6SQ统计--过程能力分析.xls
基础知识 Cp Cpk Pp Ppk Cpm Cpmk Cm Cmk谈到过程能力，首先得解释变异（或者叫波动），正是因为有了变异的存在，才出现了能力大小。产生变异的原因可以归结为两种，一种是普通原因，一种是特殊的原因。$o;zO&_%x6v2l:k所谓的普通原因就是平时一直客观存在，对过程有一定的影响但不明显，而特殊因素则是偶然出现，对过程影响很大。举例说明：在一个有空调的房间进行培训时，虽然空调可能是设定在25度，但由于房间内外温度存在差异，所以每时每刻都会有能量在和房间外进行交换，所以如果用足够精确的温度计测量房间的温度就会发现房间里的温度其实并不是恒定在25.000度，而是24.99,24.98,25.00,25.01.在微小的在一定范围内进行变化，这时我们就说受到的是普通因素的影响，而如果有人推门进来，那么在这瞬间，房间内的温度会出现较大变化，此时我们说受到了普通因素和特殊因素两种影响。.g4(b1v3n;o:f6B过程只受普通因素影响的时候在控制图上表现为过程是受控的，如果有特殊原因的影响在控制图上会有异常点的出现。*q,t.V!I7s3k)y*O3I8c所以我们如果用Cp和Cpk来衡量过程能力，前提是要过程稳定且数据是正态分布，而且数据应该在25组以上（建议最少不要低于20组，数据组越少采信结果的风险越大），也就是说计算Cp,Cpk只考虑过程受普通因素的影响。计算公式为：Cp=(usl-lsl)/6;1、Cpk=(1-k)Cp;k=|u-M|/(usl-lsl)/2;2、Cpk=min(usl-u)/3,(u-lsl)/3;注释：usl为上规格线，lsl为下规格线，u为实际测得的平均值，M为上下规格的中心点，K值表示的意思是实际平均值偏离中心值的程度，此时的2T3D4Y2O;L9N9X即为只考虑普通因素产生的变异，通常根据控制图的不同采用Rbar/d2,或者Sbar/C4,在minitab里有三种不同的估算方法。;W;&j4s-u+V-8R&YPp,Ppk的计算公式和对应的Cp,Cpk计算公式相同，所不同的就是分母部分的变差不同，在此时变差是用标准偏差的计算公式进行计算的，此时的变差包含了普通因素和特殊因素产生的两种变差，也即在同一个过程下，此变差应该大于等于上面计算Cp,Cpk只考虑普通因素时的变差，当且仅当此过程只受普通因素变差影响时，两者相等，此时Ppk=Cpk，所以说理论上Cpk应该是恒大于Ppk,但很多时候在minitab中计算出的Ppk会略微大于Cpk，这时因为Cpk的变差是估算得来的，所以会有一定的误差，但并不影响对最终过程能力大小的评价。0y5WO+6U)j(I#j因为过程只受到普通因素变差影响是理想状态下的，从长期来说过程总会受到各种特殊因素的影响，所以说CpCpk又被称为短期过程能力，也叫潜在过程能力，PpPpk又叫长期过程能力，也叫性能指数。另外因为PpPpk的计算不需要过程稳定（因为在计算公式中已经考虑了普通和特殊两种因素的影响），所以在PPPAP手册中要求在产品进行试生产过程不稳定时（此时过程受两种因素影响）用Ppk衡量过程能力，要求Ppk=1.67才能进入量产阶段，所以又把Ppk 称为初期能力指数。0H!a9a/t1ER很多公司由于对过程能力的一知半解，往往只要求计算Cpk的指数来衡量过程能力是否足够，事实上进入正常生产后应该通过CpCpkPpk三个指数之间的产别来判断过程是否有问题，如果有问题是管理上还是技术上有问题，根据上面的计算公式，当Cp1.33表明过程变差比较小（因为usl-lsl是设计或者客户已经给定的），此时还要看Cpk,当Cp和Cpk相差很大时表明过程有较大的偏移,需要做居中处理，再比较Cpk和Ppk，如果两者相差不大表明受特殊因素的影响小，如果两者相差很大表明受特殊因素的影响很大，特殊因素的影响往往比较容易找到。如果Cp值本身就很小那说明过程受普通因素的变差影响大，此时若想提升过程能力往往更多的投入和更高的决策才能使问题得到解决。所以即使有时候Cpk值很高(比如大于2,如果其与CpPpk相差较大的话还是需要对过程进行改进。9 G+U-|0 z$?7 G7 x如果Cpk比Ppk 大很多往往一种可能是过程并没有受控，控制图上有异常点的出现，计算人员错用了结论。0#S7|%j3 p9 D#d8 L9 v OCpmCpmkPpmPpmk即所谓的第二代能力指数对应的公式和上述对应公式也相同，所不同的还是下面变差部分的不同。5B(/:!h*D+_5SCpCpkPpPpk默认的是目标值和规格中心重合，而当目标值和规格中心不重合时（比如设计直径为10+0.5-0.5,此时规格中心值为10，目标值也为10，而如果是10+0.5-0.1,则规格中心值变成了10.2,而目标值仍为10）需要用CpmCpmkPpmPpmk这四个指数，具体的计算公式见图片。0OR5B-j,dCmCmk是设备能力指数，单纯的用来衡量设备的能力情况，计算公式与CpCpk相同，不同的是在进行样本采集时要求在稳定的过程下固定除设备外的其他条件.CMK取样条件与CPK的区别就是CMK样品要连续取，CPK样品取样有个INTERVAL。