SPC常用公式和参数（精编版）

1、rx一、管制图公式说明1.计量值公式管制图x管制图： n为组内样本量， m为抽样组数；标准偏差n2minmaxxxr估计标准偏差2dr全距平均值mrmrrrrmiim121.管制上限raxrndxucl22)3(中心线xcl管制下限raxrndxlcl22)3(其中nda223r 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，23431dddmxnxxxxmiin1m.32121mxxxxx.sx管制图x管制图：第 i 组之标准偏差1)(12nxxsniiimiisms11估计标准偏

2、差4cs管制上限saxsncxucl34)3(中心线xcl管制下限saxsncxlcl34)3(其中nca433s管制图：管制上限sbucls4中心线scls管制下限sblcls3x-rm 管制图rm管制图：移动全距1iiixxmrnmrmrnii1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.计数值公式不良率管制图( p chart ) 当每

3、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不良数管制图( pn chart ) 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。缺点数管制图( c chart ) 中心线ccl管制上限3 ccucl管制下限3 cclcl其中c为平均不合

4、格点数kccki 1单位缺点数管制图( u chart ) 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= ncncu二、统计指标说明1.制程能力指数( process capability indexes ) ),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( capability sigma ) 。3)-(uslcpu；：估计标准偏差( capability sigma ) 。3)(cpllsl；

5、：估计标准偏差( capability sigma ) 。),min(cplcpucpkuslxcc)(61lsluslcpcr；：估计标准偏差( capability sigma ) 。22)(6)(sllsluslcpm；：估计标准偏差( capability sigma ) 。2.制程表现指数( process performance indexes ) 6lsl)-(uslpp；：制程标准偏差( population standard sigma )。3)-(uslppu；：制程标准偏差( population standard sigma )。3)(ppllsl；：制程标准偏差( p

6、opulation standard sigma )。),min(pplppuppk)(61lsluslpppr；：制程标准偏差( population standard sigma )。22)(6)(sllsluslppm；：制程标准偏差( population standard sigma )。3.直方图 )-(uslf)zupper(per；：制程标准偏差( population standard sigma )。)(f)zupper(perlsl；：制程标准偏差( population standard sigma )。)-(usl.)zupper(cap；：估计标准偏差( capab

7、ility sigma ) 。)(.)zupper(caplsl；：估计标准偏差( capability sigma ) 。 skew ( 偏态) = iisxxnnn3)2)(1(；s：样本标准偏差， n 需大于 2 且 s 0。 kurtosis ( 峰度) = )3)(2()1( 3)3)(2)(1()1(24nnnsxxnnnnnii；s：样本标准偏差， n 需大于 2且 s 0。 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)(xxnxy

8、xxyb三、标准偏差公式 估计标准偏差( capability sigma ) 以r估计：2dr；( rxchart及 x-rm chart时使用 )。 以s估计：4cs；( sxchart时使用 )。 实际计算：kiikinjiijnxx1112) 1()( 制程标准偏差( population standard devitation ) )1()(12nxxnii四、参数表1.表 1:x(bar)-r 和 x(bar)-s 参数均值图均值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

9、.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

10、.9750.97270.2841.716110.2853.1730.2561.7440.9270.97540.3211.679120.2663.2580.2831.7170.8860.97760.3541.640130.2493.3360.3071.6930.8500.97940.3821.618140.2353.4070.3281.6720.8170.98100.4061.594150.2233.4720.3471.6530.7890.98230.4281.572160.2123.5320.3631.6370.7630.98350.4481.552170.2033.5880.3781.622

11、0.7390.98450.4461.534180.1943.6400.3911.6080.7180.98540.4821.518190.1873.6890.4031.5970.6980.98620.4971.503200.1803.7350.4151.5850.6800.98690.5101.490210.1733.7780.4251.5750.6630.98760.5231.477220.1673.8190.4341.5660.6470.98820.5341.466230.1623.8580.4431.5570.6330.98870.5451.455240.1573.8950.4511.54

12、80.6190.98920.5551.445250.1533.9310.4591.5410.6060.98960.5651.435计算控制限用的系数子组容量- 图-s 图控制图的常数和公式表全距图标准差图计算控制限用的系数2.表 2: 中位数 和 单值 参数中位数图单值图na2d2d3d4e2d2d3d421.8801.128-3.2672.6601.128-3.26731.1871.693-2.5741.7721.693-2.57440.7962.059-2.2821.4572.059-2.28250.6912.326-2.1141.2902.326-2.11460.5482.534-2.0

13、041.1842.534-2.00470.5082.7040.0761.9241.1092.7040.0761.92480.4332.8470.1361.8641.0542.8470.1361.86490.4122.9700.1841.8161.0102.9700.1841.816100.3623.0780.2231.7770.9753.0780.2231.777子组容量中位数图单值图全距图全距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3.表 3:正态分布参数表 ppm 值: x.x0 x.x1x.x2x.x3x.x4x.x5

14、x.x6x.x7x.x8x.x94.00.000033.90.000050.000050.000040.000040.000040.000040.000040.000040.000030.000033.80.000070.000070.000070.000060.000060.000060.000060.000050.000050.000053.70.000110.000100.000100.000100.000090.000090.000080.000080.000080.000083.60.000160.000150.000150.000140.000140.000130.000130.0

15、00120.000120.000113.50.000230.000220.000220.000210.000200.000190.000190.000180.000170.000173.40.000340.000320.000310.000300.000290.000280.000270.000260.000250.000243.30.000480.000470.000450.000430.000420.000400.000390.000380.000360.000353.20.000690.000660.000640.000620.000600.000580.000560.000540.00

16、0520.000503.10.000970.000940.000900.000870.000840.000820.000790.000760.000740.000713.00.001350.001310.001260.001220.001180.001140.001110.001070.001040.001002.90.00190.00180.00180.00170.00160.00160.00150.00150.00140.00142.80.00260.00250.00240.00230.00230.00220.00210.00210.00200.00192.70.00350.00340.0

17、0330.00320.00310.00300.00290.00280.00270.00262.60.00470.00450.00440.00430.00410.00400.00390.00380.00370.00362.50.00620.00600.00590.00570.00550.00540.00520.00510.00490.00482.40.00820.00800.00780.00750.00730.00710.00690.00680.00660.00642.30.01070.01040.01020.00990.00960.00940.00910.00890.00870.00842.2

18、0.01390.01360.01320.01290.01250.01220.01190.01160.01130.01102.10.01790.01740.01700.01660.01620.01580.01540.01500.01460.01432.00.02280.02220.02170.02120.02070.02020.01970.01920.01880.01831.90.02870.02810.02740.02680.02620.02560.02500.02440.02390.02331.80.03590.03510.03440.03360.03290.03220.03140.0307

19、0.03010.02941.70.04460.04360.04270.04180.04090.04010.03920.03840.03750.03671.60.05480.05370.05260.05160.05050.04950.04850.04750.04650.04551.50.06680.06550.06430.06300.06180.06060.05940.05820.05710.05591.40.08080.07930.07780.07640.07490.07350.07210.07080.06940.06811.30.09680.09510.09340.09180.09010.08850.08690.08530.08380.08231.20.11510.11310.11120.10930.10750.10560.10380.10200.10030.09851.10.13570.13350.13140.12920.12710.12510.12300.12100.11900.11701.00.15870.15620.15390.15150.14920.1469