GB T 11791-1989 正态分布变差系数置信上限.pdf

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1、中华人民共和国国家标准正态分布变差系数置信上限Upper confidence limits 01 coelficient 01 variation lor normal distribution 1 主题内容和适用范围GB/T 11 791 - 8 9 本标准规定了产品特性值2服从正态分布，均值(的、标准差未知时，根据样本及给定的置信水平，确定变差系数置信上限的方法。本标准广泛适用于结构、材料、纺织品等变差系数的估计问题。2 引用标准GB 3358 统计学名词及符号GB 3187 可靠性基本名词术语及定义3 符号样本大小样本第2个个体的特性值样本均值样本方差样本变差系数总体的变差系数总体变差

2、系数的倒数Cy-l的置信下限自由度为一1)的俨分布自由度为(.-1)的俨分布的1一分位数置信水平自由度为(n-1)、非中心参数为6的非中心t分布的1一分位数总体变差系数的皆信上限4 变差系数的估计公式设样本町，X2，川，来自正态总体N(，a2), 卢土二x，国家技术监督局1989-11-22批准n X, 二二_l_L: x, 82=ztDz-t)2 盯咀C=a/ CJI (C ;,;- 1 )L X2(n- 1) Xl_o(n- 1) 1一t_oCn-1;) C飞1990-07-01实施GB/T 11 791 - 8 9 82=兰IZu-k)2当置信水平为l-a，0时，总体变差系数的经典精确宣

3、信上限。vu出下式确定2(tJ15川)r.K. ( 1 ) 口lvvu否F王式中Kx/8=1/C，0 4. 1 查表法第一步计算JK第二步=由r.K值，查本标准的附录A(补充件)的t，_，(町的表，用线性插值得值，HPr.(C;-lc值。第三步s计算CYU = 1/(C;-)L 4. 2 计算法第一步2计算dK第二步:由J丁K值，按本标准的附录B(参考件)提供的非中心分布(1-，)分位数的计算程序求出筐，Rpr.(C，)L值。第兰步z计算Cvu = 1 / (C,) L 5 近似公式当Cv0.30、n注6时，Cvu由下列近似公式确定Cvu = r Xf-，(n一1)(I+Cs与旦)rt . .

4、川l (n -l)Cs J 6 举例一批碳环氧壳体，从中随机抽取9件进行强度试验，测得破坏值分别为(单位，1)，7.饨，7.25.7.8.58.7，6.67，6.75，6.87，6.920求置信水平为0.90时这批壳体强度的变羞系数的置信上限囚计算得g故有( i )近似方法( ii )精确方法x7. 2178 (1) 8= O. 629 5 (1) X!.，(8)=3.4日，由(2)式得:。vu=O.131 6 由r.K34.3978，查附录A的表，用线性插值得3甘r;-(C;- )L=22. 640 9 Cvu= 1/(C;-) O. 1325 本表的参数范围与表距为1一=0.70，0.80

5、，0.90，0.95，0=2(1 )50,60,70,80 =1(1)54 GB!T 1 1 7 9 1 - 8 9 附录A非中心t分布的分位数寝(补充件)1=0.70 6.0 5.0 4.0 3.0 2.0 1.0 飞寸10.0877800 8.4222810 6. 7618690 5.1127940 3.4943840 1.9632970 2 8.7805100 7.3433730 5. 9136390 4.4982770 3.1136360 1.7938490 3 8.1907900 6.8586860 5.5349870 4. 2264280 2.9464160 1.7183780 4

6、 7.8524150 6.5817250 5.3199260 4.0732410 2.8528230 1.6758230 5 7.6316650 6.4017710 5. 1809680 3. 9749430 2.7930750 1.6485270 6 7.4756830 6.2750980 5.0836490 3.9065070 2.7516600 1. 6295550 7 7.3592940 6.1809180 5.0116240 3.8561200 2.7212890 1. 6156050 8 7.2689390 6.1080340 4.9561280 3.8174450 2.69806