数据一一家家线线缆缆制制造造商商希希望望评评估估线线缆缆的的直直径径是是否否符符合合规规格格。线线缆缆直直径径必必须须为为 0.550.55 +0.050.05 cmcm 才才符符合合工工程程规规格格。分分析析员员评评估估过过程程的的能能力力以以确确保保其其满满足足客客户户的的要要求求，即即 PpkPpk 为为 1.331.33。分分析析员员每每小小时时从从生生产产线线中中取取 5 5 根根连连续续的的线线缆缆作作为为一一个个子子组组，并并记记录录直直径径。X1X2X3X4X50.5290.550.5550.5410.5590.5430.5570.5590.5810.5510.4930.5340.5270.5110.5650.5590.5190.5620.5510.530.5450.5880.5440.5610.5730.6070.5320.5620.5420.5490.5770.5260.5460.5570.5480.5460.560.530.5640.5140.5270.5450.5130.5570.5250.5570.5590.5290.5390.5910.5380.5570.5170.5210.5680.5440.550.5620.540.5370.5580.5480.5320.570.5670.560.5330.5380.5670.5570.5410.5340.5440.5370.5740.5720.5560.560.520.5780.5430.5440.5410.5260.5180.5210.5320.5240.5440.5230.550.5440.5450.5710.5270.5360.5540.5690.5310.534项目数量累计数比率%累计比率%变形60060050%50%露铝36096030%80%硬块120108010%90%暗痕6011405%95%其他6012005%100%6SQ统计-质量工具-过程能力分析.(用于计算cp,cpk,pp,ppk等)1，选择全部的黄色区域数据.2,选择标志位于第一行.(计算软件会自动忽略第一行的标题）3，填入规格上下线.4,可以选择历史平均值/历史标准差5,估计标准差的方法-可选-合并标准差(跟minitab默认的方法一样)6,还有一些其它的参数都可以根据自已的需要选择。7,确认，生成结果更多详情访问 http:/一一家家线线缆缆制制造造商商希希望望评评估估线线缆缆的的直直径径是是否否符符合合规规格格。线线缆缆直直径径必必须须为为 0.550.55 +0.050.05 cmcm 才才符符合合工工程程规规格格。分分析析员员评评估估过过程程的的能能力力以以确确保保其其满满足足客客户户的的要要求求，即即 PpkPpk 为为 1.331.33。分分析析员员每每小小时时从从生生产产线线中中取取 5 5 根根连连续续的的线线缆缆作作为为一一个个子子组组，并并记记录录直直径径。设设置置原原始始数数据据变变换换数数据据子组尺寸5子组编号X1X2X3X4X5X1规格下限0.510.5290.550.5550.5410.5590.529包括边界1、是20.5430.5570.5590.5810.5510.543规格上限0.630.4930.5340.5270.5110.5650.493包括边界1、是40.5590.5190.5620.5510.530.559目标0.5550.5450.5880.5440.5610.5730.545历史均值60.6070.5320.5620.5420.5490.607历史标准偏差70.5770.5260.5460.5570.5480.577移动极差平均长度280.5460.560.530.5640.5140.546进行Box-Cox转换2、否90.5270.5450.5130.5570.5250.527Box-Cox转换系数0100.5570.5590.5290.5390.5910.557组内标准偏差估计法3、合并标准差110.5380.5570.5170.5210.5680.538采用无偏常数120.5440.550.5620.540.5370.544组内1、是130.5580.5480.5320.570.5670.558整体2、否140.560.5330.5380.5670.5570.56150.5410.5340.5440.5370.5740.541输输出出160.5720.5560.560.520.5780.572规格下限0.5170.5430.5440.5410.5260.5180.543目标0.55180.5210.5320.5240.5440.5230.521规格上限0.6190.550.5440.5450.5710.5270.55历史均值200.5360.5540.5690.5310.5340.536历史标准偏差基本统计量子组个数20数据个数100平均值0.54646标准偏差0.019341388最小值0.493最大值0.607极差0.114正态性检验0.05AD统计量0.232611805p值0.957415871未进行Box-Cox