【国家标准(GB)】 正态分布完全样本可靠度单侧置信下限

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 reliabllity confidence lower llmlt(Normat distribution complete sample)UDC 519.28
GB 4885-85
1.1本标准所用统计学名词及符号见GB3358一82《统计学名词及符号》，可靠性名词术语见国标GB3187—82《可靠性基本名词术语及定义》。1.2本标准适用于产品特性值X可合理地认为服从正态分布的情形。其分布密度函数为f(r)=
aV2元exp [
式μ为总体期望值，为总体标准差。()\，18+8
1.3本标准基」产品特性值X来自同一总体的样本大小为n的独立随机样本a1，2，药及给
定的置信水平，当μ，未知时，对于给定的特性值上（或下）限给出了确定可靠度单侧置信下限R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下限的方法，查表法和直接法。奎表法简便易行，但精度较低。在精度要求较高的场合应采用直接法。2.1查表法
2.1.！由样本观察值1，2，.，n计算样本均值，样本标准差s：(; -)2
2.1.2据特性值上（下）限计算系数K：当规定上限U时，=-
当规定下限L时，K：
2.1.3由给定的置信水平，样本大小n及算得的K值，反本标准附录A的K系数表，即得特性国家标准局1985-01-29发布
1985-10-01实施
值X的可靠度单侧置信下限RL
GB4885—85
2.1.4*表示例
某压力容器承受内压，其抗压癌度服从正态分布。该种容器10次静力试验的破坏应力分别为：2565，2960，2685，2755，2790，2720，2634，2860，2905，2825kg/cm。容器抗压强度的下限规定为1.=2200kg/cm2。给定置信水半y=0.90，要求估让该容器可靠度单侧置信下限。根据破坏应力的10个试验数据计算样本均值和样本标准差s：=2769.9,s=123.1
2769.9-2200
根据=0.90，n=10，K=4.6300附录A的K系数表得：R,= 0.9990
即该容器在置信水乎=0.90之下的可靠度单侧置信下限为0.9990。2.2直接法
2.2.1求非线性方程
nX +nhu)
解XL。式中
「-U，给定特性值上限时
（L-，给定特性值下限时
中（·）标准正态分布函数
r(\=l)
——参数为—
的伽玛函数
2.2.2计算可靠度单侧置信下限RLR=Φ（)
本标准附录B（参考件）给出了直接法的一-种计算机程序。36
(n-1)s*h dh = 1 -y .(1)
GB 4885—85
确定正态分布可靠度单侧置信下限的K系数表（补充件）
本系数表的参数范围与表距：
=0.01,0.05,0.10,0.20,0.40(0.10)0.90,0.95,0.99R=0.50,0.60(0.05)0.95,0.99,0.925,0.93,0.935,0.9,0.945,0.95,0.96,0.9n=2(1)50(10)120
.5000000
-22.50050
.96549
.89222
.67764
-62659
.60503
.56785
，52302
.49843
.48737
.45814
-44134
-，42626
-,40629
.39443
-35565
.34761
.34010
，24971
一.21526
.6000000
-13.82057
.92414
.68526
—.61089
.55225
—，50445
.40094
.35211
—.33157
.28083
.23036
.21006
，18397
.15529
-13720
.13169
.12641
.12135
.11649
.11181
-,10731
—.10298
.09880
.09477
.09087
.08711
.08347
.07994
.07652
—.04735
.00677
.00815
.02074
.03156
.04098
GB4885—85
.6500000
-：44174
～.30959
—27839
—25124
—.04734
.03993
.03289
.00242
.00289
.00798
.01288
.01758
.02210
.02645
.03065
.03470
.03862
.04240
.04959
.05302
.05635
.08480
.10685
.12460
.15172
.16241
.17174
.7000000
：40935
.33344
.27471
.22740
.04070
.00944
.00427
.01692
.02865
.03957
.05932
.06830
.07675
.08473
.09228
.09944
.10624
.11272
.11889
.12478
.13041
.13581
.14098
.14594
.15071
.15529
.15971
.16397
.16807
.17204
.17587
.17957
.18316
.18663
.18999
.19326
.22127
-24307
.28765
-29832
.30764
.7500000
- 5.10993
·44679
-22598
-15915
—·10659
.00300
-05329
·07427
-09311
.11017
·12572
·13998
.15311
·16527
.17656
-18710
·20622
-21493
.22314
.23091
-23828
.24527
·25192
-26430
-27008
.27561
.28600
.29089
-29559
-30011
.30447
-31273
-31665
.32044
.32411
-32766
.33111
.33445
.33769
：36557
.38734
.40498
.41965
.43211
·44287
·45228
.8000000
.79235
-,11743
.03965
-01973
.06727
.10660
.13993
.16869
.21622
.23621
.25425
.27066
.28566
.29946
.31221
.32405
.33507
.34538
.36413
.37269
.38079
.38846
-40265
.40924
.41552
.42152
-42727
.43277
、43805
.44312
.44799
.45268
.45720
.46156
.46577
.46983
.47756
.48124
-48481
.48827
-49162
.49488
.52298
.54502
.56292
.57784
.59054
.60152
.61114
8500000
.14533
.00420
.08886
.15736
.21103
.25481
.29153
.32299
.35038
.37455
.41551
.43310
.44915
.47749
.49009
.50181
.51276
.52301
.53265
.54172
.55030
.55841
.56610
.57341
.58037
.58701
