本标准适用于产品试验结果为成功、失败两种状态的可靠度单侧置信下限估计，也可用于可化为此种情形的其他场合。从产品总体中随机地、独立地抽取若干个个体作为样本，本标准规定了基于这类样本确定产品可靠度单侧置信下限的方法。 GB 4087.3-1985 数据的统计处理和解释 二项分布可靠度单侧置信下限 GB4087.3-1985 标准下载解压密码：www.bzxz.net
本标准适用于产品试验结果为成功、失败两种状态的可靠度单侧置信下限估计，也可用于可化为此种情形的其他场合。从产品总体中随机地、独立地抽取若干个个体作为样本，本标准规定了基于这类样本确定产品可靠度单侧置信下限的方法。

中华人民共和国国家标准
数据的统计处理和解释
二项分布可靠度单侧置信下限
Statistical interpretation of dataOnesided reliability confidence lower limit(Binomial distribution)
UDC 519.28
GB 4087.3-85
1.1本标准所用统计学名词见GB-3358—82《统计学名词及符号》，可靠性名询见GB3187--82《可靠性基本名词术语及处义》。1.2本标准适用于产品试验结果为成功、失败两种状态的可靠度单侧置信下限估计，也可用」可化为此种情形的其他场合。从产品总体中随机地、独立地抽取若千个个体作为样本，本标准规定了基于这类样本确延产品可靠度单侧置信下限的方法。1.3对有限总体，设其大小为N，样本大小为n。当抽取是有放回时；或当抽取是无放回的，焦n/N0.1时，n次抽取可以认为是独立的。1.4本标准的主要内容以数表形式列出。1.4.1数表的计算公式
对样本大小n，失败数F，在置信水平下，可靠度R的单侧置信下限R，按以下公式计算：F=0,RL-\V1-p
(\) R-*(1R)= 1
F=n-l,RL=1-\V
F=n,Rt. = 0
对试验结巢nF及指定的，产品可靠度R不小于对应的表列值R的概率不低，即P iRR?
1.4.2数表的参数范围与表距：
?=0.50(0.10)0.90,0.95,0.99
n=1（1）70（5）100（10）140（20)200（50)1000F=0（1）20
·（2)
1.5本标准所列数表未给出的RL值可利用本标准提供的数据内插计算，也可按本标准附求A给出！的近似公式计算。
1.6应用示例
国家标准局19850129发布
19851001实施
例1：
GB4087.3—85
某爆炸螺栓试验了100件，失败一件，规定置信水平为0.90，求可靠度单侧置信下限。相应于n=100，F=1，=0.90查表得RL= 0.96166
例2：
某电f设备使用寿命服从指数分布，其任务时间t。=250小时，今试验数n=80，失败数F=2。未记求失效时间，置信水平为0.90，求该设备失效率上限入uo根据指数分布可靠性估计理论有：Rt =e -auta
au=—ln
相应于n=80，F=2，y=0.90查表得RL=0.93484
= 0,00026952
GB 4087.3--85
二项分布可靠度单侧置信下限RL数表NF
.50000
.70711
.79370
.84090
.87055
.89090
.90572
.91700
.92587
.93303
.93893
.94387
.94808
.95170
.95484
.95760
.96005
.96222
.96418
-96594
.96753
.96898
.97153
.97265
.97369
.97465
.97555
.97638
.97716
.97789
.97857
.97921
.97982
.98039
.98093
.98144
.98192
.98238
.98282
.98324
.98363
.98401
.98437
.98504
.98536
.98566
.98595
.98623
.00000
.29289
.50000
.61427
.68619
.73555
.77151
.79887
.82038
.83774
.85204
.86402
.87421
.88298
.89060
.89730
.90322
.90849
.91322
.91749
.92136
.92488
.92809
.93105
.93377
.93628
.93861
.94078
.94280
.94468
.94645
.94810
.94966
.95113
.95251
.95382
.95505
.95622
.95734
.95840
.95940
.96036
.96127
.96215
.96298
.96378
.96455
.96528
.96598
.96666
.00000
.20630
.38573
.50000
.57859
.63588
.67948
.71376
.74143
.76421
.78331
.79955
.81353
.82568
.83635
.84578
.85419
.86173
.86853
.87469
.88030
.88542
.89013
.89447
.89847
.90219
.90564
.90885
.91186
.91467
.91731
.91979
.92213
.92433
.92641
.92838
.93025
.93202
.93371
.93531
.93684
.93830
.93969
.94102
.94229
-94351
.94468
.94580
.94688
.00000
.15910
.31381
.42141
.50000
.55984
.60692
.64490
.67620
.70242
.72472
.74392
.76061
.77526
.78822
.79976
.81011
.81945
.82791
.83561
.84266
-84912
.85508
.86058
.86568
.87042
.87483
.87896
.88282
.88645
.88985
.89306
.89609
.89894
.90165
.90422
.90665
.90897
.91117
.91327
.91527
.91718
.91901
.92075
