统计基础与品质统计.ppt

1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2資料及數據3你想瞭解什麽?資訊源資訊源:分組離散型名義型 順序型 間距型“資資料料本本身身並並不不能能提提供供資資訊訊 必必須須對對資資料料加加以以處處理理以以後後才能得到資訊才能得到資訊,而處理資料的工具就是統計學而處理資料的工具就是統計學”.衡量連續型比率型文字的(AtoZ)圖示的口頭的數位的(0-9)數據4FAILPASS計時器計時器 NO-GOGO數量數量 單價單價 說明說明 總價總價 裝貨單裝貨單 離散型資料和連續型資料電氣電路電氣電路溫度溫度溫度計溫度計連續型連續型離散型離散型卡尺卡尺錯誤錯誤5$連續資料的優勢連續的連續的離散的離散的信息量少信息量多6離散型資料(通常)分組/分類是/否,合格/不合格不能計算離散型資料分級很少用很難加以計算連續型資料最常見的尺規計算時要很小心連續型資料比例關係可應用演算法的多數公式分類標簽第一、第二、第三相對高度字母順序123 0g g1 =0g g1 0g g2 =0g g2 Basic Statistics Display Descriptive StatisticsGraphs Graphical SummaryA2描述性統計圖形分析總結圖形分析總結變數：神秘中值的95%信賴區間的95%信賴區間Anderson-Darling常態測試P均的95%信賴區間s的95%信賴區間中值的95%信賴區間31資料收集時的重點資料收集時的重點Howthedataarecollectedaffectsthestatisticalappropriatenessandanalysisofadataset(資料如何收集可影響統計的適切性).Conclusionsfromproperlycollecteddatacanbeappliedmoregenerallytotheprocessandoutput.Inappropriately collected data CANNOT be used to draw valid conclusions about a process.Someaspectsofproperdatacollectionthatmustbeaccountedforare:Themanufacturing environment(製程環境製程環境)fromwhichthedataarecollected.Whenproductsaremanufacturedinbatchesorlots,thedatamustbecollectedfromseveralbatchesorlots.Randomization(隨機隨機).Whenthedatacollectionisnotrandomized,statisticalanalysismayleadtofaultyconclusions.32Continuous Manufacturing(連續)occurswhenanoperationisperformedononeunitofproductatatime.Anassemblylineistypicalofacontinuousmanufacturingenvironment,whereeachunitofproductisworkedonindividuallyandacontinuousstreamoffinishedproductsrollofftheline.TheautomotiveindustryisoneexampleofContinuousManufacturing.Otherexamplesofcontinuouslymanufacturedproductare:televisionsets,fastfoodhamburgers,computers.Lot/Batch Manufacturing(批次)occursoccurswhenoperationsareperformedonproductsinbatches,groups,orlots.Thefinalproductcomesoffthelineinlots,insteadofastreamofindividualparts.Productwithinthesamelotareprocessedtogether,andreceivethesametreatmentwhilein-process.Lot/BatchManufacturingistypicalofthesemiconductorindustryandmanyofitssuppliers.Otherexamplesoflot/batchmanufacturedproductinclude:chemicals,semiconductorpackages,cookies.Manufacturing Environment製造環境製造環境33InContinuousManufacturingthemostimportantvariationisbetweenpartsInLot/BatchManufacturing,thevariationcanoccurbetweenthepartsinalotandbetweenthelots:Productwithinthesamelotismanufacturedtogether.Productfromdifferentlotsaremanufacturedseparately.Becauseofthis,eachlothasadifferentdistribution.ThisisimportantbecauseContinuousManufacturingisabasicassumptionformanyofthestandardstatisticalmethodsfoundinmosttextbooksorQChandbooks.These methods are not appropriate for Lot/Batch Manufacturing.Different statistical methods need to be used to take into account the several sources of variation in Lot/Batch Manufacturing.