SPC统计制程管制与QC七大手法.pptx

SPC统计制程管制与QC七大手法.pptx

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CPK,SPC,GR&R&CorrelationregressionHowardLinMay,11,2005目錄1.封面.（Page1）2.目錄.（Page2）3.SPC基本概念.（Page3）4.SPC統計制程管制4.1Cpk.（Page445）4.2QC舊七大手法.（Page4681）4.3管制圖.（Page8294）5.相關回歸.（Page9598）6.GR&R.（Page99115）3.SPC-StatisticalProcessControl-統計制程管制1.SPC的焦點:

制程2.制程變異:

（變異並非全是壞事）2.1機遇原因（共同原因）2.2非機遇原因（特殊原因）3.數據:

制程取得的有用信息.4.統計:

數據通過計算生有意義的情報產.5.SPC所使用的主要工具:

5.1Cpk5.2七大手法.管制圖6.計算:

對數據進行處理的過程4.1Cpk制程能力分析常態分配通常寫為XN（:

2）其中:

常態分配的中心值（MeanMean）2：

常態分配的變異（VarianceVariance）:

常態分配的標準差（StandardDeviation）常態分配特性

（1）曲線與橫軸所圍的面積為1;

（2）以為中心呈對稱性分布;（3）變異2代表分配函數的離散程度如圖1所示,具有相同的二個常態分配（a）與（b）,（a）的離散程度比（b）小,即2a2b,所以常態分配（a）大多數的點傾向於集中的附近.圖1（a）2a（b）2b.718.2）（.21）（222edxxxfekk-3-2-1-41234PERCENTAGESOFTHENORMALDISTRIBUTIONPercentagesOfTheNormalDistribution管制圖與常態分配+k圖2X在值+k與-k之間之或然率（Probability）或稱機率如右圖.以圖中斜線部分表示,其公式為:

群體平均值=標準差=抽取一個x圖1-k群體（制程）與樣本間之關系分配之期望值分配之標準差設為樣本平均,為群體平均S=S為樣本標準差為群體標準差在統計學上注:

如可視為無限群體用式（3）為有限群體之修正系數設系有限數群體而則分配之標準差2143x）（xEnXxx101Nn101NnnNnNX.11NnNxniinsXXnn1211）（1*nXXinis12）（群體（制程）與樣本間之關系樣本平均值之分配群體平均值之分配（無限群體）xnXCpkVsDefectiveYield我們常用品品質特性的常態分產配與規格相比較,以決定品的不良率產.如右圖所示品品質特性的常態分配產.規格上限:

USL（UpperSpecificationLimit）規格下限:

LSL（LowerSpecificationLimit）落在規格上,下限外的斜線面積即品的不良率為產.LSLUSL-3-2-1+3+2+168.27%95.45%99.73%0.135%0.135%StandardDeviationfrommeanCpkValueCpkValueDefectiveDefectiveYieldYieldDistributionDistribution12700ppm99.73%+/-3Sigma1.3363ppm99.9937%+/-4Sigma1.670.57ppm99.999943%+/-5Sigma2.000.002ppm99.9999998%+/-6Sigma目前在品管里常注重制程的分散寬度,故有定義制程能力下式者為:

群體標準差每不易直接求得一般以樣本資料推定之,其推定方法有下列三式:

（1）直接由樣本特性計算時值

（2）由次數分配表計算時（3）管制圖計算時一般均采用公式（3）制程能力的數量表示法制程能力的數量表示法1.分散寬度以表示之.制程能力=（或）d2Cpk計算時用公式

（1）VdR6,6,6266RX1）（22nnXXi1）（22fffufu2dR管制界限損失第二種錯誤第一種錯誤兩種錯誤總和134562兩種錯誤之經濟平衡點Breakevenpoint,BEP通常,在管制圖使中會有兩種錯（ERROR）.第一種即是當制程仍屬管制狀態,但卻因隨機性原因點落於管制界限外時,了尋找不存為在之問題而導致成本增加.第二種即是當制程已失去管制,但數據點由於隨機問題仍落於管制界限內,因而誤判制程處於管制狀態,因而造成更大之損失.YESNOYESNOACCURACY（準確度）PRECISION（精密度）TheAccuracyofaninstrumentcanbeimprovedbyrecalibratingtoreduceitserror,butrecalibratinggenerallydoesnotimprovetheinstrumentsPrecision.（Repeatabilityalsosometimesknownas“Precision”）Accuracy&PrecisionT/2Ca（制程準確度）Tux-Ca:

