品质统计经典培训教程

1、單元(4)-A統計基礎及品質統計資料數據基礎統計學生產製造環境品質統計圖表製程能力分析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$10.00裝貨單離散型資資料和連連續型資資料電氣電路路溫度溫度計連續型離散型卡尺錯誤$連續資料料的優

2、勢勢連續的離散的信息量少少信息量多多離散型資資料(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 BasicStatisticsDisplay Descriptive StatisticsGraphsGraphicalSummaryA227.11描述性統統計圖形分析析總結變數：神神秘中值的95%信信賴區間間 的95%信賴賴區間Anderson-Darling常態測

3、試試P值0.00均值100.00標準偏差差32.38變異數1048.78偏度0.01峰度-1.63資料量500.00最小值41.77第一象限限68.69中值104.20第三象限限130.81最大值162.82的95%信賴賴區間97.5102.85s的95%信賴區區間30.4934.53中值的95%信信賴區間間82.78117.66資料收集集時的重重點Howthe dataare collectedaffects thestatisticalappropriatenessand analysis of adataset(資料如何何收集可可影響統統計的適適切性). Conclusions from

4、properlycollected datacan be appliedmoregenerallytothe processand output.Inappropriatelycollected dataCANNOT be usedtodrawvalidconclusionsabouta process.Some aspectsofproper datacollectionthat mustbeaccounted forare:Themanufacturing environment(製程環境境)from which thedata arecollected. Whenproductsare

5、manufacturedinbatches or lots, thedata mustbecollected fromseveralbatches or lots.Randomization(隨機). Whenthe datacollectionisnotrandomized,statisticalanalysismay leadtofaulty conclusions.Continuous Manufacturing(連續)occurswhenanoperationisperformed on oneunit of productatatime.Anassemblyline is typic

6、alofacontinuous manufacturingenvironment, where eachunitofproduct is workedonindividuallyand acontinuousstreamoffinishedproductsrolloffthe line. Theautomotive industry is oneexample of ContinuousManufacturing.Otherexamplesofcontinuously manufacturedproduct are:television sets,fast foodhamburgers,com

7、puters.Lot/BatchManufacturing(批次)occursoccurs whenoperationsareperformed on products in batches, groups,orlots.The final productcomesoff theline in lots, insteadofastreamofindividualparts.Productwithinthe samelot areprocessedtogether, andreceive thesame treatmentwhilein-process.Lot/BatchManufacturin

8、gistypical of thesemiconductor industry andmany of itssuppliers. Other examples of lot/batchmanufacturedproductinclude:chemicals,semiconductor packages,cookies.Manufacturing Environment製造環境境InContinuous Manufacturingthe mostimportant variationisbetweenpartsInLot/BatchManufacturing,the variationcanoc

9、curbetweenthepartsinalotandbetweenthelots:Product withinthesamelotismanufactured together.Product fromdifferent lotsare manufacturedseparately.Because of this,each lothasadifferentdistribution. Thisisimportant becauseContinuousManufacturing is abasicassumptionformanyofthestandardstatisticalmethodsfo

10、undinmost 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/BatchManufacturing,each lothasadifferentmean.Due to rando

11、mprocessing fluctuations,theselotswill varyeventhoughthe processmay be stable.Thisresults in several“levels”ofdistributions,eachlevelwith itsownvarianceand mean:A distributionofunitsofproduct withinthesamelot.A distributionofthemeansofdifferent lots.Thetotaldistribution of allunitsofproduct acrossal

12、llots.LotX12345*Distribution ofIndividual LotDistribution ofLot MeansOverall Distributionof Combined LotsVariation WithinEach LotVariation Between LotsTotal VariationThedifferent variancesofa Lot/BatchManufacturing processforma hierarchycallednesting. Datacollected fromsuchprocessesusuallyhave whati

13、scalled anesteddata structure.1121 2 3 4 51 2 3 4 5LOTS班2121 2 3 4 51 2 3 4 5Each of thelevelsinthe nestedstructurecorrespondstoasinglevariance. Withanesteddatasetfromthis process, we needtotakeeach sourceofvariationintoaccount whencollectingdata to ensurethetotalprocessvariationisrepresentedinour d

14、ataset:生產線22 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),datavaluesfromthesamelotwillbehighly

15、correlated,whiledatafrom differentlots willbeindependent:品質統計計圖表直方圖(Histograms)方框圖(Boxplots)柏拉圖(ParetoDiagrams)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 statisticssucha

16、sand s.A histogramcanbeusedto:Display thedistributionofthe data(現示數據據的分佈佈).Provide agraphical indicationofthe 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 t

17、hatdonot fitthedistribution of therest of thedata.(顯示異常常點):. .:.: :.:.:. :.:.:.:.:.:.:.-+-+-+-+-+-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

18、，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)150.7149.7154.5149.6155.3149.0160.5149.0155.3149.3149.2153.5145.5161.0151.5154.3150.9152.4150.5152.3144.5151.6151.1151.0147.5150.6147.4150.8148.3146.8148.7147.6153.0139.0153.4146.5151.4143.5149.4150.4153.1150.7149.1150.6

