1、2018/11/20,Silitek Electronics (GZ) VQM Department,1,Cpk,制程能力分析,2018/11/20,Silitek Electronics (GZ) VQM Department,2,常態分配,2018/11/20,Silitek Electronics (GZ) VQM Department,3,Percentages Of The Normal Distribution,2018/11/20,Silitek Electronics (GZ) VQM Department,4,管制圖與常態分配,+k,圖2,X值在+k與-k之間之或然率(Pro
2、bability)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,2018/11/20,Silitek Electronics (GZ) VQM Department,5,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,2,1,4,3,2018/11/20,Silitek Electronics (GZ) VQM Department,6,群體(制程)與樣本間之關系
3、,樣本平均值之分配,群體平均值之分配,(無限群體),2018/11/20,Silitek Electronics (GZ) VQM Department,7,Cpk 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 (Lower Specification Limit) 落在規格上,下限外的斜線面積即為產品的不良率.,Standard Deviation from mean,2018/11/20,Silitek El
4、ectronics (GZ) VQM Department,8,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,1分散寬度以 表示之.,制程能力= (或 ),d2,Cpk 計算時用公式(1),2018/11/20,Silitek Electronics (GZ) VQM Department,9,兩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
5、(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.,2018/11/20,Silitek Electronics (GZ) VQM Department,10,The Accuracy of an instrument can be improved by recalibrating to reduce its error, but recalibrating generally does not improve
6、 the instruments Precision.(Repeatability also sometimes known as “Precision”),Accuracy&Precision,2018/11/20,Silitek Electronics (GZ) VQM Department,11,2018/11/20,Silitek Electronics (GZ) VQM Department,12,Ca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.,2018/11/20,Silitek Electronics (GZ)
7、 VQM Department,13,2018/11/20,Silitek Electronics (GZ) VQM Department,14,工程能力指數(Cp)之處理,2018/11/20,Silitek Electronics (GZ) VQM Department,15,工程能力指數(Cp)之處理,2018/11/20,Silitek Electronics (GZ) VQM Department,16,Ca,Cp的綜合評價,1.計算方法: Z1=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
8、格上下之不良率.,2.依不良率P%分級做評定標準: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,2018/11/20,Silitek Electronics (GZ) VQM Department,17,e.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?,Key,2018/11/20,Silitek Electronics (GZ) VQM Department,18,解題步驟:,由已知得: =
9、15.7cm; =0.3cm,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:,下述步驟與上同,故略,2018/11/20,Silitek Electronics (GZ) VQM Department,19,Ca,Cp不良時的一般處理方法,1.Ca不良時的一般處理方法,製造單位為主, 技術單位為副, 品管單位為輔.,2.Cp不良時的一般處理方法,技術單位為主, 製造單位為副, 品管單位為輔.,2018/11/20,Silitek Electronics (GZ) VQ
10、M Department,20,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,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,等級,A,1.33 CpK1.67,B,C,D,CpK值,1.00 CpK1.33,0.67 CpK1.00,CpK0.67,A+,1.67 CpK,A. 雙邊規格時:,2018/11/20,Silitek Electronics (GZ) VQM Department,21,CpK之處置原則,2018/11/20,Silitek Electronics (GZ) VQM Department,22,制程能
11、力與規格之關系,或6代表制程在正常狀態下變化之範圍,稱為自然公差(Natural tolerance)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. 6 Su-SL,2018/11/20,Silitek Electronics (GZ) VQM Department,23,2. 6 Su-SL,2018/11/20,Silitek Electronics (GZ) VQM Department,24,3. 6 Su-SL,2018/11/20,Silitek Electronics (GZ) VQM Department,25,Evaluation for
12、m,2018/11/20,Silitek Electronics (GZ) VQM Department,26,2018/11/20,Silitek Electronics (GZ) VQM Department,27,Cpk為什麼要大於或等於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),DPPM,2018/11/20,Silitek Electronics (GZ) VQM Dep
13、artment,28,DR=DRL+DRR DR(Defect Rate):總不良DRL (Defect Rate Left) :左不良DRR (Defect Rate Right) :右不良,2018/11/20,Silitek Electronics (GZ) VQM Department,29,Table 1 Quality levels and Corresponding Number of Defects,2018/11/20,Silitek Electronics (GZ) VQM Department,30,Six Sigma 有多小?,2018/11/20,Silitek El
14、ectronics (GZ) VQM Department,31,Table2.The Number of Defective(Parts per Million)for Specified Off-Centering of the Process and Quality Levels,2018/11/20,Silitek Electronics (GZ) VQM Department,32,中心偏离時dppm的計算,off-center(),2018/11/20,Silitek Electronics (GZ) VQM Department,33,面積,z,常態曲線下之面積,e=2.718.
