SPC常用公式和参数

SPC常用公式和参数1/9RX一、管制图公式说明1.计量值公式管制图1.1X管制图：n为组内样本量，m为抽样组数；标准偏差n2minmaxXXR估计标准偏差2^dR全距平均值mRmRRRRmiim121......管制上限RAXRndXUCL22)3(中心线XCL管制下限RAXRndXLCL22)3(其中ndA223R管制图：R的标准偏差)(23dRdR管制上限RDdRdRRUCLR423)(33中心线RCL管制下限RDdRdRRUCLR323)(33其中23331ddD，23431ddDmxnxxxxmiin1m....32121mxxxxx......SPC常用公式和参数2/91.2SX管制图X管制图：第i组之标准偏差1)(12nxxSniiimiiSmS11估计标准偏差4CS管制上限SAXSnCXUCL34)3(中心线XCL管制下限SAXSnCXLCL34)3(其中nCA433S管制图：管制上限SBUCLs4中心线SCLs管制下限SBLCLs31.3X-Rm管制图Rm管制图：移动全距1iiixxMRnMRMRnii1管制上限MRDUCL4中心线MRCL管制下限MRDLCL3(当n=2时，3D和4D以样本数为2来查表)个别管制图管制上限23dMRxUCL中心线xCLSPC常用公式和参数3/9管制下限23dMRxLCL(当n=2时，2d以样本数为2来查表)**中位数随着计算机技术的发展，计算已经不是困难，逐步被淘汰**2.计数值公式2.1不良率管制图(PChart)当每组之样本数均相同时：中心线KiiPKP11管制上限)1,)1(3min(nPPPUCL管制下限)0,)1(3max(nPPPLCL当各组之样本数不相同时：中心线NiiiPnNP11，其中knnnN...21各组管制上下限分别为管制上限)1,)1(3min(inPPPUCL管制下限)0,)1(3max(inPPPLCL2.2不良数管制图(PnChart)中心线nPCL管制上限)1(3PPPUCLnn管制下限)1(3PPPLCLnn其中nP为各组之不合格数。nP为各组不合格数之平均值。2.3缺点数管制图(CChart)中心线CCLSPC常用公式和参数4/9管制上限3CCUCL管制下限3CCLCL其中C为平均不合格点数kCCki12.4单位缺点数管制图(UChart)中心线uCL管制上限3nuuUCL管制下限3nuuLCL其中：n=样本大小(检查的单位数)C=各组的缺点数u=各组的单位缺点数=nCnCu二、统计指标说明1.制程能力指数(ProcessCapabilityIndexes)★),max()(LSLSLSLUSLSLCa；其中：平均值SL：规格标准USL：规格上限LSL：规格下限★6LSL)-(USLCp；：估计标准偏差(CapabilitySigma)。★3)-(USLCpu；：估计标准偏差(CapabilitySigma)。★3)(CplLSL；：估计标准偏差(CapabilitySigma)。★),min(CplCpuCpkSPC常用公式和参数5/9★USLXCc★)(61LSLUSLCPCR；：估计标准偏差(CapabilitySigma)。★22)(6)(SLLSLUSLCpm；：估计标准偏差(CapabilitySigma)。2.制程表现指数(ProcessPerformanceIndexes)★6LSL)-(USLPp；：制程标准偏差(PopulationStandardSigma)。★3)-(USLPpu；：制程标准偏差(PopulationStandardSigma)。★3)(PplLSL；：制程标准偏差(PopulationStandardSigma)。★),min(PplPpuPpk★)(61LSLUSLPPPR；：制程标准偏差(PopulationStandardSigma)。★22)(6)(SLLSLUSLPpm；：制程标准偏差(PopulationStandardSigma)。3.直方图Z值、偏态、峰度★)-(USLf)Zupper(Per；：制程标准偏差(PopulationStandardSigma)。★)(f)Zupper(PerLSL；：制程标准偏差(PopulationStandardSigma)。★)-(USL.)Zupper(cap；：估计标准偏差(CapabilitySigma)。★)(.)Zupper(capLSL；：估计标准偏差(CapabilitySigma)。★Skew(偏态)=iiSxxnnn3)2)(1(；S：样本标准偏差，n需大于2且S0。★Kurtosis(峰度)=)3)(2()1(3)3)(2)(1()1(24nnnSxxnnnnnii；S：样本标准偏差，n需大于2且S0。SPC常用公式和参数6/9★Chi-Square=22)1(Sn；S：制程标准偏差，62LSLUSL。4.散布图★回归直线Y=mX+b；其中m：斜率，b：截距。22)())(()(xxnyxxynm222)(xxnxyxxyb三、标准偏差公式◎估计标准偏差(CapabilitySigma)★以R估计：2dR；(RXChart及X-RmChart时使用)。★以S估计：4CS；(SXChart时使用)。★实际计算：kiikinjiijnxx1112)1()(◎制程标准偏差(PopulationStandardDevitation)★)1()(12nxxniiSPC常用公式和参数7/9四、参数表1.