7、80 1. 6049160 9 7.1966580 6.0499370 4.9120160 3.7868820 2.6797230 1.5964630 10 。国叶二227.1374550 6.0024770 4.8761310 3.7620700 2.6648890 1.5896430 11 1.0880310 5.9629650 4.8463590 3.7415470 2.6526270 1.5839540 12 1.0461240 5. 9295480 4.8212440 3.7242790 2. 6423410 1.5792020 13 7.0101170 5. 9009020 1.7

8、997820 3.7095590 2. 6335710 1.5751570 14 6.9788270 5.8760740 4. 1812200 3.6968560 2.6260230 1.5716610 15 6.9513950 5.8543360 4. 1649950 3.6857810 2.6194410 1.5686080 16 6.9271400 5.8351480 4.7507090 3. 6760440 2.6136680 1.5659390 17 6. 9054970 5.8180810 4.7380230 3.6674120 2.60日54701.5635610 18 6.88

9、60810 5.8028030 4.7267100 3.6597110 2.6039900 1.5614530 19 6.8685850 5.7890650 4.7165050 3.6527950 2.5998920 1.5595480 20 6.8527390 5.7766010 4.7072870 3.6465530 2.5962030 1.5578500 21 6.8382860 5.7652670 4.6989150 3.6408870 2.5928510 1.5562810 22 6.8250620 5.7548960 4.6912780 3.6351250 2.5898口40. 5

10、548870 23 6.8129180 5. 7454190 4.6842820 3.6310000 2.5870100 1.5535690 24 6.8017220 5.1366540 4.6778510 3.6266610 2.5844510 1. 5523940 2S 6.7913590 5.7285790 4.6719190 3.6226390 2. 5820880 1. 5512830 26 6.7817680 5.72110-10 1.6664150 3.6189600 2. 5798970 1.5502750 27 1=0.70 6.0 5.0 4.0 3.0 2.0 1.0 二

11、?斗飞-6.7728390 5.7141430 4.6613360 3.6155280 2. 5778820 1.5493290 6.7645100 5.7076530 4.6565860 3.6123380 2.5759940 1.5484430 29 6.7567270 5.7016320 4.6521650 3.6093620 2.5742480 1.5476390 30 6.7494540 5. 6959420 4.6480150 3.6066020 2.5726130 1.5468830 31 6.7425870 5.6906740 4.6441350 3.6039680 2.571

12、0760 1.5461650 32 6.7361460 5.6856420 4.6405010 3.6015330 2.5696400 1.5455010 33 6.7300770 5.6809640 4.6370680 3.5992340 2.5682840 1.5448660 34 6.7243480 5.6765320 4.6338230 3.5970690 2.5670120 1. 5442780 35 6.7189300 5.6723320 4.6307650 3.5950240 2.5657880 1. 5437130 36 。国时6.7138030 5.6683820 4.627

13、8960 3.5930920 2.5646720 1.5431760 37 二叫226.7089350 5.6646180 4.6251690 3.5912620 2.5635940 1.5426830 38 6.7043040 5.6610440 4.6225820 3.5895290 2.5625770 1.5422130 39 6. 6999290 5.6576740 4.6201060 3.5878810 2.5616020 1.5417650 40 6.6957440 5.6544500 4.6177850 3.5863160 2.5606880 1.5413410 41 6.691

14、7460 5.6514020 4.6155270 3.5848250 2.5598150 1.5409220 42 6.6879360 5.6484390 4.6134110 3.5834050 2.5589770 1.5405380 43 6.6843150 5.6456650 4.6113890 3.5820500 2.5581790 1.5401620 44 6.6808350 5.6429830 4.6094610 3.5807560 2.5574160 1.5398130 45 6.6774950 5.6404440 4.6075790 3.5795190 2.5567110 1.5

