來來時，泵泵的實際際性能狀狀況可以以看作泵泵流量的的“分佈佈”。51.350.850.349.849.348.8403020100直方圖分分佈還是這些些資料，現在設設想將其其分組後後歸入“區間”。泵流流量點落落入指定定區間的的次數決決定區間間條的高高度。頻率加侖/分分鐘品質統計計圖表-直方圖(Histograms)150.7149.7154.5149

20、.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

21、.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品質統計計圖表-直方圖(Histograms)Multi-ModalShape(雙峰):SkewedShape(偏一邊):Data canberight-skewedorleft-skewed. Thisdataisright-skew

22、edtherighttailislongerthanthelefttail.Outliers:特異點品質統計計圖表-柏拉圖(ParetoDiagrams)Whilehistograms areused to displaythe distributionofa setofcontinuous(measured) data,Paretodiagramsareusedtodisplay thedistributionofdiscrete(counted)data,suchasdifferenttypesofdefects.Paretodiagramscan alsobeusedwith conti

23、nuous(measured)data,particularlyindisplayingvariancecomponents analysis results, as we willsee later in thiscourse.Paretodiagramsare auseful toolfor determining which problems or types of problems aremost severeoroccurmost frequently, hence shouldbegivenhigh priority forprocess improvement efforts.

24、Paretodiagramsseparatethesignificantvitalfew problems fromthetrivialmany to helpdetermine which problems to addressfirst(andwhichtoaddress later).重點中找找重點!Pareto圖分析Pareto圖根據frequency欄的內容容判斷各各個缺陷陷影響的的大小，並按從從大到小小的次序序排列。最後一組組總是標標有“其他” ，並並以默認認方式包包括所有有缺陷的的分類計計算，這這幾類缺缺陷非常常少，它它們占占總缺陷陷的5%以以下。該圖右側側Y軸表示占占總缺陷陷的

25、百分分比，左左側Y軸表示缺缺陷數。紅線(在螢幕幕上可以以看到) 表示示累積百百分比，而直方方圖表示示每類缺缺陷的頻頻率(占總量量的百分分比)。在圖圖的下方方列出所所有的值值百分比缺陷的Pareto圖計數 缺陷 計數2745943191018百分比64.813.94.3累積百分分比64.878.788.993.493.4100.0螺釘丟失失夹子丢失失襯墊泄漏漏外殼有缺缺陷零件不完完整其他 4003002001000100806040200百分比（%）品質統計計圖表-柏拉圖(ParetoDiagrams)層別Pareto圖:解解釋分組組資料上圖使用用了一個個ByVariable

26、（從屬變數數），所有的圖圖都在一一頁上。下下圖使用用同樣的的命令，沒有從從屬變數數。當選擇每每頁一張張圖時，所有的的圖的計計數(左左軸)刻刻度相同同。右右側的百百分比只只反映該該圖占總總體的百百分比。這些圖表表明，70%的記錄錄缺陷是是刮傷和和剝落的的 (下下部)，約有一一半的缺缺陷是夜夜班人員員記錄的的 (上上右圖)。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 151050151050151050151050裂紋Pareto圖4030201

27、00100806040200缺陷計數151366百分比37.532.515.015.0累積百分分比35.570.085.0100.0刮伤拨落其他污点計數 計數計數計數計數百分比（%）品質統計計圖表-柏拉圖(ParetoDiagrams)品質統計計圖表-散佈圖(Scatterplots)Untilnow, allthegraphical tools weve discussedhave beenfor examiningthedistribution of asingle processcharacteristic. Thescatterplotisa graphicaltool forexam

28、iningthe relationshipbetweentwoprocess characteristics.AscatterplotisanX-Yplotofonevariableversus another.Each unitofproductusually hasmany characteristics,processinputvariables, etc.One objectivemightbetoseewhethertwovariables or characteristicsarerelatedtoeach other (i.e.,toseewhathappens to oneof

29、thevariables whenthe other variable changes).This relationshipbetween twovariablesiscalledcorrelation. Scatterplotscanhelpusanswerthistype of question.品質統計計圖表-散佈圖(Scatterplots)Acid AgeEtch RateAcid AgeEtch RateAcid AgeEtch Rate4.0134.5134.0154.5181.5302.5233.0183.5191.0313.5195.575.044.0122.0253.521

30、2.0241.0292.0261.0283.0205.593.0195.064.5145.095.592.5272.5251.5301.531品質統計計圖表-散佈圖(Scatterplots)Inadditiontotelling uswhetherornottwo variablesarerelated,scatterplots cantell ushowthey arerelated,andthestrengthoftherelationship:StrongPositiveCorrelation強正相關關NoCorrelation無關Weak Negative Correlation弱負