表1:X(bar)-R和X(bar)-S参数均值Ｘ图均值Ｘ图计算控制限用的系数标准差估计值的除数计算控制限用的系数标准差估计值的除数nA2d2D3D4A3c4B3B421.8801.128-3.2672.6590.7979-3.27631.0231.693-2.5711.9540.8862-2.56840.7292.059-2.2821.6280.9213-2.26650.5772.326-2.1141.4270.9400-2.08960.4832.543-2.0041.2870.95150.0301.97070.4192.7040.0761.9241.1820.95940.1181.88280.3732.8470.1361.8641.0990.96500.1851.81590.3372.9700.1841.8161.0320.96930.2391.761100.3083.0780.2231.7770.9750.97270.2841.716110.2853.1730.2561.7440.9270.97540.3211.679120.2663.2580.2831.7170.8860.97760.3541.640130.2493.3360.3071.6930.8500.97940.3821.618140.2353.4070.3281.6720.8170.98100.4061.594150.2233.4720.3471.6530.7890.98230.4281.572160.2123.5320.3631.6370.7630.98350.4481.552170.2033.5880.3781.6220.7390.98450.4461.534180.1943.6400.3911.6080.7180.98540.4821.518190.1873.6890.4031.5970.6980.98620.4971.503200.1803.7350.4151.5850.6800.98690.5101.490210.1733.7780.4251.5750.6630.98760.5231.477220.1673.8190.4341.5660.6470.98820.5341.466230.1623.8580.4431.5570.6330.98870.5451.455240.1573.8950.4511.5480.6190.98920.5551.445250.1533.9310.4591.5410.6060.98960.5651.435计算控制限用的系数子组容量Ｘ-Ｒ图Ｘ-s图控制图的常数和公式表全距Ｒ图标准差Ｓ图计算控制限用的系数SPC常用公式和参数8/92.表2:中位数和单值参数中位数Ｘ图单值Ｘ图nA2d2D3D4E2d2D3D421.8801.128-3.2672.6601.128-3.26731.1871.693-2.5741.7721.693-2.57440.7962.059-2.2821.4572.059-2.28250.6912.326-2.1141.2902.326-2.11460.5482.534-2.0041.1842.534-2.00470.5082.7040.0761.9241.1092.7040.0761.92480.4332.8470.1361.8641.0542.8470.1361.86490.4122.9700.1841.8161.0102.9700.1841.816100.3623.0780.2231.7770.9753.0780.2231.777子组容量中位数图单值图全距Ｒ图全距Ｒ图计算控制限用的系数标准差估计值的除数计算控制限用的系数计算控制限用的系数标准差估计值的除数计算控制限用的系数SPC常用公式和参数9/93.表3:正态分布参数表PPM值:∣Ζ∣x.x0x.x1x.x2x.x3x.x4x.x5x.x6x.x7x.x8x.x94.00.000033.90.000050.000050.000040.000040.000040.000040.000040.000040.000030.000033.80.000070.000070.000070.000060.000060.000060.000060.000050.000050.000053.70.000110.000100.000100.000100.000090.000090.000080.000080.000080.000083.60.000160.000150.000150.000140.000140.000130.000130.000120.000120.000113.50.000230.000220.000220.000210.000200.000190.000190.000180.000170.000173.40.000340.000320.000310.000300.000290.000280.000270.000260.000250.000243.30.000480.000470.000450.000430.000420.000400.000390.000380.000360.000353.20.000690.000660.000640.000620.000600.000580.000560.000540.000520.000503.10.000970.000940.000900.000870.000840.000820.000790.000760.000740.000713.00.001350.001310.001260.001220.001180.001140.001110.001070