15、394600 46 6.6743040 5.6379710 4.6057920 3.5783350 2.5559980 1.5391310 47 6.6712400 5.6356000 4.6041100 3.5772000 2.5553470 1.吕38849048 6.6683240 5.6333690 4.6024990 3.5761130 2.5546930 1.5385420 49 6.6655020 5.6312060 4.6009130 3.5750680 2.5540780 1.5382520 50 6.6423620 5.6134950 4.5881550 3.5665590

16、 2.5490840 1.5359240 60 6.6257640 6.6132500 5.6008430 5.5913430 4.5790310 4.5721720 3.5605100 3.5559580 2. 5455280 2.5428830 1.5342660 1.5330260 70 80 1=0.70 12.0 1l.0 10.0 9.0 8.0 7.0 二之二20. 1131700 18.4406200 16.7684500 15.0968000 13.4258800 1l.7560100 )7. 4546900 16.0062400 14.5584700 13. 1115400

17、 1l.6658400 10.2218600 3 16.2456600 14.8997600 13.5546900 12.2107100 10.8682500 9.5279250 4 15.5458500 14.2596900 12.9744900 1l.6905600 10.40836口。9.1285980 5 15.0852300 13.8386600 12.5931600 1l.3490700 10.1068700 8.8673420 6 14.7568300 l3. 5387000 12.3217100 1l.1062400 9.8928320 8.6822390 7 14.50962

18、00 13.3130200 12. 1177100 10. 9239500 9.7323710 8.5437450 8 14.3160500 13.13646口。11.9581800 10.7815800 9.6072440 8.4359550 9 14. 1598800 12.9941000 1l.8296900 10.6670400 9.5067110 8.3495150 10 。国司14.0309200 12.8766600 1l.7237700 10.5727100 9.42401口。8.2785510 11 -434|2 13.9224100 12.7778500 1l.634740

19、0 10.4935100 9.3547310 8.2191960 12 13.8296700 12.6935100 1l.5588300 10.4260700 9.2957550 8. 1687320 13 13.7494200 12. 6205500 11.4932000 10.3677900 9.2448670 8. 1252960 14 13.6791600 12.5567400 11.4358500 10.3169300 9.2005620 8.0874920 15 13.6171500 12.5004100 1l.3852800 10.2721300 9. 1615300 05425

20、60 16 13.5619100 12.4503000 1l.3403000 10.23230口。9. 1269110 8.0248360 17 13.5123700 124053800 11.3000100 10.1967000 9.0959630 7. 9985710 18 13.4676500 12.3648700 ll. 2637100 10.1646200 9.0681210 7. 9749670 19 13.4270700 12.3281200 1l.2308200 10. 1356000 9.0429560 7.9536550 20 13.3900600 12.2946000 1

21、l.2008500 10.1091700 9.0200540 7.9342790 21 13.3561500 12.2639300 ll. 1734000 10.085日000 8.9991730 7.9166410 22 13.3249500 12 , 2357400 ll. 1482400 10.0628000 8.9799840 7.9004560 23 13.2961400 12.2097000 1l.1250000 10.0423700 8.9623460 7.8855810 24 13.2694500 12. 1856200 11.1034900 10.0234600 8.9460

22、260 7.8718680 25 13.2446400 13.2215500 12.1632400 12.1424000 11. 0835300 11.0649500 10.0059300 9. 9896150 8. 9309290 8.9168660 7.8591440 7.8473640 26 27 l-a二O.70 12.0 11.0 10.0 9.0 8.0 7.0 ?土飞13.1999100 12. 1228800 11.0476000 9.9744230 8.9037970 7. 8363570 13.1796900 12.1046700 11.0313800 9.9601730

23、8.8915680 7.8261000 29 13. 1606900 12.0875600 11.0161800 9.9468630 8.8801180 7.8165050 30 13. 1428100 12.0714800 11. 0018800 9.9343410 8.8693640 7.8075070 31 13.1259300 12.0562900 10.9883800 9.9225470 8.8592530 7.7990530 32 13.1100300 12.0419800 10.9756800 9.9114480 8.8497510 7.7911140 33 13.0949600

