1、Cpk Training datum Version:ACpk制程能力分析Cpk Training datum Version:A常態分配.718.2)(.21)(222edxxxfekk通常寫為XN(:2):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(Standard Deviation)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 2 a2b,所以常態分配(a)大多數 的點傾向於集
2、中的附近.圖1(a)2 a(b)2 bCpk Training datum Version:A-3-2-1-41234PERCENTAGES OF THE NORMAL DISTRIBUTIONCpk Training datum Version:A管制圖與常態分配管制圖與常態分配+k X值在+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=x-kCpk Training datum Version:A群體(制程)與樣本間之關系x)(xEnX分配之期望值分配之標準差x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
3、學上x101Nn101NnnNnNX.11NnN注:如 可視為無限群體用上式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xniinsXXnn1211)(1*nXXinis12)(2143Cpk Training datum Version:A樣本平均值之分配x群體平均值之分配nXCpk Training datum Version:ACpk Cpk Vs Defective YieldVs Defective Yield 我們常用產品品質特性的常態分配與規格相比較,以決定產品的不良率.如右圖所示產品品質特性的常態分配.規格上限:USL (Upper Specification Lim
4、it)規格下限:LSL (Lower Specification Limit)落在規格上,下限外的斜線面積即為產品的不良率.LSLUSL-3-2-1+3+2+168.27%95.45%99.73%0.135%0.135%Standard Deviation from meanC C p pk k V V a al lu ue eD D e ef fe ec ct ti iv ve eY Y i ie el ld dD D i is st tr ri ib bu ut ti io on n12700ppm99.73%+/-3 Sigm a1.3363ppm99.9937%+/-4 Sigm a1
5、.670.57ppm99.999943%+/-5 Sigm a2.000.002ppm99.9999998%+/-6 Sigm aCpk Training datum Version:A目前在品管里常注重制程的分散寬度,故有定義制程能力為下式者: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)直接由樣本特性值計算時(2)由次數分配表計算時(2)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.VdR6,6,62制程能力=(或 )66RX 1)(22nnXXi1)(22fffufu2dRd2Cpk 計算時用此公式(1)Cpk
6、 Training datum Version:A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Break even point,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,為了尋找不存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.Cpk Training datum Version:AYESNOYESNOACCURACY(準確度)PRECISION(精密度)The Accuracy of an ins
7、trument can be improved by recalibrating to reduce its error,but recalibrating generally does not improve the instruments Precision.(Repeatability also sometimes known as“Precision”)Cpk Training datum Version:AT/2Ca(制程準確度)Tux Ca:(Capability of accuracy)從生產過程中所獲得的資料其實際平均值()與規格中心值()之間偏差的程度X%規格容許差規格中心實
8、績中心 Ca%2/)(TX 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A 12.5%B12.5%25%C 25%50%D 50%Ca 值CaCaCaCaCpk Training datum Version:ACa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.Cpk Training datum Version:ACp(制程精密度)TCp:(Capability of precison)以規格公差(T)與生產中所獲得的6個估計實績標準差()其間相差的程度63規格公差規格容許差
9、Cp雙邊 X-SL 3 只有規格下限:Cp=3Su-X 只有規格上限:Cp=單邊6 6B級6 A級Cp=1.331.006C級0.836 D級規格下限SL規格中心規格上限SU等級A1.33 CpBCDCp值1.00 Cp1.330.83 Cp1.00Cp0.83Cpk Training datum Version:A工程能力指數工程能力指數(Cp)之處理之處理T3T3355Cp=1.67Cp=1.33 1.33Cp1.67顯示有足夠之工程力.對規格而言,為正常狀態,應繼續保持.2Cp處理 1.67 Cp,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.1344Cpk Trai
10、ning datum Version:A工程能力指數工程能力指數(Cp)之處理之處理TT3 1.00Cp1.33,顯示工程能力並不充足,但尚且可以.要注意有發生不良品之雇慮,必要時應提升工程之能力.Cp1.00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.333Cpk Training datum Version:AZ1=3Cp(1+Ca)由Z1查常態分配表得p1%Z2=3Cp(1-Ca)由Z2查常態分配表得p2%p%=p1%+p2%.即為推定群體超出規格上下之不良率.XSZU1XSZL2 等級 總評P%A P0.44%B 0
11、.44%P1.22%C 1.22%P6.68%D 6.68%P投影片 30或Cpk Training datum Version:Ae.g:(例題)今庫存有某圓軸6000支,其品質特性為圓軸之長度,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?KeyCpk Training datum Version:A解題步驟:由已知得:=15.7cm;=0.3cm33.13.04.03.07.151.161XSZU方法一:查標準常態分配表(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=55