31、相關關Weak Positive Correlation弱正相關關StrongNegativeCorrelation強負相關關品質統計計圖表-散佈圖(Scatterplots)Inaddition,scatterplots areanexcellenttoolfordeterminingthetypeofrelationshipbetweenthetwo variables,aswellaslooking foroutliers:LinearRelationship線性相關關Outliers特異Non-Linear Relationship非線性相相關品質統計計圖表-散佈圖(Scatterpl

32、ots)CorrelationandCausationWemust alwaystake carenot to confusecorrelationwithcausation. Thefact thattwo characteristicsarecorrelateddoes notprovethat onecausesthe other.Both mayberelated to someotherfactor which is thetrue rootcause.Number of TelevisionsNumber ofTrafficAccidents19701990Butisthereac

33、ause-effectrelationship betweenthe two?Didthe increase in TVscausethe numberofaccidentstogoup? (Notlikely.)Didthe increase in trafficaccidents cause peopletobuymoreTVs?(Not likely,either.)品質統計計圖表-趨勢圖(TrendCharts)TrendChartsStability:A processisstable if itsmean andstandarddeviationare constant andpr

34、edictableover time.A disadvantageofhistograms andnormalprobabilityplotsisthatthey cannotbeused to determinewhether theprocess is stableover time. Aplotofthedataintime order willallowustodothat.Thesetime-orderedplots, calledTrendchartsandControl chartsareessential whenexamining thestabilityofadistrib

35、utionovertime.A trend chart or acontrolchartcandetect instability if it exists.Control charts,whichare aspecialkind of trend chart,arediscussed in detailseparately in alatercourse module.可看出穩穩定性及及預測性性品質統計計圖表-趨勢圖(TrendCharts)Thetablebelowcontainsaverageplating thicknessmeasurementstakenfrom21lots of

36、product. Below thatisatrendchartofthedata.Lot #Plating ThicknessLot #Plating ThicknessLot #Plating Thickness1151.98143.815149.22147.49152.716147.53155.810147.417151.94151.711152.718141.95149.212143.819152.76153.813137.120147.47159.914142.521157.3品質統計計圖表-NoisyTheresultsofa statistical analysis canbes

37、eriouslyaffectedbythe failureofthe datatomeetcertain required assumptions.Oneofthe mostcommon assumptions is thatthedatavaluesare independentandthatthey comefroma Normaldistribution. Thisassumptioncanbeviolatedinseveralways:Outliers(points thatdonot fittherestofthedistribution)inthedata,Non-Normal-s

38、hapeddistributions(multi-modalorskeweddistributions),Data thatexhibitthesecharacteristicscan be thoughtofasnoisydata. Theprocedures in thissectionprovide techniquesfor effectivedetectionand analysis of noisy data.雜訊品質統計計圖表-NoisyBoxplotsTrendChartHistogramScatterplotNormalProb.Plot品質統計計圖表-NoisyRecomm

39、endedstrategyforhandlingoutliers:1.Identifytheoutliersusingthe methodsdescribed in thefollowingpages. If possible,find thecausesofthe outliers.Removethe outliers withidentifiedcausesfromthedataset(找原因).2.Ifallthe outliers canbeexplained, thenanalyzethedataasusual.3.However,ifthereareany outliers tha

40、tdonot haveexplanations,analyze thedata twice:includingthe outliers,excludingthe outliers.Seeifand howtheanalysisresultsdiffer.製程能力力分析與SPC統計製程控制當製程開開始產生生變異時時,其統統計分佈佈圖的形形狀也開開始變化化。通常常變化不不外下面面三種基基本狀況況的組合合:整體製程數據漂移散佈變寬中心值漂移若將每日日之統計計分佈串串起來一一起看,則又可看看到更多多變異現現象,一般可分分為兩種種如下: 時間 時間 1.突發發變異:製程中中有特殊殊或突發發原因而而產生變

41、變異,造成不穩穩定。例例:每日日生產參參數設定定漂移。2.共同同變異:製程中中只有共共同原因因的變異異此種現象象是穩定定的”不不良”。例:模模具尺寸寸超差。瞭解以上上基本觀觀念後便便開始加加入管制制的觀念念。作管管制時加加入規格格上下線線,超超出規格格則視為為不良如如下圖:製程能力好,中心值在目標上且分佈均在規格內製程能力尚可,中心值在目標上,分佈均在規格內但稍微太分散製程能力尚可,中心值有漂移,但分佈尚在規格內製程能力不好,中心值雖在目標,但分佈超出規格外製程能力力不好,中心值值不在目目標,分分佈雖集集中但超超出規格格外製程能力力最差,中心值值不在目目標,分分佈不集集中且超超出規格格外計算C