转换的正态性是是正正态态分分布布AD统计量0.232611805p值0.957415871Box-Cox转换后的正态性是是正正态态分分布布平均值/标准偏差估计平均值0.54646极差平均值（R）0.019045572标准偏差平均值（R）0.018871093合并标准偏差0.018547731移动极差平均值（MR）0.010712953102510121116818752201下规格下规格目标目标上规格上规格0.495850.5029750.51010.5172250.524350.5314750.53860.5457250.552850.5599750.56710.5742250.581350.5884750.59560.6030812502468101214161820051015202530频数组内整体下规格目标上规格运运行行图图252015105000.10.20.30.40.50.60.7企业版含有公式功能，这里更改后标准差的估算方法，结果和图表会自动变化的。更多详情访问http:/企业版含有公式功能，这里更改后数据,结果和图表会自动刷新的。超级方便吧更多详情访问http:/移动极差中位数（MMR）0.002877257MSSD0.004805475组内标准偏差（Within）0.018547731整体标准偏差（Overall）0.019341388性能组内PPMUSL1947.104938PPM总计8071.603209整体PPMUSL2818.714027PPM总计10969.28024实测PPMUSL10000PPM总计20000能力组内Cp0.898582509CPL0.834962867CPU0.962202151Cpk0.834962867CR1.11286386整体Pp0.861709956PPL0.800700891PPU0.922719021Ppk0.800700891PR1.160483285其它Zlsl2.504888602Zusl2.886606452P Zlsl0.006124498P Zusl0.001947105P总计0.008071603Cpmm0.019665896Cpm0.847490827能力图组内LCL0.490816807CL0.54646UCL0.602103193能能力力图图0.70.60.50.40.30.20.10组内标准偏差 1.85Cp .89Cpk .83整体标准偏差 1.93Pp .86Ppk .80Cpm .84组内整体规格计算出来的cp cpk,pp,ppk以及一些其它的参数结果并画出正态分布，运行图，和能力图更多详情访问http:/cpm也一起能计算出来了更多详情访问http:/运运行行图图252015105000.10.20.30.40.50.60.7整体LCL0.488435836CL0.54646UCL0.604484164统统计计量量X2X3X4X5数据个数d2d3c4c4平均值fj极差hj0.550.5550.5410.55952.32600.9399860.9252220.546810.037.5891231610.5570.5590.5810.55152.32600.9399860.9252220.558210.0387.5891231610.5340.5270.5110.56552.32600.9399860.9252220.52610.0727.5891231610.5190.5620.5510.5352.32600.9399860.9252220.544210.0437.5891231610.5880.5440.5610.57352.32600.9399860.9252220.562210.0447.5891231610.5320.5620.5420.54952.32600.9399860.9252220.558410.0757.5891231610.5260.5460.5570.54852.32600.9399860.9252220.550810.0517.5891231610.560.530.5640.51452.32600.9399860.9252220.542810.057.5891231610.5450.5130.5570.52552.32600.9399860.9252220.533410.0447.5891231610.5590.5290.5390.59152.32600.9399860.9252220.55510.0627.5891231610.5570.5170.5210.56852.32600.9399860.9252220.540210.0517.5891231610.550.5620.540.53752.32600.9399860.9252220.546610.0257.5891231610.5480.5320.570.56752.32600.9399860.9252220.55510.0387.5891231610.5330.5380.5670.55752.32600.9399860.9252220.55110.0347.5891