要注意要注意:連續和批量生產所用的統計方法有些不同連續和批量生產所用的統計方法有些不同34With Lot/Batch Manufacturing,each lot has a different mean.Due to random processing fluctuations,these lots will vary even though the process may be stable.This results in several“levels”of distributions,each level with its own variance and mean:A distribution of units of product within the same lot.A distribution of the means of different lots.The total distribution of all units of product across all lots.LotX12345*Distribution ofIndividual LotDistribution ofLot MeansOverall Distributionof Combined LotsVariation WithinEach LotVariation Between LotsTotal Variation35ThedifferentvariancesofaLot/BatchManufacturingprocessformahierarchycallednesting.Datacollectedfromsuchprocessesusuallyhavewhatiscalledanesteddatastructure.1121 2 3 4 51 2 3 4 5LOTS班班2121 2 3 4 51 2 3 4 5Eachofthelevelsinthenestedstructurecorrespondstoasinglevariance.Withanesteddatasetfromthisprocess,weneedtotakeeachsourceofvariationintoaccountwhencollectingdatatoensurethetotalprocessvariationisrepresentedinourdataset:生產線362222222X12X2212121,;X;X;XXXX+=+=總總總6原則變異數可相加,標準差則不能相加輸入變數變異數相加計算輸出中的總變異數所以那麽引起的變異數輸入變數引起的變異數輸入變數過程輸出的變異數如果37123456Lots sWithin is smalls sLot is largeprocesshassmallwithin-lotvariationandlargelot-to-lotvariation(whichisverycommon),datavaluesfromthesamelotwillbehighlycorrelated,whiledatafromdifferentlotswillbeindependent:38品質統計圖表直方圖(Histograms)方框圖(Boxplots)柏拉圖(ParetoDiagrams)散佈圖(Scatterplots)趨勢圖(TrendCharts)39品質統計圖表-直方圖(Histograms)Histograms provideavisualdescriptionofthedistributionofasetofdata.Ahistogramshouldbeusedinconjunctionwithsummarystatisticssuchasands.Ahistogramcanbeusedto:Displaythedistributionofthedata(現示數據的分佈).Provideagraphicalindicationofthecenter,spread,andshapeofthedatadistribution(較定性地顯示數據的均值,散佈及形狀).Clarifyanynumericalsummarystatistics(whichsometimesobscureinformation).(顯示較模糊的統計結果).Lookforoutliers-datapointsthatdonotfitthedistributionoftherestofthedata.(顯示異常點)40 :.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.-+-+-+-+-+-+-+-+-+-+-加侖加侖/分鐘分鐘 點圖分佈 設想有一個泵流量爲50加侖/分鐘的計量泵。按照節拍對泵的實際流量進行了100次獨立測量。畫出各個點，每點代表一個給定值的輸出“事件”。當點聚集起來時，泵的實際性能狀況可以看作泵流量的“分佈”。4151.350.850.349.849.348.84030201 00直方圖分佈還是這些資料，現在設想將其分組後歸入“區間”。泵流量點落入指定區間的次數決定區間條的高度。