.92243
.92403
.92557
.92705
.00000
.12945
.26445
.36412
.44016
.50000
.54831
.58811
.62147
.64984
.67425
.69548
.71411
.73060
.74529
.75846
.77033
.78109
.79089
.79985
.80808
.81565
.82265
.82914
.83517
.84078
.84603
.85094
.85555
.85989
.86397
.86782
.87145
.87490
.87816
.88126
.88420
.88700
.89222
-89465
.89697
.89920
.90132
.90337
.90533
.90721
.00000
.10910
-22849
.32052
.39308
.45169
.50000
.54049
.57492
.60456
.63033
.67296
.69079
.70678
.72120
.73426
.74616
.75703
.76701
.77621
.78471
.79258
.79990
.80672
.81906
.B2465
.82991
.83486
.83954
184395
.84813
.85209
.85585
.85943
.86283
.86607
.86916
.87211
.87493
.87763
.88021
.88269
.88735
.00000
.09428
.20113
.28624
.35510
.41189
.45951
.50000
.53485
.56517
.59177
.61531
.63629
.65509
.67205
.68742
.70141
.71420
.72594
-73676
-74675
.75602
.76463
.77265
.78014
.78716
.79374
.79993
.80575
.81125
.81645
.82136
.82602
.83044
.83465
.83865
.84246
.84609
.84957
.85288
.85606
.85910
.86201
.86481
.86750
.00000
.08300
.17962
.25857
.32380
.37853
.42508
.46515
.50000
.53059
.58177
-60340
.62289
.64057
.65665
.67137
.68487
.69730
.70880
.71945
.72935
.73857
.74719
.75526
.76283
.76994
.77664
.78296
.78893
.79459
.79995
.80503
.80986
.81446
.81885
.82303
.82702
.83083
.83448
183798
.84133
.84455
.84764
.00000
.07413
-16226
.23579
.35016
.39544
.43483
.46941
.50000
.52726
.55170
.57374
.59371
.61190
.62853
.64379
.67084
.68288
.69407
.70450
.71424
.72335
.73191
.73995
.74752
.75467
.76142
.76781
.77387
.77962
.78508
.79028
.79523
.79996
.80447
.80878
.81291
.81686
.82065
.82429
.82778
4087.3-85
.00000
.06697
.14796
.21669
.27528
.32575
.36967
.40823
.44234
.47274
.50000
.52458
.54686
.56714
.58569
.60271
.61839
.63287
.64630
.65878
.67041
.68128
.69145
.70099
.70996
.71841
.72638
.73391
.74103
.74779
.75420
.76029
.76609
.77162
.77689
.78192
.79133
.79574
.79997
.80402
-80791
.00000
.06107
-13598
.20045
.25608
.30452
.34705
·44830
.47542
.50000
.52238
.54284
.56163
.57893
.59491
-60973
.62350
.63633
-64832
-65954
.67007
-67997
-68929
.69808
.70639
.71425
.72171
.72878
.73550
.74190
.74800
.75381
.75937
.76468
.76975
.77462
.77928
.78375
.78805
.00000
-05613
.12579
.23939
.28589
-32704
.36371
.50000
.52054
.53946
155695
.57315
.60225
.61536
.62764
.63915
.64997
.66017
.66978
.67887
.68747
.69562
.70336
.71072
.71771
.72438
.73074
.73681
.74262
.74817
.75349
.75859
.76349
.76819
.00000
-05192
.11702
.17432
.22474
.26940
.30921
.34491
.37711
：40629
.43286
.45716
.47946
.50000
.51898
.53658
.55293
.56817
.58240
.59573
.60823
.61998
.63105
.64149
.65135
.66069
.66954
.67794
.68593
.69353
.70076
.70767
.71426
.72056
.72660
.73237
.73791
.74322
.74832
.00000
.04830
-16365
.21178
