1、Q.J 中华人民共和国航天工业部部标准QJ 138虐-88正态分布双侧容许限系数表!988-02-29发布1988-10-01实施中华人民共和噩院去工业部发布中华人民共和国航天工业部部标准正态分布双侧容许限系数表1 主题内容和适用范围1. 1 主题内容本标准给出了正态分布双ffi容许限系数表。1. 2 适用范围本标准适用于产品特性值X同时满足.B. 服从正态分布，其分布密度函数为QJ 1384-88 f (X) =一_，-I_exp(_(三二止一)2J(-= 0 b. 总体参数和未知，c. 样本大小为n的独立随机样本町X , X，来自同总体。Z 引用标准GB 3358 (统计学名词及待号)GB
2、 3187 (可靠性基本名词术语及定义S 正态分布双侧容许限系数表和参数范围3.1 iE态分布双侧容许限系数表(见表3.2 参数范围、表距及说明置信水、V.Y=0.5.0.6. 0.7. 0.75.0.8. 0.85.0.9. 0.95.0.990 双ffi概率p二0.15.0.125.0.1(-0.01) 0.01 (-0.000 0.001.0.0005.0.0001. 0.00001。样本大小n二2(1) 50 (10) 120 表中给出了标准正态分布的p分位数町，利用Up与双侧容许限系数k进行线性插值，以求得k或者p.可以提高插值精度。若参数超出本数表数值范围戎为避免插值误差，本标准附
3、录A给出了求k或求p的计算机程序。航天工业部198802-29批准1988-10-01实施QJ 1384-88 4应用实例4. 1 确定双侧容许限4. 1. 1 步骤a. 由n个样本观察值Xp飞，.凡，计算样本均值王和样本标准差s，1 .:. 2二x , . (2) n ,= 1 S I寸主(x，-x)，.(3)b. 根据给定的置信水、vY.下四川和七侧概率队和p，以及样本大小n.查-*数表分别得到汉侧谷许限系数k，和k，。C. 计算双侧容许下限L和上限U，45 ( . . . . . . . . . . . . . . . . . . . . ss 12 LA-K -+ -XFZ =一LU
4、4. 1. 2 示例某发动机推力服从正态分布.10次试验的观察值为20.05.19.03. 19.90. 20.11. 19.82. 20.01. 20.10. 19.77. 20.15. 19.81 kN.给定Y二0.8，Pl二0.05，P2=O.Ol, 要求确定该发动机推力双恤Ij容许限。根据10次观察值，按公式(2 )和(3 )算得.Z二19.875s 0 0.32715 按Y二0.8和n=10，用p，二0.05和p，oO.OI分别查丰数表得:k, 02.48256 k，二3.35717该发动机推力下、k侧容许限分别为:L x- k,so 19.06kN U二五十k，s0 20.97kN
5、 4.2 确定双侧可靠度近似下月24.2.1 步骤a. 由n个样本观察值町，x2，凡，按公式(2 )和(3 )计算样丰均值王和样本标准差sob. 根据给定的特性值下限Lo和限叭. I算双侧容t限系数k，和k，k,- x-Lo l二一一-一一. (肘s 2 QJ 1384-88 U王k，二一一一一一十一. . . . (7 ) s c. III样本大小2、按公式(自幸自(7)分别算得飞和与以及给定主古董主Jkl二，分别!3i.查本数表，得到下1割草E上纯靠在字p，军日p，od. 计算写雪在度下i5，RL = 1 - (Pl + p,) 4.2.2 示曹营在稳定的生产条件F，加工出的芯辑室径报从正
6、态分布，该轮主径的设计要求为中2012。从一批产忌巾随机抽取15件进行测量，也测量结果，按式(2 )和(3)算得样本乎均值主=19.980，样丰标准差s二札0153880给定置信杰、jy=臼.草，求满足主、下限约可靠度重f言下限。根据公式(川军丑行计算k，平Pk k z z-La 19.980一(20-0.05)E二一一一一一一一一=-一=1. 94957 s 0.015388 LUn-言20+ 0.03) - 19.980 ，-一一一一一一一=二3.24929s O.告1538理板三军y= 0.8和n二15，用k，部主2分别反查数表，经线性插值得Eu., = - 2.451131 Up= 1
7、.373喜岳8用UP1和UF2)另Ij瓷杯准正态分布分位数表得.P, = O. 007127 Pl=齿.084742该艺、教直径可靠度置信下限为2RL - 1 - (Pl+P,) =0.908131 3 正态分布汉恤容H民数表y 0.990 。问4刷刷品tl曲帽?乓;二0.15000 。125000.10000 0.09000 0.0自000队070000.06000 。.050例叶拍拍.1.03643 1. 1503 1) 1. 28155 l. 34076 1. 40507 1. 47579 1.55477 94 也hc h 睛曲也ll曲曲28 1. 83569 1. 99108 2.17
8、157 2.25348 2.34275 2.44122 2.55155 2.67777 29 1. 81677 1. 97102 2.15018 2.23149 2.32009 2.41783 2.52732 2.65260 30 1. 79904 1. 95223 2.1315 2.21089 2.29887 2.39592 2.50464 2.62904 31 1. 78240 1. 93459 2.11135 2.19155 2.27895 2.37536 2.48336 2.60692 32 l喃766721. 91799 2.09365 2.17336 2.26022 2.35602