24、 12.0284400 10.963640口9.9009600 8.8407690 7.7835880 34 13.0806800 12.0156000 10.9522900 9.8910260 8.8322560 7.7764930 35 13.0671400 12.0034700 10.9415100 9.8816300 8.8242130 7.7697820 36 。国413.0542500 11. 9919000 10.9312700 9.8726940 8.8165950 7.7634120 37 4-叫田4国13.0419800 11.9808900 10.9215300 9.86

25、42280 8.8093290 7.7573920 38 13.0303100 11.9704300 10.9122800 9.8561310 8.8024360 7.7516550 39 13.019170口11.9604400 10.9034200 9.8484260 8.7958540 7.7461880 40 13.0085400 11.9508900 10.8949800 9.8410890 8. 7896150 7.7409850 41 12.9983300 11. 9417600 10.8869300 9.8340800 8.7836270 7. 7360240 42 12.98

26、86000 11. 9330600 10.8792200 9.8274020 8.7779340 7.7312890 43 12.9792400 11.9246900 10.8718400 9.8209590 8.7724790 7.7267570 H 12.9703000 11.9167000 10.8647800 9.8148370 8.7672590 7.7224230 45 12. 961690口11.90899口。10.8579600 9.8089660 8.7622260 7.7182720 46 12.9534200 1l.9016000 10.8514700 9.8032750

27、 8.7574290 7. 7142920 47 12.9454700 11.8945000 10.8452200 9.7978670 8.7528270 7.7104540 48 12.9378200 11.8876800 10.8391800 9.7926460 8.7483950 7.7067860 49 12.9304500 11.8810900 10.8333700 9.7876130 8.7441190 7.7032590 50 12.8692800 11.82658 10.78547口。9.7462260 8. 7090560 7.67c13310 60 12.8244300 1

28、1.7867500 10.7505400 9.7161250 8.6836830 7.653,1510 70 80 lO. 70 18.0 17.0 16.0 15.0 14.0 13.0 于L30.1529日0028.4792700 26.8057400 25. 1323400 23.4591000 21.7860100 26.1527900 24.7025300 23.2524300 21.8025500 20. 3529200 18.9036000 3 24.3307100 22.9824600 21.6344300 20.2866700 19.4082000 18.9392500 17

29、.5922000 4 23.2740900 21.9851800 20.6965300 18. 1202400 16.8327600 5 22.5772500 21. 3276000 20.0782500 18.8292400 17.5806900 16.3326000 6 22.0794200 20.8579100 19.6367400 18.4159400 17.1956200 15.9758700 7 21. 7038800 20.5036800 19.3038400 18.1043900 16.9054800 15. 7071700 8 21.4091700 20.2257700 19

30、.0427200 17.8601200 16.6780500 15.4966400 9 21.1709200 20.0011300 18.8317100 17.6627600 16.4943900 15.3266900 10 。回叶20.9737400 19.8152600 18.6571500 7. 4995600 16.3425800 15. 1863000 11 443ig20.8074500 19.6585300 18.5100300 7. 3620600 16.2147000 15.0680900 12 20.6650500 19.524370口1日.384130017.244410

31、0 16.1053500 14.9670300 13 20.5415300 19.4080100 18.2749200 17.1424100 16.0105700 14.8795100 14 20.4332100 19.3059500 18.1792300 17.0530500 15.9275700 14.8028700 15 20.3373100 19.2157000 18.0945600 16.9740200 15.8541500 14.7351200 16 20.2517200 19. 1351200 18.0190200 16.9035200 15.7887300 14.6748000

