制程能力分析-(Cpk---Z值)

1、內部教育訓練1-統計製程管制 (SPC)-管制圖2-製程能力分析 (Cpk, Z值)3-量測系統分析 (MSA)製程能力分析製程能力分析 (Cpk ，DPMO，Z值值)目錄計量型數值(Variable data)計數型數值(Attribute data)Ca、Cp、Cpk Pp、PpkDefect、DPUDPO、DPMOZ值值(Sigma Level) A 規格寬度 USL LSL VOC Cp = - = - = - = - B 實際分散寬度 6 VOP製程的聲音顧客的聲音 USL LSL CPU = - CPL = - : 規格中心值 3 3 C 偏移量 Xbar Ca = - = - =

2、 - : 規格中心值 1/2A 1/2規格寬度 (USL LSL) Xbar : 平均值 USL - Xbar Xbar LSLCpk = Cp (1 Ca ) = Min ( - ， - ) = Min (CPU,CPL) 3 3 = 製程精確度x (1-偏移率) = 精確度 x 準確度Cpk = Cp (1 Ca ) =Cpk = Cp (1 Ca ) =Cp = (103-97)/(6x0.5) = 2.0Cpk = Cp (1 Ca ) = 2.0 (1- (100 99.25)/3) = 2.0(0.75) = 1.5CPU = (103-99.25)/(3x0.5) = 2.5CP

3、L = (99.25-97)/(3x0.5) = 1.55 僅有規格上限僅有規格下限5 USL - Xbar Xbar LSLCpk = Min ( - ， - ) = Min (CPU, CPL) 3 3 USL - Xbar Xbar LSL Z = Min ( - ， - ) = Min (ZU, ZL) 6 6 3種估算標準差的方法7 計量型製程能力分析 - 1給定規格界限, 才能進行製程能力分析7 計量型製程能力分析- 2資料輸入有2種資料輸入方式7 計量型製程能力分析- 3製程能力分析Stat Quality Tools Capability Analysis Normal7 計量

4、型製程能力分析- 4輸入資料位置輸入規格界限條件輸入7 計量型製程能力分析- 5604.5603.0601.5600.0598.5597.0595.5LSLUSLProcess DataSample? N90StDev(Within)1.64804StDev(Overall)1.71444LSL595Target*USL605Sample Mean599.938Potential (Within) CapabilityCCpk1.01Overall CapabilityPp0.97PPL0.96PPU0.98PpkCp0.96Cpm*1.01CPL1.00CPU1.02Cpk1.00Obser

5、ved PerformancePPM? ? USL0.00PPM? Total0.00Exp. Within PerformancePPM? ? USL1064.33PPM? Total2431.36Exp. Overall PerformancePPM? ? USL1575.02PPM? Total3562.66WithinOverallProcess Capability of camshaft_1樣本實際數據短期預估之百萬缺點數短期：(1)Z值 = (Xbar-LSL) / = (599.938-595)/1.64804 = 2.996 p(2.996)= 0.998632 缺點=1-0

6、.998632=0.001368 =1368 ppm(2)Z值 = (USL-Xbar) / = (605-599.938)/1.64804 = 3.0715 p(3.0715)= 0.998935 缺點=1-0.998935=0.001065 =1065 ppm(3)缺點總數 =1367+1064=2421 ppm長期預估之百萬缺點數短期：Cp = (USL-LSL) / 6 = (605-595)/6x1.64804 = 10/9.88824 = 1.01製程能力分析結果7 計量型製程能力分析- 6製程能力分析-6 packStat Quality Tools Capability Six

7、pack Normal7 計量型製程能力分析- 7Sample Mean1715131197531602600598_X=599.938UCL=602.149LCL=597.727Sample Range1715131197531840_R=3.833UCL=8.106LCL=0SampleValues20151050604600596603.0601.5600.0598.5597.0605600595WithinOverallSpecsWithinStDev1.64804Cp1.01Cpk1CCpk1.01OverallStDev1.71444Pp0.97Ppk0.96Cpm*Process

8、 Capability Sixpack of camshaft_1Xbar ChartR ChartLast 18 SubgroupsCapability HistogramNormal Prob PlotAD: 0.279, P: 0.640Capability PlotCpk=1 , Z值=3合併管制圖與製程能力分析8 - 1樣樣本本大大小小 不不合合格格品品不不合合格格率率樣樣本本大大小小 不不合合格格品品不不合合格格率率ndp = d / nndp = d / n198200.20115070.142104180.17125370.13397140.14135690.16499160.

9、16144950.10597130.13155680.146102290.28165390.177104210.20175290.178101140.141851100.2095560.11195290.17104860.132047100.21合合計計1424240平平均均710.17組組別別組組別別8 - 2製程能力分析-二項式分佈計數型資料屬二項式分佈或卜瓦松分佈, 因此不必進行常態檢定8 - 3填入不合格品數填入樣本數條件輸入8 - 4末端呈水平穩定,表示蒐集的組數已足夠合併管制圖與製程能力分析SampleProportion1917151311975310.30.20.10.0_P=

10、0.1664UCL=0.3294LCL=0.0034Sample%Defective201510521.019.518.016.515.0Summary Stats0.00PPM Def:166433Lower CI:147439Upper CI:186813Process Z:0.9684Lower CI:(using 95.0% confidence)0.8897Upper CI:1.0475%Defective:16.64Lower CI:14.74Upper CI:18.68Target:Sample Size%Defective1007550302010242016128406.04

11、.53.01.50.0TarBinomial Process Capability Analysis of RejectsP ChartTests performed with unequal sample sizesCumulative %DefectiveRate of DefectivesDist of %Defective不良率=16.64%良率=1-16.64%=83.36%=0.8336使用Inverse Cumulative Probability計有出Z 值= 0.9684樣本大小不同,管制界限不會水平線9 - 1代表2個機會9 - 2樣本大小樣本大小缺點數缺點數單位缺點數單位

12、缺點數樣本大小樣本大小缺點數缺點數單位缺點數單位缺點數ncu = c / nncu = c / n14. 020.50115. 550.9124. 030.75124. 520.4434. 220.48135. 240.7744. 430.68144. 220.4856. 150.82156. 350.7965. 520.36165. 940.6875. 550.91173. 200.0085. 730.53188. 480.9594. 310.23195. 430.56104. 120.49208. 570.82組號組號組號組號9 - 3製程能力分析-卜瓦松分佈9 - 4條件輸入填入缺點數填

13、入樣本數SampleSample Count Per Unit191715131197531210_U=0.648UCL=1.477LCL=0SampleDPU20151050.80.70.60.5Summary Stats0.0000Max DPU:0.9524Targ DPU:0.0000(using 95.0% confidence)Mean DPU:0.6482Lower CI:0.5034Upper CI:0.8218Min DPU:Sample SizeDPU8641.00.50.01.00.80.60.40.20.04.83.62.41.20.0TarPoisson Capability Analysis of defectsU ChartTests performed with unequal sa