9、 2.46331 2.58613 33 1. 75194 1 90233 2响。76972.15620 2.24255 2肉337782啊444472.56652 34 1. 737制1.88753 2.06120 2.13999 2.22585 2.32055 2.42664 2.54800 35 1. 72472 1. 87351 2.04627 2.1 24.64 Z咽210052.30424 2.40976 2.53047 36 1. 71216 1. 86021 2.03211 2.11009 2.19506 2.28878 2.39376 2.51385 37 1. 70022 1
10、.84767 2.01865 2.09626 2.18082 2.27409 2.37856 2.49806 38 1. 68885 1. 83555 2.00585 2.08310 2.16728 2.26011 2.36410 2.48305 39 1. 67802 1. 82409 1.99365 2.07056 2.15.37 2.24679 2.35032 2.46874 40 1. 66767 1. 81315 1. 98201 2.05860 2.14206 2.23409 2.33718 2.45510 41 1. 65779 1. 80269 1. 97088 2.04717
11、 2.13029 2.22195 2.32462 2.44206 42 1.64832 1.79268 1.96024 2.03623 2.11903 2.21034 2.31261 2.42959 43 1.63926 1.78310 1.95004 2.02576 2.10825 2.19922 2.30111 2.41765 44 1 63056 1. 77391 1. 94026 2.01571 2.09791 2.18855 2.29008 2.40620 45 1. 62221 1. /6508 1. 93088 2.00607 2.08799 2.17832 2啕279.92.3
12、9521 46 1. 61418 1.75659 1. 92186 1.99680 2.07845 2啕J68492.26932 2.38466 47 1. 60646 1. 74843 1.91318 1. 98789 2.06928 2.15903 2.25954 2.37451 48 1.59902 1. 74057 1.90482 1. 97931 2.06045 2.14992 2.25013 2.36473 49 1. 59185 1.73300 1.99678 1. 97104 2.05195 2.14115 2.24106 2.35532 50 1. 58493 1. 7257
13、0 1. 88901 1. 96307 2.04374 2.13269 2.23231 2.34625 60 1. 52702 1.66457 1. 82409 1. 89640 1.97517 2.06201 2.15924 2.27043 70 1. 48371 1. 61891 1. 77564 1.84667 1, 92403 2.00931 2.10478 2.21395 80 1. 44982 1. 58319 1. 73777 1.80782 1. 88409 1. 96816 2.0622自2.16988 90 1. 42239 1. 55431 1. 70717 1. 776
14、43 1. 85183 1.93494 2.02797 2.13431 100 1. 39962 1. 53036 1. 68181 1. 75041 1.82510 1. 90741 1.99955 2.10486 110 1.38034 1.51009 1. 66035 1.72841 1. 80250 1. 8841b t. 97553 2.07997 120 1.36376 1.49265 1. 64191 1.70950 1. 78308 1. 86415 1. 95489 2.05859 巳。-Mll翩翩工0.990气气n二、RJ勺k 0.04000 0.03000 。鼻02000
15、0.01000 。.009000.00800 0.00700 0，006川1.75069 1矗880/92.05375 2.32635 叫2.365622.40892 2.45727 -2.51215 2 233.75向46237.21303 245.44936 3 28.40012 28.82890 29.附15画4 14.29123 14.510!风15.03204 5 10.12574 10.28244 10.65631 6 8.20470 8.33278 8.63838 7 7.1069a 7.21868 7.48534 8 6.39623 6.49743 6. /3894 9 5、8
16、97325.99114 6自2150410 5.52669 5.61504 5.82589 11 5.23971 5.32384 5.52460 12 5.01031 5.09107 5.28380 13 4.82233 4.90034 5.0R649 14 4.66514 4.74084 4.92151 15 4.53151 4.60527 4.78128 16 4. 4.1 632 4.48840 4.66041 17 4.31587 4.3R649 4.55501 18 4.22736 4恫296704 46216 19 4.14812 4. ?1 692 4.37966 20 4.07