19、149.6152.5145.2150.5146.4151.3151.7145.6147.1152.6147.0148.5155.0148.4151.3148.8146.7152.7155.3146.6144.8150.9149.5151.4147.3154.9151.2148.6142.5151.6151.0152.9146.9145.3150.8150.3153.6154.6150.6148.6155.1145.4148.5157.0148.9145.0147.7151.1149.7154.4149.1151.5153.3149.5152.8150.8品質統計計圖表-直方圖(Histogra

20、ms)Multi-ModalShape(雙峰):SkewedShape(偏一邊):Data canberight-skewedorleft-skewed. Thisdataisright-skewedtherighttailislongerthanthelefttail.Outliers:特異點練習品質統計計圖表-方框圖(Boxplots)Boxplotsareagraphicaltoolvaluableforcomparing thedistributions of twoormore groups(e.g.,different lots, shifts,operators,etc.).Ea

21、chdistributiononthischartconsistsofthefollowing:A “box” representingthemiddle 50%ofthedatavalues. Thelengthofthe “box” is calledthe“InterquartileRange”(IQR). Insidethe“box”isaline representingthemedian (50thpercentile)ofthedata.Two“tails”whichextendout to theminimum andmaximum datavalues (assumingth

22、erearenooutliersinthe data).Ifthedistancebetweentheadata point andthenearer quartile is greaterthan1.5xIQR,thedatapointislabeled as an outlier, andthe“tail” on thatsideoftheboxplotisshortenedtothe outermostdata value within1.5xIQR fromthe quartile.品質統計計圖表-方框圖(Boxplots)MedianMaximumData Value75thPerc

23、entile25thPercentileOutermostdata valueswithin1.5xIQRofthe75thand25thPercentiles.OutlierNOOUTLIERSIQROUTLIERSMinimumData ValueOutlier1.5xIQR品質統計計圖表-方框圖(Boxplots)EXAMPLE :CreatingaBoxplotThefigure below is aboxplotofthe100 platingthickness measurements.The histogramforthe samedatasetisdisplayed forco

24、mparison.品質統計計圖表-方框圖(Boxplots)Lot 1Lot 2Lot 3Lot 4Lot 5Lot 6Lot 7149.18144.78146.77167.85144.51134.96152.41151.31147.18150.66164.17144.41134.7146.76150.8145.66145.11168.23146.68135.02148.19149.06147.09145.09162.88145.4134.63143.75151.73145.86145.98163.1143.3134.87153.71148.15144.64146.77166.91146.87

25、135.34145.13152.55143.67149.9165.78148.61134.6148.54Plating thicknessmeasurementscollected from7lots of product.品質統計計圖表-方框圖(Boxplots)Multi-ModalShape:SkewedShape:Outliers:練習品質統計計圖表-柏拉圖(ParetoDiagrams)Whilehistograms areused to displaythe distributionofa setofcontinuous(measured) data,Paretodiagramsa

26、reusedtodisplay thedistributionofdiscrete(counted)data,suchasdifferenttypesofdefects.Paretodiagramscan alsobeusedwith continuous(measured)data,particularlyindisplayingvariancecomponents analysis results, as we willsee later in thiscourse.Paretodiagramsare auseful toolfor determining which problems o

27、r types of problems aremost severeoroccurmost frequently, hence shouldbegivenhigh priority forprocess improvement efforts. 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frequ

28、ency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

29、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)Pareto圖分析: 創建建一個加加權的Pareto圖通過指定定金額/缺陷或或用其他他的加權權方法，可以給給次數加加權。列在C1中的缺陷陷發生次次數的價價格列在在C3(value)中，價價格乘乘以次數數等於這這類缺陷陷的費用用 (c4)。繪製費用用（cost）曲線圖，而不是是繪製次次數（count）圖，這這樣可以以更好地地說明每每個缺陷陷對業務務的影響響。缺陷的Pareto圖 缺陷計數 2320.71 1653.00 123

30、0.00 800.00 349.87 155.52 百分比 35.7 25.4 18.9 12.3 5.4 2.4累積百分比 35.7 61.0 79.9 92.2 97.6 100.0螺钉丢失螺釘丟失襯墊泄漏外殼有缺陷零件不完整其他600050004000300020001000 0100806040200計數百分比（%）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（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

31、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403020100100806040200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

32、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)練習品質統計計圖表-散佈圖(Scatterplots)Untilnow, allthegraphical tools wevediscussedhavebeen forexaminingthe distributionofa singleprocess characteristic.Thescatterplotisa graphicaltool forexaminingthe relationshipbetweentwoprocess characteristics.AscatterplotisanX-Y

33、plotofonevariableversus another.Each unitofproductusually hasmany characteristics,processinputvariables, etc.One objectivemightbetoseewhethertwovariables or characteristicsarerelatedtoeach other (i.e.,toseewhathappens to oneofthevariables whenthe other variable changes).This relationshipbetween twov