.25471
.35943
.38810
.41431
.43837
.46054
·48102
.50000
.51764
.53408
.54944
.56382
.57731
.58999
.60193
.61319
，62384
.63391
.64346
-65252
.66114
.66934
.67715
.68460
-69171
.69851
.70502
.71125
.71722
.72295
-00000
-04516
.10270
.15422
.20024
.24154
.27880
.31258
.34335
.37147
.39729
.42107
.44305
.46342
.48236
.50000
.51648
.53191
.54638
.55999
+57280
.58489
.59632
-60713
.61738
.62710
.63635
.64514
.65353
.66152
.66916
.67645
.68344
.69653
.70269
.70859
.00000
.04240
.09678
.14581
.18989
.22967
.26574
.29859
.32863
.35621
.38161
.40509
.42685
-44707
.46592
.50000
.51546
.52999
.54368
.55660
.56880
.58035
.59129
.60168
.61156
.62095
.62991
.63845
.64660
.65440
.66186
.66900
.67585
.68242
.68873
4087.3-85
.00000
.03995
.09151
.13827
.18055
.21891
.25384
.28580
.31513
.34215
.36713
.39027
.41178
-43183
：45056
.46809
.48454
.50000
.51456
.52830
.54128
.57626
.58677
.59676
.60629
.61537
.62405
.63234
.64028
.64787
.65516
.66215
.66886
.00000
.03778
.08678
.13147
.17209
-20911
.24297
.27406
.30270
.32916
.35370
.37650
.39775
.41760
.43618
.45362
.47001
.51376
.52678
.53913
.55084
.56198
.57257
.58267
.59230
.60149
.61028
.61869
.62675
.63447
.64188
.64900
.00000
.03582
.08251
.12531
.16439
.20015
.23299
.26324
.29120
.31712
.34122
.38464
.40427
-42269
.44001
.45632
.47170
.48624
.50000
.51304
.52542
.53719
.54838
.55905
.56922
.57894
.58823
.59711
.60563
.61378
.62161
.62913
.00000
.03406
.07864
.11970
.15734
.19192
.22379
.25325
.28055
.30593
.32959
.35168
.37236
.39177
.41001
-42720
.44340.
.45872
.47322
.48696
.50000
.51240
.52419
.53543
.54615
.55639
.56617
.57553
.58450
.59310
.60134
.60926
.00000
.03247
.07512
.11458
.15088
.18435
.21529
.24398
.27065
.29550
.31872
.34046
.36085
.38002
.39807
.41511
.43120
.44644
.46087
.47458
.48760
.50000
.51181
.52307
.53383
.54411
.55395
.56337
.57241
.58107
.58940
.98623
.98650
.98676
.98701
.98725
.98748
.98770
.98791
.98812
.98832
.98851
.98870
.98888
.98906
.98939
.98955
.98971
.98986
.99000
.99015
.99080
.99137
.99188
.99233
.99273
.99309
.99372
.99424
.99468
.99506
.99568
.99616
.99654
.99723
.99802
.99827
.99846
.99861
.99874
.99885
.99893
.99901
.99908
.99913
.99923
.99931
.96666
.96731
.96793
.96853
.96911
.96967
.97021
.97073
.97123
.97172
.97219
.97264
.97308
.97350
.97391
-97431
.97470
.97508
.97544
.97580
.97614
.97772
.97911
.98033
.98142
.98240
.98327bzxZ.net
.98479
.98605
.98712
.98804
.98953
.99069
.99162
.99330
.99441
.99581
.99627
.99665
.99695
.99720
.99742
.99760
.99776
.99790
.99803
.99814
.99823
.99832
GB4087.3--85
.94688
.94791
.94891
.94987
.95079
.95168
.95254
.95336
.95416
.95493
.95568
.95640
.95710
.95778
.95844
.95907
.95969
.96029
.96087
.96143