頻率加侖/分鐘42品質統計圖表-直方圖(Histograms)150.7149.7154.5149.6155.3149.0160.5149.0155.3149.3149.2153.5145.5161.0151.5154.3150.9152.4150.5152.3144.5151.6151.1151.0147.5150.6147.4150.8148.3146.8148.7147.6153.0139.0153.4146.5151.4143.5149.4150.4153.1150.7149.1150.6149.6152.5145.2150.5146.4151.3151.7145.6147.1152.6147.0148.5155.0148.4151.3148.8146.7152.7155.3146.6144.8150.9149.5151.4147.3154.9151.2148.6142.5151.6151.0152.9146.9145.3150.8150.3153.6154.6150.6148.6155.1145.4148.5157.0148.9145.0147.7151.1149.7154.4149.1151.5153.3149.5152.8150.843品質統計圖表-直方圖(Histograms)Multi-ModalShape(雙峰雙峰):Skewed Shape(偏一邊偏一邊):Datacanberight-skewedorleft-skewed.Thisdataisright-skewedtherighttailislongerthanthelefttail.Outliers:特異點特異點44練習45品質統計圖表-方框圖(Boxplots)Boxplotsareagraphicaltoolvaluableforcomparingthedistributionsoftwoormoregroups(e.g.,differentlots,shifts,operators,etc.).Eachdistributiononthischartconsistsofthefollowing:A“box”representingthemiddle50%ofthedatavalues.Thelengthofthe“box”iscalledthe“InterquartileRange”(IQR).Insidethe“box”isalinerepresentingthemedian(50thpercentile)ofthedata.Two“tails”whichextendouttotheminimumandmaximumdatavalues(assumingtherearenooutliersinthedata).Ifthedistancebetweentheadatapointandthenearerquartileisgreaterthan1.5xIQR,thedatapointislabeledasanoutlier,andthe“tail”onthatsideoftheboxplotisshortenedtotheoutermostdatavaluewithin1.5xIQRfromthequartile.46品質統計圖表-方框圖(Boxplots)MedianMaximumData Value75thPercentile25thPercentileOutermostdata valuesof the 75th and25th Percentiles.OutlierNO OUTLIERSIQROUTLIERSMinimumData ValueOutlier47品質統計圖表-方框圖(Boxplots)EXAMPLE:CreatingaBoxplotThefigurebelowisaboxplotofthe100platingthicknessmeasurements.Thehistogramforthesamedatasetisdisplayedforcomparison.48品質統計圖表-方框圖(Boxplots)Lot1Lot2Lot3Lot4Lot5Lot6Lot7149.18144.78146.77167.85144.51134.96152.41151.31147.18150.66164.17144.41134.7146.76150.8145.66145.11168.23146.68135.02148.19149.06147.09145.09162.88145.4134.63143.75151.73145.86145.98163.1143.3134.87153.71148.15144.64146.77166.91146.87135.34145.13152.55143.67149.9165.78148.61134.6148.54Platingthicknessmeasurementscollectedfrom7lotsofproduct.49品質統計圖表-方框圖(Boxplots)Multi-ModalShape:SkewedShape:Outliers:50練習51品質統計圖表-柏拉圖(ParetoDiagrams)Whilehistogramsareusedtodisplaythedistributionofasetofcontinuous(measured)data,Pareto diagramsareusedtodisplaythedistributionofdiscrete(counted)data,suchasdifferenttypesofdefects.Paretodiagramscanalsobeusedwithcontinuous(measured)data,particularlyindisplayingvariancecomponentsanalysisresults,aswewillseelaterinthiscourse.Paretodiagramsareausefultoolfordeterminingwhichproblemsortypesofproblemsaremostsevereoroccurmostfrequently,henceshouldbegivenhighpriorityforprocessimprovementefforts.Paretodiagramsseparatethesignificantvitalfewproblemsfromthetrivialmanytohelpdeterminewhichproblemstoaddressfirst(andwhichtoaddresslater).