-59334
.59940
.60521
.61078
.61612
.62126
.62620
.63096
.63555
.63998
.64426
.64840
.65240
.65628
.66003
.66367
.66720
.67063
.67395
.70274
.72540
.74385
.77242
.78380
.79379
.9000000
-70711
.12260
.23770
.31886
.38100
.43093
.47239
.50765
.53817
.56498
.58879
.61015
.62947
.64706
.67803
.69176
.70453
.71643
.72757
.73803
.74787
-75716
.76595
.77427
.78218
.78971
.79688
.80372
.81027
.81653
.82254
.82831
.83385
.83918
.84431
.84926
.85403
.85864
.86310
.86741
.87158
.87562
.87954
.88334
.88702
.89061
.89409
.92426
.94809
.96755
.98385
.99777
GB 4885-85
.9500000
.00015
.29478
.44286
.54313
-61829
.67787
.72685
.76817
.80374
.83481
.86232
.88690
.90907
.92922
.94763
.96456
.98021
.99472
.9900000
.78155
.92360
.9950000
.70758
.9990000
.96918
1,60542
168268
185065
2-04948
2·11595
2-55100
.9995000
.9999000
GB4885—85
.9999500
.9999900
.9999990
.9999999
.5000000
-73445
-57968
—.49432
-47330
—.45477
-38665
：34984
.34218
.33499
—，32825
—32189
-29487
—.29024
—.27368
-26640
.25967
.25343
.24762
.21574
.18608
，17521
.16604
.15818
-，15133
.6000000
GB 4885---85
.6500000
—.74556
—.58284
—.41311
—.31943
.28574
—25754
—,21260
.19427
.16341
.13828
：11729
—.09940
—.08392
-,07692
，04754
—.04257
.03333
.02491
.01720
.00252
.00541
.00819
.01088
.01348
.01600
.01844
.02081
.04108
.05679
.07991
.08876
.09637
.10301
.54681
.17264
.11521
.07303
—.04027
.01385
.00807
.01772
.02665
.03494
.04267
.04989
.05666
.06303
.06904
.07471
.08009
.08518
.09003
.09464
.09904
.10324
-10726
.11479
+11833
.12173
.12501
.12816
.13120
.13413
.13696
.13969
.14234
.14490
.14738
.14978
.15211
.17211
.18765
.20019
.21940
.22698
.700000
—,58033
-35547
-10333
-05980
-，02473
.00437
.02906
.05038
.06904
.08557
.10035
.11367
.12576
.13680
.14694
，15630
.16497
.17304
.18762
.19424
.20047
.20635
.21191
.21719
.22220
.22696
.23583
.23997
.24393
.24773
.25137
.25487
.25823
.26147
.26459
.26760
.27051
，27331
.27603
.27865
.28119
.28365
.28604
.28836
.30827
.34678
.35562
.36325
.36991
.7500000
—.34938
-00313
.05449
.09482
.12768
,15518
.17868
.19909
.21704
.23299
.24731
.26025
.27203
.28282
-29275
.30193
.31045
.31838
.33276
.35681
.36702
.37175
.37627
.38058
.38471
.38866
.39245
.39609
.39958
.40294
.40618
：40931
.41232bZxz.net
-41523
.41804
.42076
.42339
.42595
.42842
.43081
.43314
.45319
.46886
+48156
.49212
.50109
.50884
.51562
.8000000
：52144
，12736
.02072
-11001
.17273
.22037
.25834
.28962
.33872
.35854
.37606
.39169
：40576
.41851
.43016
.45069
.45982
.46830
.47622
.48363
.49059
.49714
.50332
.50917
.51471
.52498
.52975
.53865
.54282
.54681
-55064
.55432
.55785
.56126
-56454
.56771
.57076
.57371
.57657
.57933
.58200
.58460
.58711
，58955
，59192
.61234
.62836
.64136
.66141
.66937
.67635
.8500000
.17385
.09477
.21906
.29928
.35757
-40276
.43927
.49550
.51786
.53748
.55489
.58456
.59736
.60906
.61983
.62978
.63901
.64760
.65563
.66316
.67024
.67691
.68321
.68918
.69484
.70022
.70534
.71022
.71488
.71935
.72362
,72771
.73165
-73543
.73907
.74257
.74595
.74921
.75236
.75540
.75834
.76119
.76395
.76663
.76922
.77419
.79533
.81195
.82547
.83675
.84636
.85468
.86197
.9000000
.13802
.33448
.44389
.57482
.61904
.65521
.68557
.71157
.73419
.75412
.77187