17、829 4.14546 4.30577 21 4.01479 L081队与23918 22 3.9570 4.02263 4.17877 23 3.90470 3刷969374国1237124 3. 85fi59 3.92057 4.0132, 25 3.81232 3.87567 4响。2684;:(j 3.77143 3.83419 3.98395 27 3. 133til 3.79573 3.94420 ?A 1矗白自由. 7旦IIQr;o M户00828!1O 3 25487 1006 5 份。问时制hWAl|伽翻29 2.80025 2.98238 3.22533 3.609,2 3
18、.66533 3.72658 3.79500 3.87272 30 2.77564 2.95647 3.19770 3.57943 3.63tlb5 3.60535 3.76328 3.84044 31 2.75255 2, 93217 3.17177 3.55092 3.60567 3.66606 3.n3fi3 3.81017 32 2.73083 2.90931 3.14739 1咽52H2队578513肉63852;. 70556 1币7817033 2.71036 2.88777 3.12441 3.49886 3.S5292 3.61256 3.67920 !L7日8M 2.691
19、02 2.86742 3.10271 :l .41501 :U:;2876 3.5806 3.65Hl 3. 7?955 35 2.67272 2.R4 i1 1f 3.08217 3.45244 3.50590 3.56487 3.63076 3.70.1.1 9 36 2.65537 2.82991 3.06271 3.43105 3.48 42.1 3.54289 3肉608443.68288 37 2.63889 2.81257 3.04422 3.41074 3.16366 3.52203 3.b8724 3.66131 3. 2.62322 2.79609 3.02664 3.39
20、143 3.44409 3.50219 3.56709 3.64081 39 2.60829 2.7B038 3.00990 3.37303 3.42546 3.48:129 3.54790 3,1)2128 40 2.59405 2.76540 2.99393 3.35549 3.40769 :，46527 3.52960 3.60266 41 2.58044 2.75109 2. 97R68 3.33874 3.:39072 3.44806 3.51212 3.58487 42 2.56743 2.73740 2.96409 3.32271 :1. 37449 3.43160 3.4954
21、0 3.56787 43 2.55497 2.72430 2.95013 3.30738 3.35895 3.41584 3.47940 3.55159 44 2.54302 l. 111(4 2.93674 3.29268 3.34406 3.40074 3.46406 3.53598 45 2.53156 2.6996Y 2.92:189 3.27857 3.32977 3.38625 3.14935 3.52101 46 2.52阅日2.68811 2.91155 :5 .26502 3.31605 3.37233 3.43522 3.50683 47 2.50996 2.67697 2
22、.89969 3.25200 3. :10285 3.3589S 3, 42163 3自49281明2.49976 2.66626 2.88827 3.23946 3.29016 3刷346083.40855 3.47951 49 2.48995 2.6559j 2.自77273.22739 3.27793 3.33368 3.39596 3.46670 50 2.48048 2.64598 2.86667 :.21575 3.26614 3.:32172 3.38382 3.4fi4 34 60 2.40141 2.56288 2.77816 3.11862 3.16776 3.22197
23、3.28252 3.35129 10 2. ;i425: 2.50103 2.71231 3.04639 3.09460 3.14779 3.20720 3.27467 80 2.29660 2.45279 2.66097 2.99010 3.旧7603.08999 3.14851 3.21498 90 2.25951 2.41388 2.61957 2.94472 2.99164 3.04340 :1. 10121 316687 100 .22886 2.38167 2阳585312.U0718 2.95363 3.00486 3.06208 3.12707 110 2.20294 2.35