42、a,Cp,Cpk公式規格中心心mLSL+ 3- 3製程寬度6規格寬度TUSLSuSLCa:CapabilityofAccuracy準確度:實際中心心Ca-=Xm(T/2)-XmXCa只對雙邊邊規格適適用.分級標準準如下:等級 Ca 值A Ca 12.25%B 12.25% Ca 25%C25%50%主值計算Ca,Cp,Cpk公式規格中心心mLSL+ 3- 3製程寬度6規格寬度TUSLSuSLCp:CapabilityofPrecision精確度:實際中心心-XmX當僅有下下限時:Cp= (-SL)/(3)對雙邊規規格:Cp= T/(6)當僅有上上限時:Cp= (Su-)/(3)XX 等級Cp值

43、ACp1.33B 1.00 Cp1.33C0.67Cp1.00DCp0.67分級標準準如下:主值計算Ca,Cp,Cpk公式Cpk:指制程能能力參數數,是是Cp和Ca的綜合.對雙邊規規格:Cpk=(1-Ca)*Cp= Min(Su-)/(3),(-SL)/(3)對單邊規規格,可可以認認為T為,則則Ca=(-)/ (T/2)=0Cpk= (1-Ca)*Cp=Cp等級Cpk值評价ACpk1.33理想B1.00Cpk1.33正常CCpk1.0不足分級標準準如下:XXXSPC介紹SPC是用於研研究變動動的一種種基本工工具,它它使用統統計信號號監測並並改善過過程績效效。該工工具可用用於任何何領域：製造業業

44、、商業業，銷售售業等等等SPC是統計程程式控制制（StatisticalProcessControl）的縮寫。大多數數公司是是將SPC用於最終終産品(Y)上,而而不是用用於過程程特徵(X)。第一步是是使用統統計方法法控制公公司的輸輸出。然然而，只只有我們們將重點點放在控控制輸入入(X),而不是控控制輸出出(Y)時,我我們才能能認識到到我們在在提高質質量、生生産率及及降低成成本上的的努力收收效有多多大。什麽是統計製程控制（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

45、現現特殊原原因。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。控制圖表表是在統統計上從從時間上上跟蹤過過程和産産品參數數的方法法。控制制圖表中中包括反反映過程程隨機變變動固有有限值的的上下控制限值值。這些限值值不應與與顧客規定定限值相比較。什麽是統計製程控制（續）基本統計計原理，控制圖圖表能夠夠用於識識別過程程變數中中的非固固有（非非隨機）型式。當控制制圖表出出現非隨隨機型式式信號時時，我們們就可以以知道特特殊原因因引起的的變動改改變了過過程。我我們採用用措施修修正控制制圖表中中非隨機機型式，這是成成功使用用SPC的關鍵。控制限值值是以爲爲衡量的的Y或X建立

46、 3限值爲基基礎。過程改善善及控制制圖過程衡量系統統輸入輸出1.發現可指指定的原原因4.驗驗證結果果3.實施施修正措措施2.確定根本本原因控制圖的的益處用於提高高生産率率的已證證實的技技術有效防範範缺陷防止不必必要的過過程調整整提供診斷斷資訊提供關於過程程能力的的資訊控制圖類類型控制圖有有許多類類型，但但是它們們的根本本原理是是相同的的利用SPC和過程目目標方面面的知識識選擇正正確的類類型根據以下下幾方面面選擇控控制圖類類型：資料類型型:屬屬性性還是變變數?採樣容易易：樣本本同質性性資料分佈佈:正正常或或非正常常?分組大小小:不不變的的或變化化的?其他考慮慮控制圖的的組成KVOP的X均值圖20

47、100615605595585樣本數X=599.1UCL=613.6LCL=584.6控制下限限UCL=m+ks中線=mLCL=m- ks其中m=樣本均值值s=樣本標準準偏差k =控制限制制距中線線的差值值 (通通常爲 3)記住:控制限值值與顧客客規定限限值無關關控制上限限中線 樣本均值值常用控制圖類類型(X-S)常用控制圖類類型(X-R)短期N 30ForcontrolchartswithN 30lots,rather thanthe usual UCL(uppercontrollimit)and LCL(lowercontrollimit), there aredual setsofcontrollimits:OuterControl Limits(3s).InnerControl Limits(1s).短期N 30Anypointoutsideeitherofthe outer controllimits indicatesanunstableprocess.Allpoints fallingbetweenboth inn