（Capabilityofaccuracy）從生過程中所獲得的產資料其實際平均值（）與規格中心值（）之間偏差的程度=12.50%25%50%100%A級B級C級D級X（實績）規格中心值規格上限或下限X（實績）X（實績）等級A12.5%B12.5%25%C25%50%D50%Ca值CaCaCaCaX%規格容許差規格中心實績中心Ca%2/）（TXCa之處置原則A級:

維持原則B級:

改進為A級C級:

立即檢討改善D級:

采取緊急措施,全面檢討,必要時停止生產.Cp（制程精密度）TCp:

（Capabilityofprecison）以規格公差（T）與生中所產獲得的6個估計實績標準差（）其間相差的程度雙邊單邊66B級6A級Cp=1.331.006C級0.836D級規格下限SL規格中心規格上限SU等級A1.33CpBCDCp值1.00Cp1.330.83Cp1.00Cp0.8363規格公差規格容許差CpX-SL3只有規格下限:

Cp=3Su-X只有規格上限:

Cp=工程能力指數工程能力指數（Cp）之處理之處理T3T3355Cp=1.67Cp=1.331.33Cp1.67顯示有足之工夠程力.對規格而言,為正常狀態,應繼續保持.2Cp處理1.67Cp,顯示非常有工程能力雖然有若干製品之標準差很大,但不會出現不良品.1344工程能力指數工程能力指數（Cp）之處理之處理Cp=1.00Cp1.00TT31.00Cp1.33,顯示工程能力並不充足,但且可以尚.要注意有發生不良品之雇慮,必要時應提升工程之能力.3Cp1.00顯示工程能力不足.在這種狀況下會出現不良品.必需藉著作業方法之改善,規格之再檢討,機械設備之改善,來提升工程能力.4333Ca,Cp的綜合評價1.計算方法:

Z1=3Cp（1+Ca）由Z1常態分配表得查p1%Z2=3Cp（1-Ca）由Z2常態分配表得查p2%p%=p1%+p2%.即推定群體超出規格上下之不良率為.2.依不良率P%分級做評定標準:

等級總評P%AP0.44%B0.44%P1.22%C1.22%P6.68%D6.68%P投影片30或XSZU1XSZL2e.g:

（例題）今庫存有某圓軸6000支,其品質特性圓軸之長度為,已知其長度母平均=15.7cm,母標準差=0.3cm,試問此6000支,中長度超過16.1cm的約有幾支?

Key解題步驟:

由已知得:

=15.7cm;=0.3cm方法一:

標準常態分配表查（拉普拉斯表）得Z=-1.33時,對應值為0.0918長度超過16.1cm的支數:

6000*0.0918=550.8四舍五入得551支方法二:

下述步驟與上同,故略33.13.04.03.07.151.161XSZU33.13.07.151.163*3）1（31SuCpCaZCa,Cp不良時的一般處理方法1.Ca不良時的一般處理方法製造單位主為,技術單位副為,品管單位輔為.2.Cp不良時的一般處理方法技術單位主為,製造單位副為,品管單位輔為.制程能力指數CpK綜合Ca與Cp兩之指數值

（1）CpK之計算式有兩種值B.單邊規格時:

（2）等級判定CpK愈大值,品質愈佳.依CpK值大小分五級為等級A1.33CpK1.67BCDCpK值1.00CpK1.330.67CpK1.00CpK0.67A+1.67CpKA.雙邊規格時:

CpCaCpK）1（3）（,3）（LUSXXSMinCpKCpK之處置原則A+:

考慮管理的簡單化或成本的降低方法A:

維持原狀B:

改進為A級C:

需全數選別並管理,改善制程D:

進行品質改善,探求原因,需要采取緊急對策,並且重新檢討規格.制程能力與規格之關系6ABCDESuSL或6代表制程在正常狀態下變化之範圍,稱為自然公差（Naturaltolerance）規格上下限之差為Su-SL,則或6與Su-SL有下列三種關系（情況）如圖示:

1.6Su-SLEvaluationformCpkCpk為什麼要大於或等於為什麼要大於或等於1.33?

1.33?