24、446 2.55637 2.87549 2.92153 2.97232 3.02905 3.09347 120 2.18068 2肉331102.53153 2.84828 2.89398 2.94439 3.00070 3.06463 、，。耐hw帽hFli帽mwY二0.990Y主。国005000.OU400 。.003000.00200 0.00100 0.00050 。.000100.00001 2.57583 2.65207 2.74779 一-2自87817-甸09023响2!:l0533.71902 4.26489 2 250.53061 256.61365 264.25025 2
25、74.65308 29 1. 57267 a07刷553453-11. 74112 385.29448 3 30.48269 31.23848 32.18761 33.48106 35.58588 37.57499 41. 8331J 47.26193 4 15.35427 15.74021 16.22497 16.88575 17.96136 18.97817 21. 15569 23.93311 5 10.88713 11. 16362 11. 51095 11. 98447 1;七7554013.48433 15.04571 17.四7776 8.H2707 9.05311 9.3370
26、9 9.72427 10.35472 10.95089 12.22809 13.85784 7 7.65000 7.84726 8.09509 8.43301 8.98329 9.50369 10.61867 12.04156 6.88808 7. 06674 7.29122 7.59731 8.09578 8.56722 9.57733 10.86649 9 6.:5330 6.51894 6.72706 7. 01086 7.47304 7.91016 内468010.04223 10 5.95609 6.11208 6.30808 。.575357.01063 7.42231 8.304
27、46 9.43038 11 5.64858 5.79712 5.98375 6.2382b 的.6527:l 7.04476 7.88480 8.95698 12 5.40281 5.54540 5. /l4h6 5.96888 6.36678 6.74312 7.54955 8.5788, 13 5.20145 5.33917 5.51223 5.74821 6.13254 6.49605 7.27499 8.26920 14 5.03308 5.16675 b33470 5.563/3 5.93674 6.28954 7.04553 8.01043 15 4.88998 5.02021 5
28、.18383 札406965.77阳66.11拍76.85058 7.79061 16 4.16664 4.肉93905.05380 5.27186 5.62699 5.96287 6.68261 7刷6012217 4.65908 4.78377 4.94043 5.15407 5.50199 5.83106 6.53619 7.43616 18 4.56434 4.68675 4.84057 5.05飞1315.391削5.71498 6.40726 7.29081 19 4.48016 4.60056 4.75184 4.95811 5.29411 5.61H!6 6.29273 7.1
29、6171 20 4.40477 1.52337 4.67240 4.87560 5.20654 5.51954 肉190:!17.0461h 21 4.33682 4.45381 4.60079 4.80122 5.12763 5.43635 6自097836.94203 22 4.?7519 4, 39071 4.53585 4.73376 5.05607 5.3609U 6.U14U6 6. 1:1 4763 23 4.?1901 4.33319 4.47665 4啕6722，4.99085 5.29215 5.93772 6.76160 24 4.16754 4.28闹。-1 .4224
30、2 4.61594 4.93110 5.22916 86779 6.68281 25 4.12018 4.23202 4.mS3 4.56412 4.87614 5.17122 5.80317 6.61033 26 4.07614 4.18723 4. :12644 4.S16?S 4.82537 5.11771 5.74406 6.54339 27 4.03588 4.14571 4.28:l7l 4.47188 4.77831 5.06810 5.68900 6.48136 28 3.99815 4.10710 4.24397 4.43061 4.73454 5.02197 5.63780
31、 6.42367 。也叫咽帽.11帽帽29 3.96296 4.07107 4.20690 4.39211 4.69371 4.97894 5.59004 6.36987 30 3.93004 4.03737 4.1 7222 4. 35朋94.65552 4.93869 5.54537 6.31955 31 3, 89915 4.00576 4.13969 4.322;2 4.61/0 4.9091 5.50348 札272363:1. 3.871l12 3鼻!fr6044.10911 4币290564.58603 4.86S45 5.4ti410 6.22800 3: 3.84276 3.