32、 17 20.1748100 19.0627500 17.9511600 16.8402200 15.7299900 14.6206500 18 20. 1052600 18.9972800 17.8898200 16.7830200 15.6769300 14.5717600 19 20.0420000 18.9377900 17.8341000 16.7310400 15.6287700 14.5273600 20 19.9841600 18.8833700 17.7831600 17.7364160 16.6835700 15.5847500 14.4868400 21 19.93105

33、00 18.8334700 16.6400000 15.5444000 14.4497300 22 19.8821200 18.7874300 J7. 6933300 16.5999000 15.5072400 14. 4155400 23 19.8368500 18.7449100 17.6534900 16.5628200 15.4729000 13. 3839500 24 19.7948000 18.7054000 17.6165500 16.5284000 15.4410700 14.3546800 25 19.7556700 19.7190800 18.6686100 18.6342

34、700 17.5821500 17自550040016.49637日016.4665000 15.4114400 15.3日3790014.3274600 14.3021000 26 27 1=0.70 18.0 J7. 0 16.0 15.0 14.0 13.0 飞-二人19.6848600 18.6021200 J7. 5199700 16.4385600 15.3579600 14.2783500 19.6527200 18.5719600 17.4917900 16.4123200 15.3337300 14.25610口。29 19.6225100 18.54357日D 17.465

35、2700 16.38768口016.3644900 15.3109800 14.2352200 30 19.5940200 18.5168500 17.4403000 15.2895200 14.2155600 31 19.5671200 18.4916000 17.41674口。16.3425800 15.2693100 15.2501700 14. 1970300 32 19.5416300 18.467700 17.3944400 16.32187口。14.1794900 33 19.5175日0018.4450800 17.37328口D16.3022700 15.2320600 14

36、.1628900 34 19.4946000 18.4235900 17.3532400 16.28365口。15.2148900 14.1471800 35 19.4728200 18.4031800 17.3341900 16.2659600 15. 1985700 14.1322500 36 。国时，19.4520800 18.3837500 17.3160500 16.2491200 15.1830500 14.1180600 37 4434|2 19.4323000 18.3652200 17.2987700 16.2330900 15.1682900 14.1045200 38 1

37、9.4134200 18.3474900 17.2822700 16.2178000 15.1542200 14.0916300 39 19.3953600 18.3306100 17.2665100 16.2031700 15.14074日014.0793600 40 19.3781000 18.3144300 17.2514400 16.1892100 15.1278800 14.0676000 41 19. 3615500 18.2989500 17.2370300 16.1758500 15.1155600 14.0563600 42 19. 3457000 18.2841000 17

38、.2232000 16.1630300 15.1037800 14.0455700 43 19.3305000 18.2698400 17.2098900 16.1507300 15.09247日014.0352400 44 19.3158300 18.2561600 17.1971400 16. 1389300 15.0816100 14.0253200 45 19.3017700 18.2430100 17.1849100 16.1275900 15.0711700 14.0158200 46 19.2882500 18.2303400 17.1731100 16.1166800 15.0

39、611500 14.0066900 47 19.2752000 18.2181500 17.1617700 16. 1061900 15.0515100 )3. 9978日0048 19.2626400 18.2064000 17.1508200 16.0960800 15.0422100 13.9893900 49 19.2505200 18.1950600 17.1402900 16.0863000 15.0332600 13.9812500 50 19.1491500 18.1003900 17.0522800 16.0050300 14.9586600 13.9133800 60 19

40、.073810口19.0153900 18.0301100 17.9757100 16.9871500 16.9367800 15.9449700 15.8986100 14.90368日014.8613600 13.8634800 13.8251500 70 80 1=0.70 24.0 23目。22.0 21.0 20.0 19.0 二40.1960300 38.5220600 36.8481100 35.1742200 33.5003800 31.8266000 34.8567900 33.4059000 31.9551000 30.5043700 29.0537300 27.60320

