1、1 引言中华人民共和国国家标准正态分布完全样本可靠度单侧置信下限One sided reliability confidence low er limit (Normal distribution complete sample) UDC 町.28GB 4885-85 1 . 1 4正标准所用统ii；：.j气i司及符号见GB3358 82统计学名i司及符号B，可靠性名词术i岳见国标GB 3187 82可靠性基本名词术语及定义。I. 2 本标准适用于产品特性值X呼台F甲地认为服从正态分布的情形。其分布密度函数为！牛7主7叫（号L），x配式rj1 为总休期嘻值，为总体标准差。I. 3 本标准基11
2、品特性值X来自同一总体的样本大小为”的烛立随机样本町，x，码，反给边的置信水、，当，未知时，对于给定的特件，但I:或下限给出r确定可靠度单侧重信限矶的方法。2 可靠度单侧置信下限的确定本标准给出两种确定可靠度F限的方法，f!.法和直接法。f写是t主简便易行，但精度较低。在精度要求较尚的场合应采用直接法。2. I 查表法2. I. I 由样本观察值町，x，与计算样本均值2，样本标准差hx-土zX; n . s ！寸才x) 2. 1.2据特性值仨（阳限计算系数k: 当规；比t限U时，K=U x s ？当规ii.：下限L时，K=x L s 2. I . 3 由给定的重j，；水平，样本大小n及算得的K
3、值，反衔标准附录A的K系数去，即得特卡I:国家标准局1985-01-29发布1”10-01实施35 的X的可靠！主啦侧置f;F限RL0 2.1.4 向点，J、例GB 4885 85 某压力容器承受内压真抗压强度l报从Ii态分布。该种容器10次战）试验的破坏应）分别为：2565, 2960.12685, 2755, 2790, 2720, 2634, 2860, 2905, 2825kg/cm o容器抗压强度的下限规也为1.2200kg/cm2 0给止置信水、o. 90，要求，l I该容器可靠度单但ti置f:;FNo 根据破坏应力的10个试验数以计算样，乍均值x和样本标准差sx = 2769.9
4、, s二123.1K x L 2769.9-2200 s 123.1 =4.6300 根据0.90, n = 10, K =4.6300衔附录A1 j 1的K系数在得：RL二0.9990即该容器在置信点、i-1=0.90之F的可靠l豆单侧置估下限为0.9990。2.2 直接法2. 2. 1 求非线怆方将”- I j（疗XL刊万v) （亏l.s丁子r （乓.L)h丁e卡”1) h dh = 1 y ( 1 ) 解XL0式II I v=fx-1!_，给也特归自t版时lL z，给比特性tiF限时（）一标准i正态分布函数I（气.！）一参数为1异的伽玛函数2.2.2 计算可守在度根侧置信下限RLRL（X
5、L) 本标准附求B（参J号件）给出f!it真法的一种计算机扫序。36 . ( 2 ) GB 4885 85 附录A确定正态分布可靠度单侧置信下限的K系数表（补充件）牛J系数，：的参数范围与农liU: O.OJ, 0.05, 0.JO, 0.20, 0.40(0.10)0.90, 0.95, 0.99 RL =o.so, o.607 :l.4183 7. 0 2.!5915 2. -16758 2 59033 2.85693 :. 203111 3.5171. 8. (I 2.21483 2.52902 2.65-111 2.92592 3.27肉893.59973 9. 0 2.26216 2
6、.5812:1 2.70832 2.98454 3 343.37 3.669的210.0 2.30310 2.62639 2.75521 3.03525 3 :19914 :1. 730118 11.0 2.33903 2.66603 2. 79636 3.07975 3 1.1民083. 78.ll2 12.0 2.37092 2.70121 2.83289 3.11925 :1 191S2 :i 83021 13.0 2.3950 2.7:l275 2.8656:J 3.1S466 3.53047 :1 87242 14.0 2.42533 2.76125 2. 89523 3.l66ti
7、 3.56567 3.91057 15.0 2. 44883 2 78719 2 92216 3 .21579 3 59770 3. g, S3ll 16.0 2.47035 2.81094 2 94682 3.24246 :1 62704 3.97710 17.0 2.49016 2.83281 2 96952 3.26702 3 65405 1.00638 18 0 2 50848 2.85303 2.99052 3.28973 3 67901 4.IJJJ47 19.0 2. 52549 2.87182 3.01003 3 31083 3. 70225 4 0583 20. 2.5413
8、5 2. 88933 3.02822 3.33U51 3.72390 1 082（） 21. 0 2.55619 2.0571 3.04523 3.34891 :l14411 4 1 (L05 22.0 2.57011 2.92109 3 06120 3 36618 3 7631C, 4 12465 23.0 2. 58321 2.93555 3.07622 3.3824c! 3. 1s1o:i 1. l4404 24 .0 2.59556 2. 94920 3 09039 3 . 1977 7 3 79791 1 16233 25.0 2.60724 3.10380 3.41228 3 81