34、ariablesiscalledcorrelation.Scatterplotscanhelpusanswerthistype of question.品質統計計圖表-散佈圖(Scatterplots)Acid AgeEtch RateAcid AgeEtch RateAcid AgeEtch Rate4.0134.5134.0154.5181.5302.5233.0183.5191.0313.5195.575.044.0122.0253.5212.0241.0292.0261.0283.0205.593.0195.064.5145.095.592.5272.5251.5301.531品質統計

35、計圖表-散佈圖(Scatterplots)Inadditiontotelling uswhetherornottwo variablesarerelated,scatterplotscantellushowthey arerelated,andthestrengthoftherelationship:StrongPositiveCorrelation強正相關關NoCorrelation無關Weak Negative Correlation弱負相關關Weak Positive Correlation弱正相關關StrongNegativeCorrelation強負相關關品質統計計圖表-散佈圖(Sc

36、atterplots)Inaddition,scatterplotsareanexcellent toolfor determining thetypeofrelationshipbetweenthetwo 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(Scatterplots)CorrelationandCausationWemust alwaystake carenot to confusecorrelationw

37、ithcausation. Thefact thattwo characteristicsarecorrelateddoes notprovethat onecausesthe other.Both mayberelated to someotherfactor which is thetrue rootcause.Number of TelevisionsNumber ofTrafficAccidents19701990Butisthereacause-effectrelationship betweenthe two?Didthe increase in TVscausethe numbe

38、rofaccidentstogoup? (Notlikely.)Didthe increase in trafficaccidents cause peopletobuymoreTVs?(Not likely,either.)練習品質統計計圖表-趨勢圖(TrendCharts)TrendChartsStability:A processisstable if itsmean andstandarddeviationare constant andpredictableover time.A disadvantageofhistograms andnormalprobabilityplotsis

39、thatthey cannotbeused to determinewhether theprocess is stableover time. Aplotofthedataintime order willallowustodothat.Thesetime-orderedplots, calledTrendchartsandControl chartsareessential whenexamining thestabilityofadistributionovertime.A trend chart or acontrolchartcandetect instability if it e

40、xists.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 product. Below thatisatrendchartofthedata.Lot #Plating ThicknessLot #Plat

41、ing ThicknessLot #Plating Thickness1151.98143.815149.22147.49152.716147.53155.810147.417151.94151.711152.718141.95149.212143.819152.76153.813137.120147.47159.914142.521157.3練習品質統計計圖表-NoisyTheresultsofa statistical analysis canbeseriouslyaffectedbythe failureofthe datatomeetcertain required assumptio

42、ns.Oneofthe mostcommon assumptions is thatthedatavaluesare independentandthatthey comefroma Normaldistribution. Thisassumptioncanbeviolatedinseveralways:Outliers(points thatdonot fittherestofthedistribution)inthedata,Non-Normal-shapeddistributions(multi-modalorskeweddistributions),Data thatexhibitth

43、esecharacteristicscan 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-NoisyRecommendedstrategyforhandlingoutliers:1.Identifytheoutliersusingthe methodsd

44、escribed in thefollowingpages. If possible,find thecausesofthe outliers.Removethe outliers withidentifiedcausesfromthedataset(找原因).2.Ifallthe outliers canbeexplained, thenanalyzethedataasusual.3.However,ifthereareany outliers thatdonot haveexplanations,analyze thedata twice:includingthe outliers,exc

45、ludingthe outliers.Seeifand howtheanalysisresultsdiffer.製程能力力分析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: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

46、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Ca,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)-Xm

47、XCa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%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ACp1.33B 1.00 Cp1.33C0.67Cp1.00DCp0.67分級標準準如下: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

48、: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:XXX練習SPC統計製程控制SPC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、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

49、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

50、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 3限值爲基基礎。沒有正確確訓練X或Y的SPC=牆紙警示信號號用於發現現缺陷。一旦生生産成爲爲1#優優先度，操作者者將學會會忽略或或切警示信號!實施S.O.P以發

51、現缺缺陷。這這種措施施不能短短期或長長期保持持。用經過充充分訓練練的操作作者對X或Y進行統計程式式控制（SPC）。操作者已已受過訓訓練並瞭瞭解SPC的規定，但管理理層不准准許他們們停下來來或進行行研究。第3種類型修修正措施施=檢查查：實施短期期遏制政政策的措措施，這這種措施施有可能能發現由由錯誤條條件引起起的缺陷陷。常用用的遏制制政策是是審查或或100%檢查查。對遵守規規定的操操作者和和職員進進行充分分訓練，用他們對對X或Y進行統計計程式控控制（SPC）。一旦圖表表顯示出出現問題題，每個個人瞭解解SPC規定，並並由於識識別和消消除特殊殊原因而而同意停停止。第2種類型修修正措施施=標記記：對那些

52、錯錯誤條件件已經出出現的過過程進行行改善。該標記記使設備備停工，以免缺缺陷繼續續發展。第1種類型修修正措施施=防範範措施：改善過程程，消除除錯誤條條件發生生的情況況，缺陷陷永遠也也不會發發生。在在防錯或或設計變變更形式式上，這這也可作作爲長期期的修正正措施。控制方法法最差最優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

53、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20100615605595585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)

54、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 inner controllimits indicatesa stableprocess.Ifanypoints