12、0.8四舍五入得551支方法二:33.13.07.151.163*3)1(31SuCpCaZ下述步驟與上同,故略Cpk Training datum Version:ACpk Training datum Version:A制程能力指數CpK綜合Ca與Cp兩值之指數(1)CpK值之計算式有兩種CpCaCpK)1(B.單邊規格時:(2)等級判定 CpK值愈大,品質愈佳.依CpK值 大小分為五級3)(,3)(LUSXXSMinCpK等級A1.33 CpK1.67BCDCpK值1.00 CpK1.330.67 CpK1.00CpK0.67A+1.67 CpKA.雙邊規格時:Cpk Training
13、datum Version:ACpK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.Cpk Training datum Version:A制程能力與規格之關系制程能力與規格之關系6ABCD ESuSL 或或6 6代表制程在正常狀態下變化之範圍代表制程在正常狀態下變化之範圍,稱為自然公差稱為自然公差(Natural tolerance)Natural tolerance)規格上下限之差為規格上下限之差為S Su u-S-SL,L,則則 或或6 6與與S Su u-S-SL
14、L有下列三種關系有下列三種關系(情況情況)如圖示如圖示:661.61.6 Su-SLCpk Training datum Version:AEvaluation formCpk Training datum Version:ACpk Training datum Version:ACpkCpk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在圖例上表示為中心沒有偏移(實際中心值與規格中心重合)DRLDRRLC
15、LUCL6T=8XYDPPMCpk Training datum Version:ADR=DRL+DRRDR(Defect Rate):總不良 DRL(Defect Rate Left):左不良 DRR(Defect Rate Right):右不良XLCLUCLDRLDR=DRL+DRRDRRXCpk Training datum Version:ATable 1 Quality levels and Corresponding Number of DefectsCpk Training datum Version:ATable2.The Number of Defective(Parts p
16、er Million)for SpecifiedOff-Centering of the Process and Quality LevelsCpk Training datum Version:A中心偏离時dppm的計算off-center()Cpk Training datum Version:A面積面積z常態曲線下之面積常態曲線下之面積dzzzZPzFez2221)()(e=2.718.0Z=(x-)/投影片 16Cpk Training datum Version:ACpk Training datum Version:ACpk Training datum Version:ACpk
17、Training datum Version:A1.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.設定生產線的機器;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.Cpk Training datum Version:AVersion:1.1A.Trial Run Data Collection Sample Size110112021303140415051606170718042.78742.82442.77242.70642.83242.87442.80642.702
18、42.77542.71742.83642.84542.82542.83342.80542.70842.79242.78042.82342.77442.83642.89842.80742.69542.77842.80342.80142.69242.80742.78542.80742.72842.79142.75842.83642.86342.82942.84242.84042.84042.81042.82542.83642.86142.83242.84542.83642.86342.72942.75942.81742.83642.82442.82342.79642.67042.85042.696
19、42.83042.86542.83042.84242.82242.80342.79142.77942.82742.78042.83342.89142.80542.69542.85042.69642.83042.86542.83042.84242.82242.803Calculation=42.804Sigma=0.051Max=42.898Min=42.670(at Design Phase)How to Define Specification&Verify the Process Capability Input Areafor DataCpk Training datum Version
20、:AItemNo.Quality LevelSpecification FormatLSLUSLDRL(Dppm)DRR(Dppm)DR(Dppm)11 Sigma1 Sigma42.804 42.753 42.855 158655.26 158655.26 317310.5221.5 Sigma1.5 Sigma42.804 42.727 42.88066807.2366807.23 133614.4632 Sigma2 Sigma42.804 42.702 42.90622750.0622750.0645500.1242.5 Sigma2.5 Sigma42.804 42.676 42.9
21、316209.686209.6812419.3653 Sigma3 Sigma42.804 42.650 42.9571349.971349.972699.9363.5 Sigma3.5 Sigma42.804 42.625 42.982232.67232.67465.3574 Sigma4 Sigma42.804 42.599 43.00831.6931.6963.3784.5 Sigma4.5Sigma42.804 42.574 43.0333.403.406.8095 Sigma5 Sigma42.804 42.548 43.0590.2871050.2871050.57105.5 Si
22、gma5.5 Sigma42.804 42.523 43.0840.0190360.0190360.04116 Sigma6 Sigma42.804 42.497 43.1100.000990.000990.00Prepared by:VQM/Xu Gang Approved by:Howard Lin B.Quality Level(For your reference and choosing)Cpk Training datum Version:ATimesQuality LevelNominal T/2()SpecLSLSpecUSLToleranceOff-Center (Sigma