9、385 1.1796: 26.0 2.61831 2.974 4 3.11650 3.42602 3.82899 1 9603 27. 0 2. 62883 2. 98595 3 .12856 3.43907 3 8433王4.21161 28.0 2.63882 2 99700 3.14004 3.4514B 3 85702 1.22642 29.0 2.64835 3.00753 3. l5097 3.46332 3. 87001 4. 2,1154 30.0 2. 65745 3. 01758 3.1614! 3 47462 .J 8824 7 1.25402 31. 0 2.66614
10、 3.02718 3.7139 3.48S42 :1 893G ,j 26691 32. 0 2.67446 3.03638 3 18094 3.49576 :l.90574 4 27925 33.0 z. 68244 3.04519 3.19010 3.50567 3.9166! 4 29108 34.0 2. 69009 3.05365 3.19889 3.51518 J 92711 1. 302,13 35.0 2.69744 3. 06178 3.20733 3.52432 3.93717 4 31331 36.0 2.70452 3.06960 3 21545 3.5331 l :1
11、. 94685 1. 32:J8. 37.0 2.71133 3 07713 3.22328 3.54158 3.95617 1.3339.! 38 0 2 71789 3.08439 3. 23082 3.54974 :l.96515 j 34369 39.0 2. 72422 3.09139 3. 23809 3.55761 3.97382 1. 3o3U9 40.0 2.73034 3.09815 3.24511 3.56522 3 98219 .t.3621(i 41. 0 2.73625 3.10468 3.25190 3.57256 3.99028 4.37的442.0 2.741
12、96 3.11100 3.25847 3.57967 3.99811 4. 3791 43.0 2.74749 3.11712 3-26482 3.58655 1. 00.168 4. 387fi.j 44.D 2.75285 3.12305 3.27098 3.59322 1.01302 4. 09560 45.0 2.75804 3 .12879 3 27695 3.5996日-1.0:!013 ,J. 40:l32 46.0 2.76308 3.13436 3.28273 3.60595 4.0270:1 4 . 11080 47.0 2.76797 3.13977 3.28835 3.
13、61203 4.03373 l.41807 48.口2. 77272 3 145U2 3.29381 3.61794 4.04024 4.12512 49.0 2.77734 3.15013 3.29911 3.62368 4. 04606 1. li7 . 16Zii9 . :07 :l .05232 . l 11581 . 272-1:! 6IJ 61125:1 .29illl .14821 .00127 1552:1 :1 1880 7. (I 5-1118 .21!111 . 1 (I7J.1!1117 I !291 :!5474 片.II 51!021i .21:71i . (17
14、J坷坞.1!731 i，二二29J.38373 ，仆. 16161 l附q斗3. ii-I：1(191111 .21771 .10781 1 !l I:/ :lfi . 1591111 .1121155 12ux.1 .2J.87ll 、1282们11 . II .1117:1 13纠.1I iJI l l .1:1912 286日，.J . J；，纠l12. II . :!1:59 .12074 .01:,70 l SS 55 :io2:1马.J Iii飞每l :l. . :J7Ll I 5 . llJ53 ll:,IJl2 .l0714.U :1011Rc, .n916n .111:117
15、 1K?.:l6 .3285j .187, 15.0 4729 750 .115511 . i臼i7.ll9t; .lI码JIlfi.11 3311 , .1168S7 . ll61i60 .20389 .:11901 . 508:l9 17 0 32 21 II玉8GH.07S20 .2319 .:l588G 51755 18 () .:11428 . 041Jli1 08393 22171 367 2G .5i51“ L 9. II . 30521 .11!136 . II 9 1妇：122904 .:17501 .1337:1 20.(1 2968l 113:1 /.! 111932 2
16、67 l . 3821; .5102 i）.2821 . ll2f行9i6 243183钝880.517Gl 22. 28210 .112Ul5 1120,:i . 2 l日73:l150; SS:l86 23 () .27550 .014(15 11 817 .c1i5.pI too阳.55971 24.0 - 26933 008.14 . l 2Hlil 守2日IOS . 406:li .56521 25.11 2G:l57 .0029 1 2925 .26Gl9 .11142 . S7o:l8 26.11 .25816 .11020 13.J lb .27103 .41626 .5f,i
17、26 27.0 Z5:Hl7 .11067l.1R J纣27.i61 .-12082 :i7Y月828. II 守24827.0112;) 113 17 .27;1!112515 08426 29. , 2-1373 1540 l-1733 28405 129 2(i 088-12 30. - 2:1943 . II 1Yi1 . ol 27 .287!lo l:l:l 1 Ii . 592:18 :n . 23号36.112:i:14 I f币02.29166 -1368 咀ofliii.i32. II . 2:ll .8 02fi吵7 15859 2952 ,14043 .50975 J:
18、l. II .22779 .11311,J . i(iCOO .c98S8 44381 . on:n 9 34.11 . 2212” .113:175 . (;,25 301 月l. 44706 60618 :5. II 222 .O:Hi92 . I i;日l7. :J01Hl .loOlli . 6 （臼li136 () 217711 .0,1l9i 1 7130 .30787 l 53 1斗.bl21i7 :17. (I .1111;:1 .02制17 121 1072 .;:.ron .blo:i7 :18.ll .111H8 . IJ,oCS . I Yh!lli .:ll15 45
19、只75.61837 39.11 .211881 01833 . 1706什31G08 4RJ:l9 .;z t 06 10. II .2ll612 o,o.ll .18211 . 31日61.16:! . G2:1fifl 4 I . 11 20而l05:1:1 18LiH .12105 .41;(;3 . 62616 42 () .2U089 .110578 .1861 :123.10 啕.JG871i. (i2858 43 () .1856 (I臼U9. I月q2:1 . : . 6l2日3100.0 129G2 .251111 .2SSJ .:19211 :)386 10020 110.
20、0 12294 l :J09:J .261!il :1gw12 .54471 7(1619 1211.11 .11761 . IJ6lll .266民1.1035,; 5 500:1 .1119;1 1 1 GB 4885 85 . 1 0 :;.8500000 .90000。, C,（）门00099000011 9950000 .9990000 153:17 0257 _717:11 1.22I 1 i丰3973:11.74058 3. ii .3087G .5 3178 .81005 1.36082 1.54215 l.!0734 L II . :19642 (i /07 .112238
21、! .4S520 1.64277 2.02230 :i . II .45623 .6 7525 .98218 1 52151 1.71068 2.10051 6. 0 . 50(179 .i 19 I l I . 02822 I. 57830 1. 77399 2.1717 7. II .53580 . 7 5450 l6iil6 1.62165 I 8202 2.22435 8 0 .5G432 . 7 83:13 I 095 70 I . 6576.I 1 s; sss 2. 2680:1 CJ ! I .58串18.8 07三9I 12153 1.68817 1.8911.i 2.305
22、12 IO. 0 .60854 .828-10 1 14378 I 71451 I 91 !129 2.33717 11 . I) .fiZ621 .8 4653 l庐Ifi32c 1 73763 l Qt395 2. :6526 12. 6-1173 .862S1 l 18011 1.75约10I. 96:80 :! 39017 13. ) . 65553 .87071 !.19576 l.77till I. 8导36l. 412,6 1,1 0 .66790 .8895-l I 20臼C8I 79292 2.00301 2.43259 1日，, 67907 0112 1 22213 I.
23、80/H3 2.01905 2.40088 1 . 0 .689! 刊11ti8 l 2:l3.8 l.82165 2.0J372 2.4fi7Gl 17. 0 . 6!855 92136 I 21119 1 .树：！4262 04720 2.48300 18. () 70711 .n302B 1.2037!1 I. 8591 2.05865 2. 49722 19. () .71502 .!13853 1.26277 1.85,71 2.07121 2.51041 20 II 72236 94620 I. 2711:1 I . 8li677 2.州I17 2勘52c7o21 . 7292G
24、. 953:15 I, 78)3 . 87自In2 09200 Z，王341922.0 . 73559 . 6004 1.28621 I . 8”4B7 。101,112 5,149r, 2:l (I 74158 Hf.631 I. 2931 l. X93。32.110.ll 2.55509 24 II 74721 .97222 1. 29fJ5fi l.!IOIO:i 。I18lili 2.56463 25 0 75252 97779 I . ;,OS66 1 . 1081. 2. 12b5! 2.57365 26 . 0 75754 983115 l . ：飞ij : . 91、：；l 0
25、 2 1:1103 2 . i8220 27 0 76228 . 98804 I 1690 I. 220: 2.11111 2. 590:10 28.0 . 7667院. 99278 l.02209 1 . Hc8.l 1 117月52 598111 21 0 77106 【诩728I . 32704 1.9:J.O 2.IS-127 2. 605.5 30，。.77514 l. IJOl.7 I 331 ?:i ！.101)1 ?.16;i:i . 612.C, 31. 0 .77B02 I 00566 I. 33625 I .！01!? 2.IGG?:.1711 士，620.133 0 .