1.Cp=0.67時,穩態控制下不合格品率為4.6%;2.Cp=1.00時,穩態控制下不合格品率為0.27%;3.Cp=1.33時,穩態控制下不合格品率為0.0063%=63PPM在圖例上表示中心沒有偏移為（實際中心與規格中心重合值）DRLDRRLCLUCL6T=8XYDPPMDR=DRL+DRRDR（DefectRate）:

總不良DRL（DefectRateLeft）:

左不良DRR（DefectRateRight）:

右不良XLCLUCLDRLDR=DRL+DRRDRRXTable1QualitylevelsandCorrespondingNumberofDefectsSigmaCpkDPPM拼拼錯錯字字620.002大型圖書館所有書籍中僅一錯字51.670.5742小型圖書館所有書籍中僅一錯字41.3363.37大英百科全書中僅一錯字312,700一本書中每30頁僅一錯字20.6745,500一本書中每1.5頁僅一錯字10.33317,310一本書中每頁錯5個字SixSigma有多小?

Table2.TheNumberofDefective（PartsperMillion）forSpecifiedOff-CenteringoftheProcessandQualityLevels中心偏离時dppm的計算off-center（）面積面積z常態曲線下之面積常態曲線下之面積e=2.718.0Z=（x-）/投影片16dzzzZPzFez2221）（）（制程能力研究之應用1.對設計單位提供基本資料;2.分派工作到機器上;3.用來驗收全新或翻新調整過的設備;4.選用合格的作業員;5.設定生線的機器產;6.根據規格公差設定設備的管制界限;7.當制程能力超越公差時,決定最經濟的作業水準;8.找出最好的作業方法.Version:

1.1A.TrialRunDataCollectionSampleSize110112021303140415051606170718042.78742.82442.77242.70642.83242.87442.80642.70242.77542.71742.83642.84542.82542.83342.80542.70842.79242.78042.82342.77442.83642.89842.80742.69542.77842.80342.80142.69242.80742.78542.80742.72842.79142.75842.83642.86342.82942.84242.84042.84042.81042.82542.83642.86142.83242.84542.83642.86342.72942.75942.81742.83642.82442.82342.79642.67042.85042.69642.83042.86542.83042.84242.82242.80342.79142.77942.82742.78042.83342.89142.80542.69542.85042.69642.83042.86542.83042.84242.82242.803Calculation=42.804Sigma=0.051Max=42.898Min=42.670（atDesignPhase）HowtoDefineSpecification&VerifytheProcessCapabilityInputAreaforDataItemNo.QualityLevelSpecificationFormatLSLUSLDRL（Dppm）DRR（Dppm）DR（Dppm）11Sigma1Sigma42.80442.75342.855158655.26158655.26317310.5221.5Sigma1.5Sigma42.80442.72742.88066807.2366807.23133614.4632Sigma2Sigma42.80442.70242.90622750.0622750.0645500.1242.5Sigma2.5Sigma42.80442.67642.9316209.686209.6812419.3653Sigma3Sigma42.80442.65042.9571349.971349.972699.9363.5Sigma3.5Sigma42.80442.62542.982232.67232.67465.3574Sigma4Sigma42.80442.59943.00831.6931.6963.3784.5Sigma4.5Sigma42.80442.57443.0333.403.406.8095Sigma5Sigma42.80442.54843.0590.2871050.2871050.57105.5Sigma5.5Sigma42.80442.52343.0840.0190360.0190360.04116Sigma6Sigma42.80442.49743.1100.000990.000990.00Preparedby:

VQM/XuGangApprovedby:

HowardLinB.QualityLevel（Foryourreferenceandchoosing）TimesQualityLevelNominalT/2（）SpecLSLSpecUSLToleranceOff-Center（Sigma）1442.8040.20442.59943.0080.4080.002442.7800.20442.57642.9840.4080.4634.4642.7800.22842.55243.0080.4550.46CaCpCpKGradeDRL（Dppm）DRR（Dppm）DR（Dppm）0.001.331.33A31.6931.6963.370.121.331.18B4.05202.05206.100.101.491.33A0.4332.0332.46Preparedby:

VQM/XuGangApprovedby:

HowardLinVerificationItemRemark:

Greenmeansitcanbechangedormodified,Yellowmeansitcannotbechangedormodified.C.ChooseQualityLevelandDefineSpecificationD.ProcessCapabilityVerification231Returnd2XBarRA2D4個別值管制圖最大值與最小值管制圖X圖管制界限管制界限界限系數AA1A2C21/C2B1B2B3B4d21/d2d3D1D2D3D4A3D5D6E2A0m3A2C322.1213.7601.8800.56421.77250.0001.8430.0003.2671.1280.88650.8530.0003.6850.0003.2672.2240.0003.8652.6602.6951.8800.60331.7322.3941.0230.72361.38200.0001.8580.0002.5681.6930.59070.8880.0004.3580.0002.5751.2650.0002.7451.7721.8261.1870.46341.5001.8800.7290.79791.25330.0001.8080.0002.2662.0590.48570.8800.0004.6980.0002.2820.8290.0002.3751.4571.5220.7960.38951.3421.5960.5770.84071.18940.0001.7560.0002.0392.3260.42890.8640.0004.9180.0002.1150.7120.0002.1791.2901.3630.6910.34161.2251.4100.4830.85851.15120.0261.7110.0301.9702.5340.39460.3480.0005.0780.0002.0040.5620.0002.0551.1841.2630.5490.30871.1341.2770.4190.88821.12590.1051.5720.1181.8822.7040.36980.3330.2055.2050.0761.9240.5200.0781.9671.1091.1910.5090.28281.0611.1750.3730.90271.10780.1671.6380.1851.8152.8470.35120.8200.3875.3070.1361.8640.4410.1391.9011.0541.1430.4320.26291.0001.0940.3370.91391.09420.2191.6090.2391.7612.9700.33670.8080.5465.3940.1841.8160.4190.1871.8501.0101.1040.4120.246100.9491.0280.3080.92271.08370.2621.5840.2841.7163.0780.32490.7970.6875.4690.2231.7770.3690.2271.8090.9751.0720.3630.232110.9050.9730.2850.93001.07530.2991.5610.3211.6793.1730.31520.7870.8125.5340.2561.744120.8660.9250.2660.93591.06840.3311.5410.3541.6453.2580.30690.7780.9245.5920.2841.716130.8320.8340.2490.94101.06270.3591.5230.3821.6183.3360.29980.7701.0265.6460.3081.692140.8020.8480.2350.94531.05790.3841.5070.4061.5943.4070.29350.7621.1215.6930.3291.671150.7750.8160.2230.94901.05370.4061.4920.4281.5723.4720.28800.7551.2075.7370.3481.652160.7500.7880.2120.95231.05010.4271.4780.4481.5523.5320.28310.7491.2855.7790.3641.636170.7280.7620.2030.95511.04700.4451.4650.4661.5343.5880.27870.7431.3595.8170.3791.621180.7070.7380.1940.95761.04420.4611.4540.4821.5183.6400.27470.7381.4265.8540.3921.608190.6880.7170.1870.95991.04180.4771.4430.4971.5033.6890.27110.7331.4905.8880.4041.596200.6710.6970.1800.96151.03960.4911.4330.5101.4903.7350.26770.7291.5485.9220.4141.586210.6550.6790.1730.96381.03760.5041.4240.5231.4773.7780.26470.7241.6065.9500.4251.575220.6400.6620.1670.96551.03580.5161.4150.5341.4663.8190.26180.7201.6595.9790.4341.566230.6260.6470.1620.96701.03420.5271.4070.5151.4553.8580.25920.7161.7106.0060.4431.567240.6120.6320.1570.96841.03270.5381.3990.5551.4553.8950.25670.7121.7596.0310.4521.548250.6000.6190.1530.96961.03130.5481.3920.5651.4353.9310.25440.7091.8046.0580.4591.541平均數管制圖中位數管制圖管制圖常用系數表管制界限全距管制圖管制界限中線管制界限標準差管制圖中線取樣數n管制界限Model:

PartsName:

DataSource:

MeasuredBy:

MeasureDate:

MeasuredBy:

ISLVENDORDifferenceUSLLSLMAX0.00000.00000.0000MIN0.00000.00000.0000AVG0.00000.00000.0000STD0.00000.00000.0000Ca-#VALUE!

Cp#DIV/0!

#DIV/0!

#DIV/0!

Cpk#DIV/0!

#DIV/0!

#DIV/0!

Grade0.00000.0000DRL%0.00000.00000.0000DRR%0.00000.00000.0000DR%0.00000.00000.000010.000020.000030.000040.000050.000060.000070.000080.000090.0000100.0000110.0000120.0000130.0000140.0000150.0000160.0000RangeFrequencyNorm