重點中找重點!52Pareto圖分析Pareto 圖圖根據frequency欄的內容判斷各個缺陷影響的大小，並按從大到小的次序排列。最後一組總是標有“其他”，並以默認方式包括所有缺陷的分類計算，這幾類缺陷非常少，它們占總缺陷的5%以下。該圖右側Y軸表示占總缺陷的百分比，左側Y軸表示缺陷數。紅線(在螢幕上可以看到)表示累積百分比，而直方圖表示每類缺陷的頻率(占總量的百分比)。在圖的下方列出所有的值百分比缺陷的Pareto圖計數缺陷缺陷 計數2745943191018累積百分比螺釘丟失夹子丢失襯墊泄漏外殼有缺陷零件不完整其他4003002001000100806040200百分比（%）品質統計圖表-柏拉圖(ParetoDiagrams)53Pareto圖分析:創建一個加權的Pareto圖通過指定金額/缺陷或用其他的加權方法，可以給次數加權。列在C1中的缺陷發生次數的價格列在C3(value)中，價格乘以次數等於這類缺陷的費用(c4)。繪製費用（cost）曲線圖，而不是繪製次數（count）圖，這樣可以更好地說明每個缺陷對業務的影響。缺陷的Pareto圖缺陷缺陷計數2320.711653.001230.00800.00349.87155.52百分比35.725.418.912.35.42.4累積百分比35.761.079.992.297.6100.0螺钉丢失螺釘丟失襯墊泄漏外殼有缺陷零件不完整其他6000500040003000200010000100806040200計數百分比（%）品質統計圖表-柏拉圖(ParetoDiagrams)54層別Pareto圖:解釋分組資料上圖使用了一個By Variable（從屬變數），從屬變數），所有的圖都在一頁上。下圖使用同樣的命令，沒有從屬變數。當選擇每頁一張圖時，所有的圖的計數(左軸)刻度相同。右側的百分比只反映該圖占總體的百分比。這些圖表明，70%的記錄缺陷是刮傷和剝落的(下部)，約有一半的缺陷是夜班人員記錄的(上右圖)。此外，記錄缺陷是刮傷和剝落的比例，對白班和夜班的來說似乎也差不多。然而，晚班和周末班出現的缺陷樣式是不同的。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缺陷缺陷計數151366百分比37.532.515.015.0累積百分比刮伤拨落其他污点計數計數計數計數計數百分比（%）品質統計圖表-柏拉圖(ParetoDiagrams)55練習56品質統計圖表-散佈圖(Scatterplots)Untilnow,allthegraphicaltoolswevediscussedhavebeenforexaminingthedistributionofasingleprocesscharacteristic.Thescatterplot isagraphicaltoolforexaminingtherelationshipbetweentwoprocesscharacteristics.AscatterplotisanX-Yplotofonevariableversusanother.Eachunitofproductusuallyhasmanycharacteristics,processinputvariables,etc.Oneobjectivemightbetoseewhethertwovariablesorcharacteristicsarerelatedtoeachother(i.e.,toseewhathappenstooneofthevariableswhentheothervariablechanges).Thisrelationshipbetweentwovariablesiscalledcorrelation.Scatterplotscanhelpusanswerthistypeofquestion.57品質統計圖表-散佈圖(Scatterplots)AcidAgeEtchRateAcidAgeEtchRateAcidAgeEtchRate4.0134.5134.0154.5181.5302.5233.0183.5191.0313.5195.575.044.0122.0253.5212.0241.0292.0261.0283.0205.593.0195.064.5145.095.592.5272.5251.5301.53158品質統計圖表-散佈圖(Scatterplots)Inadditiontotellinguswhetherornottwovariablesarerelated,scatterplotscantellushowtheyarerelated,andthestrengthoftherelationship:Strong Positive Correlation強正相關強正相關No Correlation無關無關Weak Negative Correlation弱負相關弱負相關Weak Positive Correlation弱正相關弱正相關Strong Negative