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1、rx一、管制圖公式說(shuō)明1.計(jì)量值公式管制圖x管制圖: n為組內(nèi)樣本量, m為抽樣組數(shù);標(biāo)準(zhǔn)偏差n2minmaxxxr估計(jì)標(biāo)準(zhǔn)偏差2dr全距平均值mrmrrrrmiim121.管制上限r(nóng)axrndxucl22)3(中心線xcl管制下限r(nóng)axrndxlcl22)3(其中nda223r 管制圖:r的標(biāo)準(zhǔn)偏差)(23drdr管制上限r(nóng)ddrdrruclr423)(33中心線rcl管制下限r(nóng)ddrdrruclr323)(33其中23331ddd,23431dddmxnxxxxmiin1m.32121mxxxxx.sx管制圖x管制圖:第 i 組之標(biāo)準(zhǔn)偏差1)(12nxxsniiimiisms11估計(jì)標(biāo)準(zhǔn)偏

2、差4cs管制上限saxsncxucl34)3(中心線xcl管制下限saxsncxlcl34)3(其中nca433s管制圖:管制上限sbucls4中心線scls管制下限sblcls3x-rm 管制圖rm管制圖:移動(dòng)全距1iiixxmrnmrmrnii1管制上限mrducl4中心線mrcl管制下限mrdlcl3(當(dāng) n=2時(shí),3d和4d以樣本數(shù)為 2來(lái)查表 ) 個(gè)別管制圖管制上限23dmrxucl中心線xcl管制下限23dmrxlcl(當(dāng) n=2時(shí),2d以樣本數(shù)為 2 來(lái)查表 ) * 中位數(shù)隨著計(jì)算機(jī)技術(shù)的發(fā)展,計(jì)算已經(jīng)不是困難,逐步被淘汰* 2.計(jì)數(shù)值公式不良率管制圖( p chart ) 當(dāng)每

3、組之樣本數(shù)均相同時(shí):中心線kiipkp11管制上限)1,)1(3min(npppucl管制下限)0,)1 (3max(nppplcl當(dāng)各組之樣本數(shù)不相同時(shí):中心線niiipnnp11,其中knnnn.21各組管制上下限分別為管制上限)1,)1(3min(inpppucl管制下限)0,)1(3max(inppplcl不良數(shù)管制圖( pn chart ) 中心線npcl管制上限)1 (3pppuclnn管制下限)1 (3ppplclnn其中np為各組之不合格數(shù)。np 為各組不合格數(shù)之平均值。缺點(diǎn)數(shù)管制圖( c chart ) 中心線ccl管制上限3 ccucl管制下限3 cclcl其中c為平均不合

4、格點(diǎn)數(shù)kccki 1單位缺點(diǎn)數(shù)管制圖( u chart ) 中心線ucl管制上限3nuuucl管制下限3nuulcl其中: n = 樣本大小(檢查的單位數(shù) ) c = 各組的缺點(diǎn)數(shù)u = 各組的單位缺點(diǎn)數(shù)= ncncu二、統(tǒng)計(jì)指標(biāo)說(shuō)明1.制程能力指數(shù)( process capability indexes ) ),max()(lslslsluslslca;其中:平均值sl:規(guī)格標(biāo)準(zhǔn)usl:規(guī)格上限lsl:規(guī)格下限6lsl)-(uslcp;:估計(jì)標(biāo)準(zhǔn)偏差( capability sigma ) 。3)-(uslcpu;:估計(jì)標(biāo)準(zhǔn)偏差( capability sigma ) 。3)(cpllsl;

5、:估計(jì)標(biāo)準(zhǔn)偏差( capability sigma ) 。),min(cplcpucpkuslxcc)(61lsluslcpcr;:估計(jì)標(biāo)準(zhǔn)偏差( capability sigma ) 。22)(6)(sllsluslcpm;:估計(jì)標(biāo)準(zhǔn)偏差( capability sigma ) 。2.制程表現(xiàn)指數(shù)( process performance indexes ) 6lsl)-(uslpp;:制程標(biāo)準(zhǔn)偏差( population standard sigma )。3)-(uslppu;:制程標(biāo)準(zhǔn)偏差( population standard sigma )。3)(ppllsl;:制程標(biāo)準(zhǔn)偏差( p

6、opulation standard sigma )。),min(pplppuppk)(61lsluslpppr;:制程標(biāo)準(zhǔn)偏差( population standard sigma )。22)(6)(sllsluslppm;:制程標(biāo)準(zhǔn)偏差( population standard sigma )。3.直方圖 )-(uslf)zupper(per;:制程標(biāo)準(zhǔn)偏差( population standard sigma )。)(f)zupper(perlsl;:制程標(biāo)準(zhǔn)偏差( population standard sigma )。)-(usl.)zupper(cap;:估計(jì)標(biāo)準(zhǔn)偏差( capab

7、ility sigma ) 。)(.)zupper(caplsl;:估計(jì)標(biāo)準(zhǔn)偏差( capability sigma ) 。 skew ( 偏態(tài)) = iisxxnnn3)2)(1(;s:樣本標(biāo)準(zhǔn)偏差, n 需大于 2 且 s 0。 kurtosis ( 峰度) = )3)(2()1( 3)3)(2)(1()1(24nnnsxxnnnnnii;s:樣本標(biāo)準(zhǔn)偏差, n 需大于 2且 s 0。 chi-square = 22)1(sn;s:制程標(biāo)準(zhǔn)偏差,62lslusl。4.散布圖 回歸直線y = mx + b ; 其中 m:斜率, b:截距。22)()()(xxnyxxynm222)(xxnxy

8、xxyb三、標(biāo)準(zhǔn)偏差公式 估計(jì)標(biāo)準(zhǔn)偏差( capability sigma ) 以r估計(jì):2dr;( rxchart及 x-rm chart時(shí)使用 )。 以s估計(jì):4cs;( sxchart時(shí)使用 )。 實(shí)際計(jì)算:kiikinjiijnxx1112) 1()( 制程標(biāo)準(zhǔn)偏差( population standard devitation ) )1()(12nxxnii四、參數(shù)表1.表 1:x(bar)-r 和 x(bar)-s 參數(shù)均值圖均值圖計(jì)算控制限用的系數(shù)標(biāo)準(zhǔn)差估計(jì)值的除數(shù)計(jì)算控制限用的系數(shù)標(biāo)準(zhǔn)差估計(jì)值的除數(shù)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計(jì)算控制限用的系數(shù)子組容量- 圖-s 圖控制圖的常數(shù)和公式表全距圖標(biāo)準(zhǔn)差圖計(jì)算控制限用的系數(shù)2.表 2: 中位數(shù) 和 單值 參數(shù)中位數(shù)圖單值圖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子組容量中位數(shù)圖單值圖全距圖全距圖計(jì)算控制限用的系數(shù)標(biāo)準(zhǔn)差估計(jì)值的除數(shù)計(jì)算控制限用的系數(shù)計(jì)算控制限用的系數(shù)標(biāo)準(zhǔn)差估計(jì)值的除數(shù)計(jì)算控制限用的系數(shù)3.表 3:正態(tài)分布參數(shù)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

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