23、)1442.8040.204 42.599 43.0080.4080.002442.7800.204 42.576 42.9840.4080.4634.4642.7800.228 42.552 43.0080.4550.46Ca CpCpKGradeDRL(Dppm)DRR(Dppm)DR(Dppm)0.001.331.33A31.6931.6963.370.121.331.18B4.05202.05206.100.101.491.33A0.4332.0332.46Prepared by:VQM/Xu Gang Approved by:Howard Lin VerificationItemRe
24、mark:Green means it can be changed or modified,Yellow means it can not be changed or modified.C.Choose Quality Level and Define SpecificationD.Process Capability Verification231Cpk Training datum Version:A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/d2d3D1D2D3D4A3D5D6E2A0m3A2C322.121 3.760
25、1.8800.56421.77250.000 1.8430.000 3.267 1.1280.88650.853 0.000 3.685 0.000 3.2672.224 0.000 3.8652.6602.6951.880 0.60331.732 2.394 1.0230.72361.38200.000 1.8580.000 2.568 1.6930.59070.888 0.000 4.358 0.000 2.5751.265 0.000 2.7451.7721.8261.187 0.46341.500 1.880 0.7290.79791.25330.000 1.8080.000 2.26
26、6 2.0590.48570.880 0.000 4.698 0.000 2.2820.829 0.000 2.3751.4571.5220.796 0.38951.342 1.596 0.5770.84071.18940.000 1.7560.000 2.039 2.3260.42890.864 0.000 4.918 0.000 2.1150.712 0.000 2.1791.2901.3630.691 0.34161.225 1.410 0.4830.85851.15120.026 1.7110.030 1.970 2.5340.39460.348 0.000 5.078 0.000 2
27、.0040.562 0.000 2.0551.1841.2630.549 0.30871.134 1.277 0.4190.88821.12590.105 1.5720.118 1.882 2.7040.36980.333 0.205 5.205 0.076 1.9240.520 0.078 1.9671.1091.1910.509 0.28281.061 1.175 0.3730.90271.10780.167 1.6380.185 1.815 2.8470.35120.820 0.387 5.307 0.136 1.8640.441 0.139 1.9011.0541.1430.432 0
28、.26291.000 1.094 0.3370.91391.09420.219 1.6090.239 1.761 2.9700.33670.808 0.546 5.394 0.184 1.8160.419 0.187 1.8501.0101.1040.412 0.246100.949 1.028 0.3080.92271.08370.262 1.5840.284 1.716 3.0780.32490.797 0.687 5.469 0.223 1.7770.369 0.227 1.8090.9751.0720.363 0.232110.905 0.973 0.2850.93001.07530.
29、299 1.5610.321 1.679 3.1730.31520.787 0.812 5.534 0.256 1.744120.866 0.925 0.2660.93591.06840.331 1.5410.354 1.645 3.2580.30690.778 0.924 5.592 0.284 1.716130.832 0.834 0.2490.94101.06270.359 1.5230.382 1.618 3.3360.29980.770 1.026 5.646 0.308 1.692140.802 0.848 0.2350.94531.05790.384 1.5070.406 1.5
30、94 3.4070.29350.762 1.121 5.693 0.329 1.671150.775 0.816 0.2230.94901.05370.406 1.4920.428 1.572 3.4720.28800.755 1.207 5.737 0.348 1.652160.750 0.788 0.2120.95231.05010.427 1.4780.448 1.552 3.5320.28310.749 1.285 5.779 0.364 1.636170.728 0.762 0.2030.95511.04700.445 1.4650.466 1.534 3.5880.27870.74
31、3 1.359 5.817 0.379 1.621180.707 0.738 0.1940.95761.04420.461 1.4540.482 1.518 3.6400.27470.738 1.426 5.854 0.392 1.608190.688 0.717 0.1870.95991.04180.477 1.4430.497 1.503 3.6890.27110.733 1.490 5.888 0.404 1.596200.671 0.697 0.1800.96151.03960.491 1.4330.510 1.490 3.7350.26770.729 1.548 5.922 0.41
32、4 1.586210.655 0.679 0.1730.96381.03760.504 1.4240.523 1.477 3.7780.26470.724 1.606 5.950 0.425 1.575220.640 0.662 0.1670.96551.03580.516 1.4150.534 1.466 3.8190.26180.720 1.659 5.979 0.434 1.566230.626 0.647 0.1620.96701.03420.527 1.4070.515 1.455 3.8580.25920.716 1.710 6.006 0.443 1.567240.612 0.632 0.1570.96841.03270.538 1.3990.555 1.455 3.8950.25670.712 1.759 6.031 0.452 1.548250.600 0.619 0.1530.96961.03130.548 1.3920.565 1.435 3.9310.25440.709 1.804 6.058 0.459 1.541平均數管制圖中位數管制圖管 制 圖 常 用 系 數 表管 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Return d2X Bar RA2D4
