1、innovative Display Solution ProviderCPK,SPC,GR&R&Correlation regressioninnovative Display Solution Provider目目 錄錄1.封面封面.(Page1) 2.目錄目錄 .(Page2) 3.SPC基本概念基本概念.(Page3) 4.SPC統計制程管制統計制程管制 4.1 Cpk.(Page445) 4.2 QC舊七大手法.(Page4681) 4.3 管制圖.(Page8294)5.相關回歸相關回歸.(Page9598)6.GR&R. (Page99 115)innovative Displa
2、y Solution Provider3.SPC-Statistical Process Control-統計制程管制統計制程管制1.SPC的焦點:制制 程程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:數據通過計算產生有意義的情報.5.SPC所使用的主要工具: 5.1 Cpk 5.2七大手法 .管制圖6.計算:對數據進行處理的過程innovative Display Solution Provider4.1Cpk制程能力分析innovative Display Solution Provider常態分配.7
3、18.2)(.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 的點傾向於集中的附近.圖1(a) 2 a(b)2 binnovative Display Solution Provider-3-2 -1-
4、41234PERCENTAGES OF THE NORMAL DISTRIBUTIONinnovative Display Solution Provider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 -kinnovative Display Solution Provider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學上x101Nn101NnnNnNX.11NnN注:如 可視為無限群體用
5、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xniinsXXnn1211)(1*nXXinis12)(2143innovative Display Solution Provider樣本平均值之分配x群體平均值之分配nX(無限群體)innovative Display Solution ProviderCpkCpk Vs Defective Yield Vs 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 Limit)規格下限:LSL
6、(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. 670. 57
7、ppm99. 999943%+/-5 Sigm a2. 000. 002ppm99. 9999998%+/-6 Sigm ainnovative Display Solution Provider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(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.VdR6,6,62制程能力= (或 ) 66RX 1)(22nnXXi1)(22fffufu2dRd2Cpk 計算時用
8、公式(1)innovative Display Solution Provider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.innovative Display Solution ProviderYESNOYESNOACCURACY(準確度)PRECISION
9、(精密度)The Accuracy of an instrument can be improved by recalibrating to reduce its error, but recalibrating generally does not improve the instruments Precision.(Repeatability also sometimes known as “Precision”)innovative Display Solution ProviderT/2Ca (制程準確度)Tux Ca:(Capability of accuracy)從生產過程中所獲得
10、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CaCaCaCainnovative Display Solution ProviderCa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.innovative Display Solution ProviderCp (制程精密度)TCp:(Capabilit
11、y of precision) 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 Cp1.00Cp0.83innovative Display Solution Provider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,
12、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.1344innovative Display Solution Provider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.333innovative Display Solution ProviderZ1=3Cp(1+Ca)由Z1查常
13、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 0.44%P1.22% C 1.22%P6.68% D 6.68%P投影片 30或innovative Display Solution Providere.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?Keyinnovative Display Solution Provider解題步驟
14、: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=550.8四舍五入得551支方法二:33. 13 . 07 .151 .163*3)1 ( 31SuCpCaZ下述步驟與上同,故略innovative Display Solution Providerinnovative Display Solution Provider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CpCaCp
15、K)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:innovative Display Solution ProviderCpK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.innovative Display Solution Provider制程能
16、力與規格之關系制程能力與規格之關系6ABCD ESuSL 或或66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66與與S Su u-S-SL 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. 6 Su-SL1. 6innovative Display Solution ProviderEvaluation forminnovative Display Solution Prov
17、iderinnovative Display Solution ProviderCpkCpk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)DRLDRRLCLUCL6T=8XYDPPMinnovative Display Solution ProviderDR=DRL+DRRDR(Defect Rate):總不良 DRL (Defect Rate L
18、eft) :左不良 DRR (Defect Rate Right) :右不良XLCLUCLDRLDR=DRL+DRRDRRXinnovative Display Solution ProviderTable 1 Quality levels and Corresponding Number of Defectsinnovative Display Solution ProviderSigmaSigmaCpkCpkDPPMDPPM拼拼拼拼錯錯錯錯字字字字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312,7