32、94803 4.080ao 4咽260644.55431 4.83202 5.42699 6.18621 34 3.81692 3.92159 4.05309 4.23238 4.52435 4.80045 5.39197 6.14676 35 乃.7924R3.R9657 4.02735 4.20566 4.49601 4.77059 5.35883 6.10944 36 3.76日313.87286 4.00295 1. 18033 4.46916 4.74229 5.32744 6 07408 37 3.747 3.85035 3旷79794.15628 4.44367 4.71543
33、5.29763 6.0105 38 3.72641 3.82895 3.95777 4.13342 4.41943 1. 68989 5.26929 6.00860 39 3 70649 3.80856 3嗣9:16804蜗111644.39634 .66556 性肉242315.97821 40 3.68749 3.7892 3.!)1 680 4.09088 1.37433 4, 64237 5.21658 5.94924 4 3.66935 3.77056 3.89770 4 07105 4.35331 4.62022 5.19201 5.92157 42 3.65201 3. 7fj2
34、81 3.87944 01.05209 1. 33321 59905 5恫685生5.89512 43 3.63541 3.73581 3 86196 4肉033944.3139R 4啕578785户14601 .22882 4.48906 5.04653 5, 75776 49 3.54883 :.64721 3.77081 3.93932 21369 4.47312 5.0288, 5.73786 50 3.5362:1 3.63432 3.75755 3.Y2b5 4.19010 4.4577 5.01180 5.71867 60 3.43114 3.52679 3.64694 3.80
35、74 4.07743 4.32959 4.86968 5.55869 .10 3.35301 3.44684 3.56472 3.7254 3.98702 4.2M35 4.76410 5.43986 80 3.29214 3.38457 3.50067 3.6b89 :,) 3.91661 4.16020 4.6819 5.34736 90 3. 24:l09 3.33438 3.44906 3.60539 3.85988 4.10016 4.61570 5.27286 100 3.20251 3.20288 :l.40638 3.56110 3.81297 4.05107 4.56095
36、5.21128 110 3.16826 3.旦与784:l. 37035 3.52372 3.17338 4蛐009384.51476 5.15931 120 3.13886 3.22777 3.3394: 3.4964 3.73941 3.97361 4.47513 5.11473 巳。时刷刷品tl幢幢0.15000 0.12500 。币100000.09000 0.08000 0.07仙。0.06000 0.05000 1. 03643 1. 15035 1. 28155 1. 34076 1. 40501 1. 41519 2.512152 9.12666 9.64080 10.3241
37、7 1l .40108 11. 55620 11.72723 11. 91820 12.13497 3 4.71020 4.98417 5.34858 5.92335 6.00618 6.09752 6.19952 6晒315324 3刷7464.1:1.96954 4.26634 4.73461 4.80211 4.87654 4.95967 5.05404 5 3.31530 3.51625 3.78364 4.20555 4.26637 4.33343 4.40834 4.49337 6 3.06534 3.25376 3.50448 3.90011 3.95715 4.02004 4.
38、09028 4.17003 7 2.89963 3.盯9903.31979 3.69833 3 75290 3.81308 3.88028 3.95659 8 2.78041 2.95491 3.18712 3.55356 3.60639 3.66464 3.72970 3.80357 2刷689782.85996 3.08643 3.11379 3.49531 3.55212 3.61556 3.68760 10 2.61812 2.78493 3.00690 3.35717 3.41!766 3.46334 3.5255:1 3.59613 11 2.55975 2.72384 2.942
39、19 3.28674 3.33641 3.39118 3.45235 3.52180 12 2.51110 2.67295 2.88830 3.22813 3.27711 3.33113 3.39147 3.4日99613 2.46980 2.62975 2.84259 3.17843 3.22684 3.28023 3.33986 3.40755 14 2.43419 2.59253 2.80321 3.13565 3.18357 3.23641 3.29543 3.36244 15 2.40311 2.56004 2.76886 3.09834 3. 14!i84 3.19821 3.25
40、671 3.32311 16 2.37569 2.53139 2.73857 3.06546 3.11258 3.16455 3.22258 3.28847 17 2.35128 2.50589 2.71162 3.03622 3.08301 3.13461 3.19223 3.25765 18 2.32937 2.48302 2.68745 3.01000 3.05649 3.10776 3.16502 3.23003 19 2.30958 2.46235 2.66561 2.98632 3.03255 3.08353 3.14046 3.20510 20 2.29l59 2.44357 2