Correlation強負相關強負相關59品質統計圖表-散佈圖(Scatterplots)Inaddition,scatterplotsareanexcellenttoolfordeterminingthetypeofrelationshipbetweenthetwovariables,aswellaslookingforoutliers:Linear Relationship線性相關線性相關Outliers 特異特異Non-Linear Relationship非線性相關非線性相關60品質統計圖表-散佈圖(Scatterplots)Correlation and CausationWemustalwaystakecarenottoconfusecorrelationwithcausation.Thefactthattwocharacteristicsarecorrelateddoesnotprovethatonecausestheother.Bothmayberelatedtosomeotherfactorwhichisthetruerootcause.Number of TelevisionsNumber ofTrafficAccidents19701990Butisthereacause-effectrelationshipbetweenthetwo?DidtheincreaseinTVscausethenumberofaccidentstogoup?(Notlikely.)DidtheincreaseintrafficaccidentscausepeopletobuymoreTVs?(Notlikely,either.)61練習62品質統計圖表-趨勢圖(TrendCharts)Trend ChartsStability:Aprocessisstableifitsmeanandstandarddeviationareconstantandpredictableovertime.Adisadvantageofhistogramsandnormalprobabilityplotsisthattheycannotbeusedtodeterminewhethertheprocessisstableovertime.Aplotofthedataintimeorderwillallowustodothat.Thesetime-orderedplots,calledTrend charts andControl charts areessentialwhenexaminingthestabilityofadistributionovertime.Atrendchartoracontrolchartcandetectinstabilityifitexists.Controlcharts,whichareaspecialkindoftrendchart,arediscussedindetailseparatelyinalatercoursemodule.可看出穩定性及預測性可看出穩定性及預測性63品質統計圖表-趨勢圖(TrendCharts)Thetablebelowcontainsaverageplatingthicknessmeasurementstakenfrom21lotsofproduct.Belowthatisatrendchartofthedata.Lot#PlatingThicknessLot#PlatingThicknessLot#PlatingThickness1151.98143.815149.22147.49152.716147.53155.810147.417151.94151.711152.718141.95149.212143.819152.76153.813137.120147.47159.914142.521157.364練習65品質統計圖表-NoisyTheresultsofastatisticalanalysiscanbeseriouslyaffectedbythefailureofthedatatomeetcertainrequiredassumptions.OneofthemostcommonassumptionsisthatthedatavaluesareindependentandthattheycomefromaNormaldistribution.Thisassumptioncanbeviolatedinseveralways:Outliers(pointsthatdonotfittherestofthedistribution)inthedata,Non-Normal-shaped distributions(multi-modalorskeweddistributions),Datathatexhibitthesecharacteristicscanbethoughtofasnoisy data.Theproceduresinthissectionprovidetechniquesforeffectivedetectionandanalysisofnoisydata.雜訊66品質統計圖表-NoisyBoxplotsTrend ChartHistogramScatterplotNormal Prob.Plot67品質統計圖表-NoisyRecommendedstrategyforhandlingoutliers:1.Identifytheoutliersusingthemethodsdescribedinthefollowingpages.Ifpossible,findthecausesoftheoutliers.Removetheoutlierswithidentifiedcausesfromthedataset(找原因).2.Ifalltheoutlierscanbeexplained,thenanalyzethedataasusual.3.However,ifthereareanyoutliersthatdonothaveexplanations,analyzethedatatwice:includingtheoutliers,excludingtheoutliers.Seeifandhowtheanalysisresultsdiffer.68製程能力分析69當製程開始產生變異時,其統計分佈圖的形狀也開始變化。