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統計統計統計統計1统计统计运用及品管运用及品管实务实务工具工具統計統計統計統計2資料及數據2统计运用及品管实务工具統計統計統計統計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3统计运用及品管实务工具統計統計統計統計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1$10.00$10.003$1.50$4.5010$10.00$10.002$5.00$10.00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4统计运用及品管实务工具統計統計統計統計5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 0歪斜歪斜凹凸平坦凹凸平坦Shape(形狀形狀)22统计运用及品管实务工具統計統計統計統計23母體均值母體均值樣本均值樣本均值母體標準偏差母體標準偏差樣本標準偏差樣本標準偏差常用計算公式母體母體變異變異樣本樣本變異變異23统计运用及品管实务工具統計統計統計統計24ThemostimportantandusefuldistributionshapeiscalledtheNormal distribution,whichissymmetric(對稱),uni-modal(單峰),andfreeofoutliers(沒有特異點):Normal Distribution常態分佈常態分佈“常態”分佈是具有某些一致屬性的資料的分佈這些屬性對理解基礎過程(資料從該過程中收集)的特徵非常有用.大多數自然現象和人爲過程都符合常態分配,可以用常態分配表示,故大部份統計都假設是常態分佈。即使在資料不完全符合常態分配時,分析結果也很接近。特別不正常的分佈若假設為常態而去分析則有可能得到誤導結果。有數學技術可將其轉變成常態分佈來作分析。24统计运用及品管实务工具統計統計統計統計25ANormalprobabilityplotisacumulativedistributionplotwheretheverticalscaleischangedinsuchawaythatdatafromaNormaldistributionwillformastraightline:HistogramCumulativeDistribution NormalProbability Plot常態概率圖Normal Distribution常態分佈常態分佈25统计运用及品管实务工具統計統計統計統計26第一個屬性:只要知道下面兩項就可以完全描述常態分配:均值標準差常態分配的好處-簡化第一個分佈第一個分佈第二個分佈第二個分佈第三個分佈第三個分佈這三個分佈有什麽不同這三個分佈有什麽不同?26统计运用及品管实务工具統計統計統計統計27常態曲線和其概率43210-1-2-3-440%30%20%10%0%99.73%第二個屬性:曲線下方的面積可以用於估計某“事件”發生的累積概率95%68%樣本值的概率樣本值的概率距離均值的標準偏差數距離均值的標準偏差數得到兩值之間的值的累得到兩值之間的值的累積概率積概率27统计运用及品管实务工具統計統計統計統計28常態概率圖1 301 201 1 01 00908070603002001 000C 2常態概率圖頻率1 1 01 0090807060504030201 00500C 1常態概率圖頻率807060504030201 003002001 000C 3常態概率圖頻率1 301 201 1 01 0090807060.999.99.95.80.50.20.05.01.001平均:70標準偏差:10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1 069686766656463626.999.99.95.80.50.20.05.01.001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我們可以用常態概率圖檢驗一組給定的資料是否可以描述爲“常態”如果一個分佈接近常態分配,則常態概率圖將爲一條直線。28统计运用及品管实务工具統計統計統計統計29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.29统计运用及品管实务工具統計統計統計統計30Continuous 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.生產製造環境生產製造環境30统计运用及品管实务工具統計統計統計統計31InContinuousManufacturingthemostimportantvariationisbetweenpartsInLot/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31统计运用及品管实务工具統計統計統計統計32With 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 Variation32统计运用及品管实务工具統計統計統計統計332222222X12X2212121,;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33统计运用及品管实务工具統計統計統計統計34123456Lots sWithin is smalls sLot is largeprocesshassmallwithin-lotvariationandlargelot-to-lotvariation(whichisverycommon),datavaluesfromthesamelotwillbehighlycorrelated,whiledatafromdifferentlotswillbeindependent:34统计运用及品管实务工具統計統計統計統計35實用品質統計工具直方圖(Histograms)柏拉圖(ParetoDiagrams)散佈圖(Scatterplots)趨勢圖(TrendCharts)35统计运用及品管实务工具統計統計統計統計36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)36统计运用及品管实务工具統計統計統計統計37 :.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.-+-+-+-+-+-+-+-+-+-+-加侖加侖/分鐘分鐘 49.00 49.50 50.00 50.50 51.0049.00 49.50 50.00 50.50 51.00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”。