26、78628 I . 01332 I 344u7 l. 9f5日叶 l/7J8 2庐6315734 n 78968 1 01690 I . 3-1862 l 960-l 2 182.12 2.63145 35.0 7929l 1 ()2034 1.352111 1.96S08 2. 18725 2.64310 36.0 .7607 1.02364 I 1Sti05 I . 969玉12.121JIJ 2 fj.JR53 37.0 79907 I 02682 I. 35955 l 97377 2 19651 2.65376 38 n 80196 I.02988 1 30292 I . 97787
27、2. 2011!ltifi 2 07fi55 2. 30686 2.78025 90.0 .R79,19 t .l 1227 1 15129 2.08961 2. 32088 2.7ij3G I 00。4何8709I 12040 l 46）日52.l0ll76 2. :l32Rc 2.8101.l 110 0 89367 l 12744 1 -17121 2.11043 2.34326 2 .82207 120.0 . 89!l1. 4.40132 27.0 2.76450 3.13620 3.28473 3.60828 4. 02980 4.41395 28.0 2.77260 3.1451
28、5 3. 29403 3.61834 4 .04087 4.42595 29.0 2.78031 3 15367 3. 30288 3.62793 4.05142 4.43739 30.U 2.78767 3.16180 3.31133 3.53707 4.06148 4. 4483() 31. 0 2.79170 3. 16957 3.31940 3.64580 4.07109 4.45民7332.0 2.80142 3.17701 3.32712 3. 65416 4. 08030 4.46871 33.0 Z.80786 3. 18413 3.33452 3.66217 . 0891 l
29、 4.47827 34.0 2.81404 3.19096 3.34162 3.66986 4.09757 4.48744 35.0 2.81998 3. 19753 3.34844 3.67724 4.10570 4.49625 36.0 2.82569 3.20384 3.35499 3.68434 4.11351 4 504 73 37.0 2.83118 3.20991 3,36131 3.69117 4.!2103 4.51288 38 0 2.83647 3.21577 3.36739 3.69775 4.12828 4.52074 39.0 2.84158 3.22141 3.3
30、7325 3.70410 4.13527 4. 52832 40.D 2.84651 3. 22686 3.37891 3. 71023 4.14202 4.53564 41. 0 2.85127 3.23212 3. 38438 3. 71615 4.14853 4.54271 4?. 0 2. 85587 3.23721 3. 38967 3.72188 4.15484 4.54955 43.0 2.86(32 3.24214 3.39479 3.72742 4.16091 4.55617 44.0 2.86463 3.2469 3.39974 3. 73278 4. 16685 4. 5
31、6258 45.0 2.8681 3.25153 3.40455 3.73798 4. I 7257 1.56879 46 0 2.87286 3.25601 3.4092(1 3.74303 4.17813 1 57181 47.0 2.87680 3.26036 3.41372 3.74792 4.18351 1.58065 48.0 2. 88061 3.26459 3.4181! 3.75267 4. 18875 4.58633 49. 0 2.88432 3.26869 3.42237 3.75729 4. 19383 4.59184 50.0 2.88793 3.27268 3.4
32、2652 3.76178 4.19877 4.59720 60.0 2.91920 3.30729 3.46248 3.80072 4.24166 1. 64373 70.0 2.94394 3.33467 3.49094 3.83154 4.27561 l. 68056 80.0 2.96416 3. 35706 3.51421 3.85675 4.30338 4. 71069 90.0 2.98111 3.37583 3.53371 3.87788 4 32666 4. 73596 100. 0 2. 99559 3.39187 3.55038 3.89594 4.34656 4.7575
33、5 110.0 3.00816 3.40578 . 56485 3.91162 4.36383 4.77629 120. 0 3.01920 3.41801 3. 57756 3.92540 4.7901 4. 79277 16 GB 4885 85 3 0 20 子之L.5000000 6000000 .65011000 .7000000 . 7500000 .80000110 97325 .49282 .28503 . 0908 .091l96 .28164 3.0 - 61237 - .27587 - .11588 . 1131 .20518 .377:8 4.0 . 48924 .18
