05Minitab过程能力分析课件

1、. . . . . . .a)b)c). . .X. . .6LSLUSLToleranceNaturalTolerancegEngineerinCpProcess is centeredProcess is not centered. . .a)b)c)a) Process is highly capable (Cp2)b) Process is capable (Cp=1 to 2)c) Process is not capable (Cp1). . .XXXXR. . .a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk 1. . . . . . 你可以计

2、算任何给定x值对应的Z值. Z 是x值与平均值间距离对标准偏差的倍数.m m+1+1 +2+2+3+3 +4+4zxmxZ. . .43210-1-2-3-449.0047.4445.8844.3242.7641.2039.6438.0836.52Standard DeviationsUnits of MeasureUSLProbability of a defect greater than USLZUSLLSLProbability of a defect less than LSLZLSLx. . . WithinOverall Sample Size30 50 units 100 un

3、itsNumber of Lotssingle lotseveral lotsPeriod of Timehours or daysweeks or monthsNumber of Operatorssingle operatordifferent operatorsProcess Potential Cp PpProcess Performance Cpk Ppk. . . S/NX1X2 XkMeanRangeStd Dev1x1,1x2,1 xk,1 X1 R1 S12x1,2x2,2 xk,2 X2 R2 S2: : : : : : :mx1,mx2,m xk,m Xm Rm Sm O

4、verall 1nxxc11n xc12m1ik1jij42m1ik1jij4Overall . . .Within whered2 is a Shewhart constant = (k)wherec4 is a Shewhart constant = (k) 2WithindR4WithincS 1n1n1nS1nS1nS1nc1m212mm2222114Within+. . . Within 1iiiXXMR2WithindMR2WithindMR. . . . .ucllclucllcl. . . . .LSLUSLLSLUSL. . . . . . .SampleSample Mea

5、n191715131197531600.5600.0599.5599.0_X=599.548UCL=600.321LCL=598.775SampleSample Range1917151311975313210_R=1.341UCL=2.835LCL=0Xbar-R Chart of Supp1Supp1Percent60260160059959899.99995908070605040302010510.1Mean0.029599.5StDev0.6193N100AD0.844P-ValueProbability Plot of Supp1Normal . . .19171513119753

6、1600.0599.5599.0样样本本均均值值_X =599.548UCL=600.321LCL=598.7751917151311975313.01.50.0样样本本极极差差_R=1.341UCL=2.835LCL=02015105601.5600.0598.5样本样本值值601.50600.75600.00599.25598.50597.75LSLUSLLSL 598USL 602规格602600598组内整体规格标准差0.576429Cp1.16Cpk0.9组内标准差0.619299Pp1.08Ppk0.83Cpm*整体供应商 1 的 Process Capability Sixpac

7、k供应商 1 的 Process Capability SixpackXbar 控制图Xbar 控制图R 控制图R 控制图最后 20 个子组最后 20 个子组能力直方图能力直方图正态 概率图正态 概率图AD:0.844，P: 0.029能力图能力图. . .191715131197531602600598样样本本均均值值_X =600.23UCL=602.474LCL=597.986191715131197531840样样本本极极差差_R=3.890UCL=8.225LCL=02015105604600596样本样本值值604.5603.0601.5600.0598.5597.0LSLUSLL

8、SL 598USL 602规格605600595组内整体规格标准差1.67231Cp0.4Cpk0.35组内标准差1.87388Pp0.36Ppk0.31Cpm*整体11供应商 2 的 Process Capability Sixpack供应商 2 的 Process Capability SixpackXbar 控制图Xbar 控制图R 控制图R 控制图最后 20 个子组最后 20 个子组能力直方图能力直方图正态 概率图正态 概率图AD:0.287，P: 0.615能力图能力图. . .1715131197531602600598样样本本均均值值_X =599.938UCL=602.247L

9、CL=597.6291715131197531840样样本本极极差差_R=4.003UCL=8.465LCL=015105604600596样本样本值值603.0601.5600.0598.5597.0LSLUSLLSL 598USL 602规格605600595组内整体规格标准差1.72106Cp0.39Cpk0.38组内标准差1.70963Pp0.39Ppk0.38Cpm*整体供应商 2 的 Process Capability Sixpack供应商 2 的 Process Capability SixpackXbar 控制图Xbar 控制图R 控制图R 控制图最后 18 个子组最后 18

10、 个子组能力直方图能力直方图正态 概率图正态 概率图AD:0.279，P: 0.640能力图能力图. . . . .R. . . . . . . .7.56.04.53.01.50.0USLLSL*目标*USL8样本均值2.92307样本 N100标准差（组内）1.75687标准差（整体）1.78597过程数据Cp*CPL*CPU0.96Cpk0.96Pp*PPL*PPU0.95Ppk0.95Cpm*整体能力潜在（组内）能力PPM USL20000.00PPM 合计20000.00实测性能PPM USL1927.68PPM 合计1927.68预期组内性能PPM USL2236.81PPM 合计

11、2236.81预期整体性能组内整体扭曲 的过程能力扭曲 的过程能力1086420-2-499.99995908070605040302010510.1扭曲扭曲百百分分比比均值2.923标准差1.786N100AD1.028P 值0.010扭曲 的概率图扭曲 的概率图正态 数据不服从正态分布数据不服从正态分布Cpk = 0.96 被显示被显示. 但这个值是不可靠的但这个值是不可靠的或不准确的，因数据不服从正态分布或不准确的，因数据不服从正态分布. . .543210-1-2403020100LambdaLambda标标准准差差CL 下限CL 上限限估计0.43CL 下限0.20CL 上限0.65

12、取整值0.50（使用 95.0% 置信）Lambda扭曲 的 Box-Cox 图扭曲 的 Box-Cox 图 。. . .2.82.42.01.61.20.80.4已变换数据USL*USL*2.82843样本均值*1.62374标准差（组内）*0.52794标准差（整体）*0.537984LSL*目标*USL8样本均值2.92307样本 N100标准差（组内）1.75687标准差（整体）1.78597LSL*目标*变换后过程数据Cp*CPL*CPU 0.76Cpk 0.76Pp*PPL*PPU 0.75Ppk 0.75Cpm*整体能力潜在（组内）能力PPM USL 20000.00PPM 合计

13、20000.00实测性能PPM USL*11248.77PPM 合计11248.77预期组内性能PPM USL*12569.47PPM 合计12569.47预期整体性能组内整体扭曲 的过程能力扭曲 的过程能力使用 Box-Cox 变换，Lambda = 0.5Cpk 从从0.96下降到下降到0.76。此为正确的制程能力。此为正确的制程能力指数。指数。. . . . .SampleProportion1917151311975310.260.240.220.20_P=0.22643UCL=0.25552LCL=0.19733Sample%Defective201510523.523.022.522.021.5Summary Stats0.00PPM Def:226427Lower CI:222241Upper CI:230654Process Z:0.7507Lower CI:(using 95.0% confidence)0.7367Upper CI:0.7646%Defective:22.64Lower CI:22.22Upper CI:23.07Target:Sample Size%Defective2000192018402624222024201612