37统计运用及品管实务工具統計統計統計統計3851.350.850.349.849.348.84030201 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38统计运用及品管实务工具統計統計統計統計39品質統計圖表-直方圖(Histograms)150.7149.7154.5149.6155.3149.0160.5149.0155.3149.3149.2153.5145.5161.0151.5154.3150.9152.4150.5152.3144.5151.6151.1151.0147.5150.6147.4150.8148.3146.8148.7147.6153.0139.0153.4146.5151.4143.5149.4150.4153.1150.7149.1150.6149.6152.5145.2150.5146.4151.3151.7145.6147.1152.6147.0148.5155.0148.4151.3148.8146.7152.7155.3146.6144.8150.9149.5151.4147.3154.9151.2148.6142.5151.6151.0152.9146.9145.3150.8150.3153.6154.6150.6148.6155.1145.4148.5157.0148.9145.0147.7151.1149.7154.4149.1151.5153.3149.5152.8150.839统计运用及品管实务工具統計統計統計統計40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40统计运用及品管实务工具統計統計統計統計41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!41统计运用及品管实务工具統計統計統計統計42Pareto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2745943191018百分比64.813.910.24.52.44.3累積百分比64.878.788.993.493.4100.0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)42统计运用及品管实务工具統計統計統計統計43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(%)品質統計圖表-柏拉圖(ParetoDiagrams)43统计运用及品管实务工具統計統計統計統計44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.44统计运用及品管实务工具統計統計統計統計45品質統計圖表-散佈圖(Scatterplots)AcidAgeEtchRateAcidAgeEtchRateAcidAgeEtchRate4.0134.5134.0154.5181.5302.5233.0183.5191.0313.5195.575.044.0122.0253.5212.0241.0292.0261.0283.0205.593.0195.064.5145.095.592.5272.5251.5301.53145统计运用及品管实务工具統計統計統計統計46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46统计运用及品管实务工具統計統計統計統計47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47统计运用及品管实务工具統計統計統計統計48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.)48统计运用及品管实务工具統計統計統計統計49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49统计运用及品管实务工具統計統計統計統計50品質統計圖表-趨勢圖(TrendCharts)Thetablebelowcontainsaverageplatingthicknessmeasurementstakenfrom21lotsofproduct.Belowthatisatrendchartofthedata.Lot#PlatingThicknessLot#PlatingThicknessLot#PlatingThickness1151.98143.815149.22147.49152.716147.53155.810147.417151.94151.711152.718141.95149.212143.819152.76153.813137.120147.47159.914142.521157.350统计运用及品管实务工具統計統計統計統計51品質統計圖表-NoisyTheresultsofastatisticalanalysiscanbeseriouslyaffectedbythefailureofthedatatomeetcertainrequiredassumptions.OneofthemostcommonassumptionsisthatthedatavaluesareindependentandthattheycomefromaNormaldistribution.Thisassumptioncanbeviolatedinseveralways:Outliers(pointsthatdonotfittherestofthedistribution)inthedata,Non-Normal-shaped distributions(multi-modalorskeweddistributions),Datathatexhibitthesecharacteristicscanbethoughtofasnoisy data.Theproceduresinthissectionprovidetechniquesforeffectivedetectionandanalysisofnoisydata.雜訊51统计运用及品管实务工具統計統計統計統計52品質統計圖表-NoisyBoxplotsTrend ChartHistogramScatterplotNormal Prob.Plot52统计运用及品管实务工具統計統計統計統計53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.53统计运用及品管实务工具統計統計統計統計54製程能力分析與SPC統計製程控制54统计运用及品管实务工具統計統計統計統計55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:時間時間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。