GB T 4885-1985 正态分布完全样本可靠度单侧置信下限.pdf

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

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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

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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

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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

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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

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