231610.5340.5440.5370.57452.32600.9399860.9252220.54610.047.5891231610.5560.560.520.57852.32600.9399860.9252220.557210.0587.5891231610.5440.5410.5260.51852.32600.9399860.9252220.534410.0267.5891231610.5320.5240.5440.52352.32600.9399860.9252220.528810.0237.5891231610.5440.5450.5710.52752.32600.9399860.9252220.547410.0447.5891231610.5540.5690.5310.53452.32600.9399860.9252220.544810.0387.589123161102510121116818752201下规格下规格目标目标上规格上规格0.495850.5029750.51010.5172250.524350.5314750.53860.5457250.552850.5599750.56710.5742250.581350.5884750.59560.6030812502468101214161820051015202530频数组内整体下规格目标上规格运运行行图图252015105000.10.20.30.40.50.60.7企业版含有公式功能，这里更改后数据,结果和图表会自动刷新的。超级方便吧更多详情访问http:/运运行行图图252015105000.10.20.30.40.50.60.7能能力力图图0.70.60.50.40.30.20.10组内标准偏差 1.85Cp .89Cpk .83整体标准偏差 1.93Pp .86Ppk .80Cpm .84组内整体规格计算出来的cp cpk,pp,ppk以及一些其它的参数结果并画出正态分布，运行图，和能力图更多详情访问http:/直直方方图图标准偏差移动极差移动极差(l=2)离差平方和区间个数160.012008330.0005768区间宽度0.0071250.0141844990.01140.01140.0008048No.组下界组上界组中值频数0.0269258240.03220.03220.002910.49228750.49941250.4958510.0188334810.01820.01820.001418820.49941250.50653750.50297500.0187803090.0180.0180.001410830.50653750.51366250.510120.0292796860.00380.00380.003429240.51366250.52078750.51722550.0185121580.00760.00760.001370850.52078750.52791250.52435100.0209093280.0080.0080.001748860.52791250.53503750.531475120.0174585220.00940.00940.001219270.53503750.54216250.5386110.0237065390.02160.02160.00224880.54216250.54928750.545725160.0221743090.01480.01480.001966890.54928750.55641250.5528580.0098893880.00640.00640.0003912100.55641250.56353750.559975180.0154596250.00840.00840.000956110.56353750.57066250.567170.0147139390.0040.0040.000866120.57066250.57778750.57422550.0161090040.0050.0050.001038130.57778750.58491250.5813520.0226097320.01120.01120.0020448140.58491250.59203750.58847520.0117175080.02280.02280.0005492150.59203750.59916250.595600.0094710080.00560.00560.0003588160.59916250.6070.6030812510.0157892370.01860.01860.00099720.0162388420.00260.00260.0010548规格线原值作图值下规格0.51.580521071.58052107目标0.558.5747508318.574750831上规格0.615.5689805915.56898059高度25.790486140Nd2D3D4c4c4121.1283.267 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