15、,0,Z=(x- )/,投影片 16,2018/11/20,Silitek Electronics (GZ) VQM Department,34,2018/11/20,Silitek Electronics (GZ) VQM Department,35,2018/11/20,Silitek Electronics (GZ) VQM Department,36,2018/11/20,Silitek Electronics (GZ) VQM Department,37,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
16、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.,2018/11/20,Silitek Electronics (GZ) VQM Department,38,2018/11/20,Silitek Electronics (GZ) VQM Department,39,Item,No.,Quality,Level,Specification,Format,LSL,USL,DRL,(Dppm),DRR,(Dppm),DR,(Dppm),1,1 Sigma,1 Sigma,42.804,42.753,42.8
17、55,158655.26,158655.26,317310.52,2,1.5 Sigma,1.5 Sigma,42.804,42.727,42.880,66807.23,66807.23,133614.46,3,2 Sigma,2 Sigma,42.804,42.702,42.906,22750.06,22750.06,45500.12,4,2.5 Sigma,2.5 Sigma,42.804,42.676,42.931,6209.68,6209.68,12419.36,5,3 Sigma,3 Sigma,42.804,42.650,42.957,1349.97,1349.97,2699.93
18、,6,3.5 Sigma,3.5 Sigma,42.804,42.625,42.982,232.67,232.67,465.35,7,4 Sigma,4 Sigma,42.804,42.599,43.008,31.69,31.69,63.37,8,4.5 Sigma,4.5Sigma,42.804,42.574,43.033,3.40,3.40,6.80,9,5 Sigma,5 Sigma,42.804,42.548,43.059,0.287105,0.287105,0.57,10,5.5 Sigma,5.5 Sigma,42.804,42.523,43.084,0.019036,0.0190
19、36,0.04,11,6 Sigma,6 Sigma,42.804,42.497,43.110,0.00099,0.00099,0.00,Prepared by :VQM /Xu Gang,Approved by: Howard Lin,B.Quality Level (For your reference and choosing),2018/11/20,Silitek Electronics (GZ) VQM Department,40,Times,Quality,Level,Nominal,T/2(),Spec,LSL,Spec,USL,Tolerance,Off-Center,(Sig
20、ma),1,4,42.804,0.204,42.599,43.008,0.408,0.00,2,4,42.780,0.204,42.576,42.984,0.408,0.46,3,4.46,42.780,0.228,42.552,43.008,0.455,0.46,Ca,Cp,CpK,Grade,DRL,(Dppm),DRR,(Dppm),DR,(Dppm),0.00,1.33,1.33,A,31.69,31.69,63.37,0.12,1.33,1.18,B,4.05,202.05,206.10,0.10,1.49,1.33,A,0.43,32.03,32.46,Prepared by :V
21、QM /Xu Gang,Approved by: Howard Lin,Verification,Item,Remark: Green means it can be changed or modified , Yellow means,it can not be changed or modified .,C.Choose Quality Level and Define Specification,D.Process Capability Verification,2,3,1,2018/11/20,Silitek Electronics (GZ) VQM Department,41,Return d2,X Bar R,A2,D4,