.78782
.80226
.81543
.82749
.83861
.84890
.85846
.86738
.87572
188355
.89092
.89788
.90445
.91068
.91660
.92222
.92758
.93270
.93759
.94227
.94675
.95106
.95519
.95917
.96299
.96668
.97024
.97367
.97699
.98020
.98330
.98631
.98922
.99205
.99479
.99745
GB 4885-
.9500000
.47479
.63914
.74330
.81778
.87477
.92037
.95803
.98987
1-01730
.9900000
.95381
.9950000
.9990000
24、0
.9995000
2,70452
.9999000
GB4885
.9999500
.9999900
.9999990
.9999999
.5000000
: 1.08866
.68667
：54418
.50025
.16661
.34729
.33515
-32421
-30521
.29689
.28921
.28210
.26933
.25816
.25307
.24827
.241373
.23943
，23536
.23148
.22779
.22092
.21770
.21168
.2088.1
.20612
.19622
.19177
.18966
.18563
.18372
.15.166
.11.119
.13610
.12294
.11764
.6000m0
.46298
.36269
.21275
.18333
138-14
.12074
.07950
-06857
.04136
.02669
.02015
.01405
-00834
.00299
-00677
.01125
.02697
.03044
-03375
-03692
.03995
.04286
.04833
.05091
.05339
.05578
.05809
.06032
.06247
.06455
-06656
.06851
-07040
-07224
.08795
.10015
.10998
.11812
.12500
.13093
.13610
GB4885
.6500000
.92143
.2950m
.07088
.043.1
.02055
.00111
.01570
013042
.043.47
.05514
.06565
.07520
.08393
.09193
.09932
.11253
.11847
.12403
.12925
.13416
.13879
.14733
.15127
.15502
.15859
.16200
.16525
.16837
.17135
.17421
-17696
.17960
.18214
.18459
.18695
.18923
.19343
.19761
.19954
,20111
.20322
.21880
.23093
.24071
.21883
,25571
.26164
.26681
.7000000
.6195-1
.26085
.12982
105232
-00127
.0-11.17
.07319
.09911
.13942
.15655
.1619174
.18236
.19367
.20389
.21319
.22171
.22954
.23677
.243-18
.24473
.25557
.26105
.26619
.27103
.27361
.27991
-28405
.28795
.29166
.29858
.30181
.30191
.30787
.31072
.31345
.31608
.31861
.32105
.32340
.32567
.32787
.32999
，33204
.33103
.33596
.33783
.35523
.36740
.39234
-39832
7500000
.33295
.07533
.03632
.10584
.15523
.19291
.22299
.21778
.26870
，28667
.30233
-31619
.32854
，33961
.34969
.35886
136726
.37501
.38217
.38883
.39504
.10085
.40630
.41142
.41626
，42082
.12515
1-13688
.44381
.44706
.15016
14560m
.45875
，46139
.46391
.46639
.46871
.47326
.47540
.17747
.47948
:48142
：48331
.48514
.50091
-51325
.53155
.55003
.08379
.11142
.20878
.27243
.35474
.38373
.40781
，12826
4-1591
、17507
.49837
：50839
.52596
.53373
.54092
.55386
.55971
.56521
.57038
.57526
：57988
.58426
.58842
.59238
.60319
.60618
.60964
.61267
.61557
.61837
-62106
.62366
-62616
.62858
.63091
：63535
163747
.63952
.6-151
.64343
.64531
.66145
-67410
.68437
.69293
.70020
.71199
.8500000
.30876
.39642
-50079
.53580
.56432
.58818
.60854
.62621
.64173
.66790
.67907
.68924
.69865
.70711
.71502
.72236
.72920
.73559
.74158
.74721
.75252
.75754
.76228
.76678
.77106
.77514
.77902
.78273
.78628
.78968
.79294
.79607
.79907
.80196
.80475
.80743
.81002
.81253
.81494
.81728
.81955
.82174
.82387
.82593
.82793
.82987
.81665
.85983
.87055
.87949
.88709
.89367
.89943
.9000000
.40257
.53478
.61707
.67525
.71941
.75450
.78333
.80759
.82840
.84653
.86251
.87674
.88954
.90112
.91168
.92136
.03028
.93853
.94620
.95335
.96004
.96631
.97222
-97779
,98804
.99278
.99728
1-00957
GB4885--85
.950n000
.71731
.84005
.92238
.98218
1,41536
.9900000
.9950000
2,09203
.9990000
.9995000
.9999000
GB 4885--85
.9999500
.9999900
.9999990
4、16685
.9999999