.96198
.96451
.96671
.96866
.97040
.97195
.97335
.97576
.97778
.97948
.98095
.98332
.98517
.98665
.98932
.99110
.99237
.99332
.99406
.99466
.99514
.99589
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.99644
.99666
.99686
.99703
.99719
.99733
.92705
.92847
.92984
.93115
.93242
.93364
.93482
.93596
.93705
.93811
.93914
.94013
.94109
.94202
.94292
.94380
.94465
.94547
.94627
.94704
.94779
.95126
.95429
.95697
.95935
.96148
.96340
.96672
.96949
.97183
.97383
.97710
.97964
.98167
.98533
.98777
.98952
.99083
.99185
.99266
.99333
.99388
.99435
.99476
.99511
.99541
.99568
.99592
.99614
.99633
.90721
.90901
.91075
.91243
.91404
.91559
.91709
.91853
.91993
-92128
.92259
.92385
.92507
.92625
.92740
.92851
.92959
.93063
.93165
.93263
.93359
.93800
.94186
.94526
.94829
.95101
.95345
.95767
.96118
.96416
.96672
.97087
.97410
.97668
.98134
.98445
.98667
.98833
.98963
.99066
.99151
.99222
.99282
.99333
.99377
.99416
.99451
.99481
.99508
.99533
.88735
.88955
.89166
.89369
.89565
.89753
.89935
.90280
.90444
.90602
.90756
.90904
.91047
.91187
.91321
.91452
.91579
.91702
.91822
.91938
.92473
.92942
.93355
.93723
.94052
.94349
.94861
.95288
.95650
.95960
.96856
.97170
.97735
.98112
.98382
.98584
.98741
.98867
.98970
.99056
.99128
.99190
.99244
.99292
.99370
.99403
.99433
.86750
.87008
.87256
.87495
.87725
.87947
.88161
.88367
.88567
.88759
.88946
.89126
.89300
.89469
.89633
.89792
.89946
.90095
.90240
.90381
.90517
.91147
.91698
.92184
.93004
.93353
.93955
.94457
.94883
.95247
.95840
.96302
.96671
.97336
.97779
.98096
.98334
.98519
.98667
.98788
.98889
.98974
.99048
.99111
.99167
.99216
.99259
.99298
.99333
.84764
.85061
.85346
.85621
.85885
.86140
.86386
.86624
.86853
.87075
.87496
.87697
.87891
.88079
.88262
.88439
.88610
.88777
.88939
.89096
.89820
.90453
.91013
.91510
.91955
.92356
.93049
.93627
.94116
.94535
.95217
.95747
.96172
.96936
.97446
.97811
.98084
.98297
.98467
.98606
.98821
.98905
.98978
.99042
.99098
.99148
.99193
.99233
.82778
.83113
.83436
.83746
.84045
.84334
.84612
.84880
.85139
.85390
.85632
.85866
-86093
.86313
.86525
.86732
-86932
.87126
.87314
.87497
.87675
.88493
.89209
.89841
.90404
.90907
.91360
.92143
.92796
.93349
.93823
.94593
.95193
.95673
.96537
.97114
.97526
.97835
.98075
.98267
.98425
.98556
.98667
.98762
.98845
.98917
.98981
.99037
.99088
.99133
.80791
，81166
.81525
.81872
.82205
.82527
.82837
.83136
.83426
.83705
.83975
.84236
.84734
.84971
.85201
.85424
.85641
.85851
.86055
.86253
.87166
.87964
.88670
.89297
.89858
.90364
.91237
.91965
.92582
.93110
.93970
.94638
.95174
.96138
.96781
.97240
.97585
.97853
.98068
.98243
.98389
.98513
.98619
.98711
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