19、00一本書中每 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innovative Display Solution ProviderTable2.The Number of Defective(Parts per Million)for SpecifiedOff-Centering of the Process and Quality Levelsinnovative Display Solution Provider中心偏离時dppm的計算off-center()innovative Display Solution P
20、rovider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 16innovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Provider1.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
21、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.innovative Display Solution ProviderVersion:1.1A. Trial Run Data Collection Sample Size110112021303140415051606170718042.78742.82442.77242.70642.83242.87442.80642.70242.77542.71742.83642.84542.82542.83342.80542.70842.79242.78042.82342.77442.83642.89842.80742.69542.778
22、42.80342.80142.69242.80742.78542.80742.72842.79142.75842.83642.86342.82942.84242.84042.84042.81042.82542.83642.86142.83242.84542.83642.86342.72942.75942.81742.83642.82442.82342.79642.67042.85042.69642.83042.86542.83042.84242.82242.80342.79142.77942.82742.78042.83342.89142.80542.69542.85042.69642.830
23、42.86542.83042.84242.82242.803Calculation=42.804Sigma=0.051Max=42.898Min=42.670(at Design Phase)How to Define Specification & Verify the Process Capability Input Areafor Datainnovative Display Solution ProviderItemNo.Quality LevelSpecification FormatLSLUSLDRL(Dppm)DRR(Dppm)DR(Dppm)11 Sigma1 Sigma42.
24、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 42.9316209.686209.6812419.3653 Sigma3 Sigma42.804 42.650 42.9571349.971349.972699.9363.5 Sigma3.
25、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 Sigma5.5 Sigma42.804 42.523 43.0840.0190360.0190360.04116 Sigma6 Sigma42.804 42.497 43.1100.00
26、0990.000990.00Prepared by :VQM /Xu Gang Approved by: Howard Lin B.Quality Level (For your reference and choosing)innovative Display Solution ProviderTimesQuality LevelNominal T/2()SpecLSLSpecUSLToleranceOff-Center (Sigma)1442.8040.204 42.599 43.0080.4080.002442.7800.204 42.576 42.9840.4080.4634.4642
27、.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 VerificationItemRemark: Green means it can be changed or modified , Yellow means it can not be
28、changed or modified .C.Choose Quality Level and Define SpecificationD.Process Capability Verification231innovative Display Solution Provider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 1.8800.56421.77250.000 1.8430.000 3.267 1.1280.88650.853 0.000 3.
29、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 2.266 2.0590.48570.880 0.000 4.698 0.000 2.2820.829 0.000 2.3751.4571
30、.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 2.0040.562 0.000 2.0551.1841.2630.549 0.30871.134 1.277 0.4190.888
31、21.12590.105 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 0.26291.000 1.094 0.3370.91391.09420.219 1.6090.239 1.761 2.9700.3
32、3670.808 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 0.2850.93001.07530.299 1.5610.321 1.679 3.1730.31520.787 0.812 5.534 0.256 1.744120.
33、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 1.594 3.4070.29350.762 1.121 5.693 0.329 1.671150.775 0.816 0.2230.9
34、4901.05370.406 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 3.5880.27870.743 1.359 5.817 0.379 1.621180.707 0.738 0.1940.95761.04420.461 1.4
35、540.482 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 0.414 1.586210.655 0.679 0.1730.96381.03760.504 1.4240.523 1.477 3.77
36、80.26470.724 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
37、 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 RA2D4innovative Display Solution ProviderModel: Parts Name: Data Source: Measured By: Measure Da
38、te:Measured By: 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%0.00000.00000.000010.000020.000030.000040.000050.00006
39、0.000070.000080.000090.0000100.0000110.0000120.0000130.0000140.0000150.0000160.0000RangeFrequency Normal Dist.RangeFrequencyNormal Dist.170.00000.00000#NUM!0.00000#NUM!180.00000.00000#NUM!0.00000#NUM!190.00000.00000#NUM!0.00000#NUM!200.00000.00000#NUM!0.00000#NUM!210.00000.00000#NUM!0.00000#NUM!220.