34、658 .03873 .11075 .26580 .43213 5.0 .42081 .13296 仙50.15470 .30646 .47031 6.0 37540 - .09578 4366 .18649 . 33645 .49908 7 0 一.34232.06793 .06962 .21097 .35984 .52175 8. 0 .31679 .11459日.09025 .23061 .37877 .54025 9. 0 .29630 - . 02812 .1 0720 .24685 .39452 55574 10. 0 . 27936 .01317 .12144 .26058 .4
35、0791 .56897 11. 0 .26505 - .00042 .13365 .27239 .41948 .58045 12. 0 - .25274 .01062 .14426 28270 .42960 . 59053 13.0 .24202 . 0232 . 15361 .29180 43858 .59948 l !9 .36610 .51261 .57417 30.0 .15595 .10015 .23156 .36866 .51518 .67679 31. 0 - .15334 .10263 .23400 .37110 .51764 .67928 32. ) - .15086 104
36、99 .23633 37342 .51997 .68167 33 II .14849 10724 .23856 .37564 . 52221 .68395 34. ) .14623 .1094 .24068 .37776 且243568613 35.0 .14407 .11145 .24272 .37979 52640 .68822 36.0 .14200 .11342 .24467 .38174 .$2836 .69022 37 0 . 14002 .11532 .24654 38361 .53025 .69215 38.0 .13812 11713 24834 .38541 53206 6
37、9401 39.0 .13630 .11888 . 25007 .38714 .53381 .69579 40.0 .13454 . 12055 .25173 . 38880 .53549 .69751 41. 0 .13286 12217 . 25333 . 39011 .53711 .69917 42.0 .13123 .12373 .25488 .39195 . 5386 .70077 43.0 -.12966 .12523 .25637 . 39345 .54019 .70232 44.0 .12Hl5 .12669 .25781 39489 .54165 .70382 45 0 .1
38、2669 .12809 .25921 39629 . 54307 .70526 46.0 l Z28.12945 .26056 39764 _5,j4,j3 .70666 47.0 12巳391.13076 .26186 .39895 .34且76. 70802 48. 0 .12259 .13203 .26313 .40022 . 54705 . 70934 49.0 1 2131 .13327 .26435 .40145 .54829 .71062 50.0 -.12007 13446 26554 . 40264 .54950 . 71186 60.白.1094-1 14473 .2757
39、7 .41291 .55993 . 72257 70.0 .10122 .15272 .28373 .42093 . .6809 .73096 80.0 - .09461 . 1591且29017 .42742 57469 .73776 90.0 . 0 8914 .lfi449 2955 I 43282 .58019 .74343 100.0 - .08453 . l 6901 .3IQ03 43739 豆8486.74825 110.0 - .08056 .17290 .30393 .44133 . 58889 7.5 ll 120. 0 .07711 .17629 .30733 .444
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41、 60. 7 （） 拭II. II ;111.11 1011.0 l I） 120.11 S 85()1()111川.4日377St、i8li9Ii 1926 6558:l . G8.I约4.7116211 I .! j 5甘71”“/ 专7币33671;.lliJ 77二12 ：均12.7刊2:1飞，。7”91:181i6 14 .”1260 .81826 82350 82837 .832创）.83714 81111 8!185 .8 J8.l7 851/0 85485 问司784削（阔. 8 liJ.l9 .86;17 约6814. 8779 7305 .87522 .87729 .878
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44、.10557 2. !ii781i 2.llilll只,.11223 2. ll32 2.1163! 2.11830 2.121121 z 122117 2. l381 I !.1508几2.1611;1 l时72 17727 c, I扫：；6!J ！”9且可9950000 1.8149 1 81将50!,”7067 。l刀；7.11491111 2 117”。11.111101 2.123-1臼2.J,JJ71 2.15781 2 1721 2. 18-1!):1 2.1lf币52 20710 2.21017 2.22567 2 23390 2.24155 2.24867 2. 2553:1
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