通常變化不外下面三種基本狀況的組合:整體製程數據漂移散佈變寬中心值漂移若將每日之統計分佈串起來一起看,則又可看到更多變異現象,一般可分為兩種如下:1.突發變異:製程中有特殊或突發原因而產生變異,造成不穩定。例:每日生產參數設定漂移。2.共同變異:製程中只有共同原因的變異此種現象是穩定的”不良”。例:模具尺寸超差。70瞭解以上基本觀念後便開始加入管制的觀念。作管制時加入規格上下線,超出規格則視為不良如下圖:71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不好,中心值不在目標,分佈雖集中但超出規格外製程能力最差,中心值不在目標,分佈不集中且超出規格外72計算Ca,Cp,Cpk公式規格中心LSL+3-3製程寬度6規格寬度TUSLSuSLCa:CapabilityofAccuracy準確度:實際中心Ca-=X(T/2)-XXCa只對雙邊規格適用.分級標準如下:等級等級 Ca 值值A Ca 12.25%B 12.25%Ca 25%C25%50%73計算Ca,Cp,Cpk公式規格中心LSL+3-3製程寬度6規格寬度TUSLSuSLCp:CapabilityofPrecision精確度:實際中心-XX當僅有下限時:Cp=(-SL)/(3)對雙邊規格:Cp=T/(6)當僅有上限時:Cp=(Su-)/(3)XX等級Cp值ACp1.33B1.00Cp1.33C0.67Cp1.00DCp0.67分級標準如下:74計算Ca,Cp,Cpk公式Cpk:指制程能力參數,是Cp和Ca的綜合.對雙邊規格:Cpk=(1-Ca)*Cp=Min(Su-)/(3),(-SL)/(3)對單邊規格,可以認為T為,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不足分級標準如下:XXX75練習76SPC統計製程控制77SPC介紹SPC是用於研究變動的一種基本工具,它使用統計信號監測並改善過程績效。該工具可用於任何領域：製造業、商業，銷售業等等SPC是統計程式控制（StatisticalProcessControl）的縮寫。大多數公司是將SPC用於最終産品(Y)上,而不是用於過程特徵(X)。第一步是使用統計方法控制公司的輸出。然而，只有我們將重點放在控制輸入(X),而不是控制輸出(Y)時,我們才能認識到我們在提高質量、生産率及降低成本上的努力收效有多大。78什麽是統計製程控制（SPC）所有過程都有固有變動（由於一般原因）和非固有變動（由於特殊原因），我們使用SPC來監測並改善過程。SPC的使用使我們能夠通過失控信號發現特殊原因。這些失控信號無法說明過程失控的原因，只能表明過程處於失控狀態。控制圖表是在統計上從時間上跟蹤過程和産品參數的方法。控制圖表中包括反映過程隨機變動固有限值的上下控制限值。這些限值不應與顧客規定限值相比較。79什麽是統計製程控制（續）基本統計原理，控制圖表能夠用於識別過程變數中的非固有（非隨機）型式。當控制圖表出現非隨機型式信號時，我們就可以知道特殊原因引起的變動改變了過程。我們採用措施修正控制圖表中非隨機型式，這是成功使用SPC的關鍵。控制限值是以爲衡量的Y或X建立3限值爲基礎。80沒有正確訓練X或Y的SPC=牆紙警示信號用於發現缺陷。一旦生産成爲1#優先度，操作者將學會忽略或切警示信號!實施以發現缺陷。這種措施不能短期或長期保持。用經過充分訓練的操作者對X或Y進行統計程式控制（SPC）。操作者已受過訓練並瞭解SPC的規定，但管理層不准許他們停下來或進行研究。第3種類型修正措施=檢查：實施短期遏制政策的措施，這種措施有可能發現由錯誤條件引起的缺陷。常用的遏制政策是審查或100%檢查。對遵守規定的操作者和職員進行充分訓練，用他們對X或Y進行統計程式控制（SPC）。一旦圖表顯示出現問題，每個人瞭解SPC規定，並由於識別和消除特殊原因而同意停止。第2種類型修正措施=標記：對那些錯誤條件已經出現的過程進行改善。該標記使設備停工，以免缺陷繼續發展。第1種類型修正措施=防範措施：改善過程，消除錯誤條件發生的情況，缺陷永遠也不會發生。在防錯或設計變更形式上，這也可作爲長期的修正措施。控制方法最差最差最優最優81過程改善及控制圖過程過程衡量系統衡量系統輸入輸入輸出輸出1.發現可指定的原因發現可指定的原因4.驗證結果驗證結果2.確定根本原因確定根本原因82控制圖的益處用於提高生産率的已證實的技術有效防範缺陷防止不必要的過程調整提供診斷資訊提供關於過程能力的資訊83控制圖類型控制圖有許多類型，但是它們的根本原理是相同的控制圖有許多類型，但是它們的根本原理是相同的利用利用 SPC和過程目標方面的知識選擇正確的類型和過程目標方面的知識選擇正確的類型根據以下幾方面選擇控制圖類型根據以下幾方面選擇控制圖類型：資料類型:屬性還是變數?採樣容易：樣本同質性資料分佈:正常或非正常?分組大小:不變的或變化的?其他考慮84控制圖的組成KVOP的X均值圖201 0061 5605595585樣本數X=599.1UCL=61 3.6LCL=584.6控制下限UCL=+k中線=LCL=-k其中=樣本均值=樣本標準偏差k=控制限制距中線的差值(通常爲3)記住:控制限值與顧客規定限值無關控制上限中線樣本均值85常用控制圖類型(X-S)86常用控制圖類型(X-R)87短期N30ForcontrolchartswithN30lots,ratherthantheusualUCL(uppercontrolli