40、00000.00000#NUM!0.00000#NUM!230.00000.00000#NUM!0.00000#NUM!240.00000.00000#NUM!0.00000#NUM!250.00000.00000#NUM!0.00000#NUM!260.00000.00000#NUM!0.00000#NUM!270.00000.00000#NUM!0.00000#NUM!280.00000.00000#NUM!0.00000#NUM!290.00000.00000#NUM!0.00000#NUM!300.00000.00000#NUM!0.00000#NUM!310.00000.00000#
41、NUM!0.00000#NUM!320.00000.00000#NUM!0.00000#NUM!Measure Method轉換公式轉換公式:(y=bx+a)r a b x=#DIV/0!#DIV/0!#DIV/0!#DIV/0!y=#DIV/0!comments:(P.S.: CP:Caliper; MM:Micrometer; CM:CMM; PJ:Projetor; HG:Height Gauge; PG:Pin Gauge M:螺 紋 規螺 紋 規 )Prepared by: 曾 如 華曾 如 華Approved by : Howard Lin Ver. 2.1a : 截距截距 0.8
42、=|R|=0.3 弱相關弱相關b : 斜率斜率 0.3=|R|=0 錯相關錯相關相關分析相關分析 Process Capability & Correlation Analysis Worksheet Part Number :Vendor name:Drawing ver: r : 相關系數相關系數 |R|=0.8 強相關強相關制程能力比較分析表制程能力比較分析表A DataB DataLocationCustomer name:ISL Normal Distribution0001110.000.000.000.000.000.000.000.000.000.000.000.000.000
43、.000.000.0000.20.40.60.81Vendor Normal Distribution0001110.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.0000.20.40.60.81Correlation Illustration0.00000.50001.00001.50000.00000.20000.40000.60000.80001.0000innovative Display Solution Provider4.2.QC4.2.QC七大手法七大手法innovative Display Soluti
44、on Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Provideri
45、nnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Provider項目項目不良數（特性值）不良數（特性值） 不良率不良率影 影响 响度 度累 累计 计影 影响 响度
46、 度冷气不冷气不凉 凉喷 喷漆 漆脱 脱落 落喷 喷漆不均漆不均其它其它合合计 计innovative Display Solution Provider不良率A累计影响度innovative Display Solution Provider不良项目8月11日8月12日8月13日8月14日8月15日合计容器破损11容器瑕疵污点51冲压瑕疵污点57接着剂20其它14内包装瑕疵16内包装破损39外包装破损6合计4936434443215innovative Display Solution Providerinnovative Display Solution Providerinnovativ
47、e Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Provider111011101291311781217127193101081212111213169117610126111781199131114104151181014101081210101
48、31413111114157871210111181110951613111210129innovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinnovative Display Solution Providerinno
49、vative Display Solution ProviderNO温度产量NO温度产量NO温度产量144.620.62651.623.85143.421.5250.3242746.322.15243.420.4346.221.12846.321.35347.821.8446.922.52948.322.55445.721.5548.921.33047.721.15544.121.1643.721.33150.923.75646.322.4748.823.2324922.25749.521.6846.621.63348.522.75844.821.3947.321.93450.521.8594
50、923.11051.722.13546.820.86044211145.622.13644.221.9614321.41244.621.83745.522.36250.723.51345.421.43849.321.56346221446.4223945.820.86448.121.71547.920.94048.122654722.91649.222.24145.922.66644.221.91749.223.84243.1116747.922.91847.522.64345.521.56847.822.11943.521.14451.123.66947.122.3205022.64549.