55统计运用及品管实务工具統計統計統計統計56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:56统计运用及品管实务工具統計統計統計統計57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57统计运用及品管实务工具統計統計統計統計58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%主值主值58统计运用及品管实务工具統計統計統計統計59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:主值主值59统计运用及品管实务工具統計統計統計統計60統計統計統計統計61SPC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。61统计运用及品管实务工具統計統計統計統計62什麽是統計製程控制(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。62统计运用及品管实务工具統計統計統計統計63什麽是統計製程控制(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。63统计运用及品管实务工具統計統計統計統計64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3.實施修正措施實施修正措施2.確定根本原因確定根本原因64统计运用及品管实务工具統計統計統計統計65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65统计运用及品管实务工具統計統計統計統計66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66统计运用及品管实务工具統計統計統計統計67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67统计运用及品管实务工具統計統計統計統計68常用控制圖類型(X-S)68统计运用及品管实务工具統計統計統計統計69常用控制圖類型(X-R)69统计运用及品管实务工具統計統計統計統計70短期N30ForcontrolchartswithN30lots,ratherthantheusualUCL(uppercontrollimit)andLCL(lowercontrollimit),therearedual sets of control limits:Outer Control Limits(3s s).Inner Control Limits(1s s).70统计运用及品管实务工具統計統計統計統計71短期N30Anypointoutsideeitheroftheoutercontrollimitsindicatesanunstableprocess.Allpointsfallingbetweenbothinnercontrollimitsindicatesastableprocess.Ifanypointsfallinsideeither“uncertaintyzone”(butnoneareoutsidetheoutercontrollimits),wecannotsaywhetherornottheprocessisstable,becausewedonotyethaveenoughlotstobesureatthistime.71统计运用及品管实务工具統計統計統計統計72Withfewlots,thecontrolcharthaswideuncertaintyzones.Itispossibletodetermineprocessstability,butinmostcasesmorelotswillberequired.Withmorelots,thecontrolcharthasnarrowuncertaintyzones.Itiseasiertodetermineprocessstability,butitisstillpossiblethatmorelotswillberequired.OncethereareN30lots,theusualcontrollimitsareused(i.e.,therearenouncertaintyzones).Thereisfullabilitytodetermineprocessstability.72统计运用及品管实务工具統計統計統計統計73控制圖代表的含義Asinglepointonthechartisoutsideeithercontrollimit.Thistestdetectsverylarge,suddenshiftsintheprocessmeanorstandarddeviation.9ormoreconsecutivepointsareonthesamesideofthecenterline.Thistestdetectssmallshiftsortrendsintheprocessmeanorstandarddeviation.6(ormore)consecutivepointsareincreasing(ordecreasing)steadily,withoutachangeindirection.Thistestdetectsstrongtrendsintheprocessmeanorstandarddeviation73统计运用及品管实务工具統計統計統計統計7414(ormore)consecutivepointsarealternatingupanddown.Thistestdetectssystematiceffects,suchasalternatingmachines,operators,suppliers,etc.4(or5)outof5consecutivepointsonthechartaremorethan1standarddeviationawayfromthecenterline,onthesameside.Thistestdetectsmoderate-sizedchangesintheprocessmeanorstandarddeviation.2(or3)outof3consecutivepointsonthechartaremorethan2standarddeviationsawayfromthecenterline,onthesameside.Thistestdetectslargechangesintheprocessmeanorstandarddeviation.74统计运用及品管实务工具統計統計統計統計7515(ormore)consecutivepointsareallwithin1standarddeviationofthecenterline.Thistestdetectsadecreaseinprocessvariation.8(ormore)consecutivepointsareonbothsidesofthecenterline,butnonearewithin1standarddeviationofit.Thistestdetectsanincreaseinprocessvariation.End75统计运用及品管实务工具
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