41、.64578 2.96482 3.01080 3.06152 3.11815 3.18245 21 2. 27G14 2.42640 2.62765 2.94517 2.99094 3.04141 3.09778 3.16177 22 2.26003 2.41064 2.61101 2.92714 2.97271 3.02296 3.07908 3.14279 23 2.24610 2.39610 2.59567 2.91052 2.95590 3.00595 3.06184 3.12529 24 2.23320 2.38264 2.58146 2.89514 2.94035 2.99021
42、3.04589 3.10910 25 2.22121 2.370B 2.56826 2.880属52.92590 2.97558 3.03107 3.09400 26 2.21003 2.35847 2.55596 2.86753 2.91244 2.96196 3.01726 3.08005 27 2.19957 2.34757 2.54446 2.85508 2.89985 2.94922 3.00436 3.06696 28 2喃189772.33735 2.53368 2.84341 2.88806 2.93729 2.99226 3.05468 自。-帽也-ll辅相29 2.1805
43、5 2.32774 2.5234, 2.83245 2.87697 2.97. 607 2.98090 3.04315 30 2.17187 2.31868 2.51400 2.82212 2.86653 2.91550 2.97020 3.03229 31 2.16367 2.31013 2.50498 2.81237 2.85668 2.90553 2.96009 3.02203 32 2.15591 2.30205 2.49646 2.80315 2.84735 2.89610 2.95053 3.01234 33 2.14855 2.29438 2.48837 2.79441 2.83
44、852 2.88716 2.94148 :1. 00315 34 2.14157 2.28710 2.48070 2.78611 2.83013 2.87867 2.93288 2.99442 35 2.13492 2.28017 2.47340 2.77822 2.82216 2喃870602.92471 2.9抱61336 2.12859 2.27358 2.46645 2.77071 2.81456 2目62922.91692 2.97823 :17 2.12255 2.26728 2.45982 2.76354 2.80731 2.85558 2.90949 2.97069 38 2.
45、11678 2.26127 2.45348 2.75669 2.80039 2.84858 2.90240 2.96350 39 2.11126 2.25552 2.44742 2.75014 2.79317 2.84189 2.89567. 2.95661 40 2罔105972.25001 2.44162 2.74387 2.78744 2.83547 2.88912 2.95002 11 2.10090 2.24473 2.43605 2.73786 2.78136 2.82933 2.88289 2.94371 12 2.09603 2.23966 2.43071 2.73209 2.
46、77553 2.82343 2.87692 2.93764 43 2.09135 2.23478 2.42558 2.72655 2.76993 2.81776 2.87117 2.93182 2.08685 2.23010 2.42065 2.72122 2.76454 2.81231 2国865652.92622 15 2.08252 2.22559 2.41589 2.71609 2.75935 2.80706 2.86034 2纠208216 2.07835 2.22124 2.41132 2.71114 2.75435 2.80200 2.85522 2.91563 17 2.074
47、32 2.21704 2.40690 2.70637 2.74954 2.79713 2.85028 2.91062 18 2.07043 2.21300 2.40264 2.70177 2町744882喃792422.81551 2.90578 19 2.06667 2.20909 2.39852 2.69733 2.74039 2.78788 2.84091 2.90111 50 2.06304 2.20530 2.39454 2.69303 .73605 2.78348 2.83646 2.89660 50 2.03234 2.17334 2.:l609。2.65672 2.69935
48、2.74637 2.79886 2.85847 10 2 00901 2.14907 2.335:l6 2.62918 2.67152 2.71821 2.77035 2.82955 ，。1.99054 2.12985 2.31515 2.60739 2.64950 2.69594 2.74780 2.80667 帕1. 97546 2.11417 2.29865 2.58961 2.63154 2.67777 2.72940 2.78801 )0 1. 96284 2.10105 2.28486 2.57475 2.61652 2.66259 2.71403 2.77242 10 1.95210 2.08988 2.27312 2自562102.60374 2.64066 2.70094 2自75915w 1. 94280 2.08022 2.26297 2.55116 2.59269 2.63849 2.68963 2 74768 一 M 。问制帽晶ll曲曲y - 0.800 吨之二nl飞P 0.00500 0.00400 0.00300 0.00200 0.00100 0.00050 。.000100.00001 2.57583 2.65207 - 2.74