41、00 3 32.4233100 31.0742700 29.7253300 28.3764700 27.0277400 25.6791400 4 31.0112200 29.7213800 28.4316400 27. U202口。25.8525400 24.56322口。5 30.0792900 28.8285800 27.5780000 26.32755口。25.0772600 23.8271500 6 29.4130200 28.1903500 26.9678100 25.7454200 24.5232100 23.3012100 7 28.9100100 27.7085500 26.5

42、072300 25.3060900 24.1051200 22.9口4380口8 。目HJ434|228.5149700 27.3302100 26. 1456000 24.9611600 23.7769400 22.5929200 9 28.1953300 27.0241000 25.8530300 24.6821600 23.5114900 22.3410600 10 27.9306000 26.7706100 25.6107600 24.4511400 23.2917300 22.1325600 11 27.7071300 26.5566600 25.4063100 24.2562400

43、 23.1063400 21.9567600 12 27.5156100 26.3732800 25.2311600 24.0892300 22.9475300 21.8061300 13 27.3493300 26.2141100 25.0790600 23.9442700 22.8097300 21.6754500 14 27.2033900 26.0743900 24.9456400 23.8170900 22.6888100 21.5608500 15 27. 0741000 25.9506600 24.8274400 23.7044600 22.5817600 21.4593500

44、16 26.9585900 25.8401300 24.7218900 23.6038900 22.4861500 21.3687700 17 26.8547000 25.7407500 24.6269600 23.5134700 22.4002300 21.2873300 18 26.7606800 25.6507300 24.5410500 23.4316300 22.3224700 21.2136600 19 26.6750600 25.5688500 24.4628900 23.3571800 22.2517400 21.1466800 20 26.5967800 25.4939400

45、 24.3913600 23.2川89060022. 1870800 21.0854000 21 26.5248000 25.4251200 24.3256700 23.2265100 22.1276700 21.0291500 22 26.4584000 25.3616200 24.2650800 23. 1688200 22.072日80020.9772800 23 26.3969200 25.3028300 24.2089700 23.1154100 22.0221800 20.929300口24 26.3397900 25.2482000 24.1568500 23.0658000 2

46、1.9750700 20.8847200 25 26.2865500 26.2367900 25.1972900 25. 1497000 24. 1082800 24.0629100 23.0195800 22.9764100 21.9312000 21.8902200 20.8431900 20.8044400 26 27 -a=0.70 24.0 23.0 22!。21.0 20.0 19.0 千二人26. 1901400 25.1051600 24.0203900 22.9359400 21.8518300 20.76812口。26. 1463500 25.0632600 23. 980

47、4500 22.8979600 21.8158100 20.73403口。29 26.1051100 26.0661900 25.0238500 23.9428600 22.86222口。21.7818800 20.70195口。30 24.9866600 23. 9074100 22.8285000 21.7499000 20.6717100 31 26.0294300 24. 9515100 23.8739200 22.7966000 21.7196700 20.6431600 32 25.9945700 24. 9182500 23. 8421100 22.7664500 21.6910

48、700 20.6161200 33 25.9615200 24.88665础。23.8120700 22.7378200 21.6639400 20.5904800 34 25.9301300 24.8566700 且3.783520022.7106700 21.6382000 20.5661700 35 25.9002600 24.8281400 23.7562900 22.6848200 21.6137100 20.5430300 36 。国425.8717800 24.80095口。23.7304000 22.6602000 21.5903800 20.5209700 37 4434|2

49、 25.8446200 24.7750000 23.70568口023.6820800 22.6367000 21.5681400 20.4999500 38 25.8186800 24.7502100 22.6142700 21.5468800 20也79920039 25.7938500 24.7265100 23.6595000 22.5928200 21.52656口。20.4607300 40 25.7700500 24.7038200 23.6378600 22.5722900 21.5071000 20.44233口。41 25.7472400 24.6820600 23. 6171600 22.5526100 21. 4884600 20.4247500 42 25.7253900 24.6611800 23.5972700 22.5337400 21.4705900 20.4078900 43 25.7044000 24.6411000 23.57