This standard applies to the estimation of the one-sided lower confidence limit of the reliability of products with test results of success and failure, and can also be used in other occasions that can be transformed into such situations. Several individuals are randomly and independently selected from the product population as samples. This standard specifies the method for determining the one-sided lower confidence limit of the product reliability based on such samples. GB 4087.3-1985 Statistical processing and interpretation of data One-sided lower confidence limit of reliability of binomial distribution GB4087.3-1985 standard download decompression password: www.bzxz.net
This standard applies to the estimation of the one-sided lower confidence limit of the reliability of products with test results of success and failure, and can also be used in other occasions that can be transformed into such situations. Several individuals are randomly and independently selected from the product population as samples. This standard specifies the method for determining the one-sided lower confidence limit of the product reliability based on such samples.

National Standard of the People's Republic of China
Statistical interpretation of dataOnesided reliability confidence lower limit(Binomial distribution)
UDC 519.28
GB 4087.3-85
1.1 The statistical terms used in this standard can be found in GB-3358-82 "Statistical Terms and Symbols", and the reliability terms can be found in GB3187--82 "Basic Terms and Meanings of Reliability". 1.2 This standard is applicable to the estimation of the one-sided lower confidence limit of reliability when the product test results are in the two states of success and failure, and can also be used in other occasions that can be transformed into such a situation. Several individuals are randomly and independently selected from the product population as samples. This standard specifies the method of determining the one-sided lower confidence limit of product reliability based on such samples. 1.3 For a finite population, let its size be N and the sample size be n. When the sampling is with replacement; or when the sampling is without replacement, when n/N0.1, the n samplings can be considered independent. 1.4 The main contents of this standard are listed in the form of a table. 1.4.1 Calculation formula of the table
For sample size n, number of failures F, at the confidence level, the one-sided confidence lower limit R of the reliability R is calculated according to the following formula: F=0,RL-\V1-p
(\) R-*(1R)= 1
F=nl,RL=1-\V
F=n,Rt. = 0
For the test result nF and the specified, the probability that the product reliability R is not less than the corresponding tabulated value R is not low, that is, P iRR?
1.4.2 Parameter range and table distance of the numerical table:
?=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 RL values ​​not given in the numerical tables listed in this standard can be calculated by interpolation using the data provided in this standard, or by the approximate formula given in Appendix A of this standard.
1.6 Application Examples
National Bureau of Standards 19850129 Issued
19851001 Implementation
Example 1:
GB4087.3-85
100 pieces of explosive bolts were tested, and one failed. The confidence level is 0.90. Find the one-sided confidence lower limit of reliability. Corresponding to n=100, F=1, =0.90, the table shows RL= 0.96166
Example 2:
The service life of an electrical equipment follows an exponential distribution, and its mission time t. =250 hours. Now the number of tests n=80, the number of failures F=2. The failure time is not recorded, the confidence level is 0.90, and the upper limit of the failure rate of the equipment is calculated. According to the exponential distribution reliability estimation theory, Rt =e -auta
au=—ln
Corresponding to n=80, F=2, y=0.90, the table shows RL=0.93484
= 0,00026952
GB 4087.3--85
Reliability one-sided confidence lower limit RL table of binomial distribution NF
.50000
.70711
.79370
.84090
.87055
.89090
.90572
.91700
.92587
.93303
.93893
.94387
.94808
.95170
.95484
.95760||t t | ||.97555
.97638
.97716
.97789
.97857
.97921
.97982
.98039
.98093||tt| |.98144
.98192
.98238
.98282
.98324
.98363
.98401
.98437
.98504
.98536
.9 8566
.98595
.98623
.00000
.29289
.50000
.61427
.68619
.73555
. 77151
.79887
.82038
.83774
.85204
.86402
.87421
.88298
.89060
.89730
.9 0322
.90849
.91322
.91749
.92136
.92488
.92809
.93105
.93377
.936 28
.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|| tt||.63588
.67948
.71376
.74143
.76421
.78331
.79955
.81353
.82568|| tt | t||.89847
.90219
.90564
.90885
.91186
.91467
.91731
.91979
.92213||tt ||.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| |tt||.82791|| tt||.83561
.84266
-84912
.85508
.86058
.86568
.87042||tt ||.87483
.87896
.88282
.88645
.88985
.89306
.89609||tt| |.89894
.901 65
.90422
.90665
.90897
.91117
.91327
.91527
.91718
.91901
.92075
.92243
.92403
.92557
.92705
.00000| |tt||.12945||tt| |.26445
.36412
.44016
.50000
.54831
.58811
.62147
.64984
.67425
.69548
.71411
.73060
.74529
.75846
. 77033
.78109| |tt||.79089
.79985
.80808
.81565
.82265
.82914
.83517|| tt||.84078
.84603
.85094
.85555
.85989
.86397
.86782||tt ||.87145
.8 7490
.87816
.88126
.88420
.88700
.89222
-89465
.89697
.89920
.90132
.90337
.90533
.90721
.00000
.10910| |tt||-22849||tt ||.32052
.39308
.45169
.50000
.54049
.57492
.60456||tt| |.63033
.67296
.69079
.70678
.72120
.73426
.74616
.75703
.7670 1
.77621
.78471
.79258
.79990
.80672
.81906
.B2465
.82991
.83486
.83954
184395
.84813
.85209
.85585|| tt||.85943
. 86283
.86607
.86916
.87211
.87493
.87763
.88021
.88269
.88735
.00000
.09428
.20113
.28624
.35510
.41189| |tt||.45951|| tt||.50000
.53485
.56517
.59177
.61531
.63629
.65509||tt ||.67205
.68742
.70141
.71420
.72594
-73676
-74675||tt| |.75602
.764 63
.77265
.78014
.78716
.79374
.79993
.80575
.81125
.81645
.82136
.82602
.83044
.83465
.83865
.84246| |tt||.84609||tt| |.84957
.85288
.85606
.85910
.86201
.86481
.86750
.00000
.08300
.17962
.25857
.32380
.37853
.42508
. 46515
.50000| |tt||.53059
.58177
-60340
.62289
.64057
.65665
.67137|| tt||.68487
.69730
.70880
.71945
.72935
.73857
.74719||tt ||.75526
.7 6283
.76994
.77664
.78296
.78893
.79459
.79995
.80503
.80986
.81446
.81885
.82303
.82702
.83083
.83448| |tt||183798||tt ||.84133
.84455
.84764
.00000
.07413
-16226
.23579||tt| |.35016
.39544
.43483
.46941
.50000
.52726
.55170
.57374
.5937 1
.61190
.62853
.64379
.67084
.68288
.69407
.70450
.71424
.72335
.73191
.73995
.74752
.75467
.76142| |tt||.76781
.77387
.77962
.78508
.79028
.79523
.79996
.80447
.80878
.81291
.81686
.82065
.82429
.82778
4087.3-85
.00000
.066 97
.14796
.21669
.27528
.32575
.36967
.40823
.44234
.47274
.50000
.52458
.54686
.56714
.58569
.60271| |tt||.61839||tt| |.63287
.64630
.65878
.67041
.68128
.69145
.70099
.70996
.71841
.72638
.73391
.74103
.74779
.75420
. 76029
.76609
.77162
.77689
.78192
.79133
.79574
.79997
.80402| |tt||-80791
.00000
.06107
-13598
.20045
.25608
.30452|| tt||.34705
· 44830
.47542
.50000
.52238
.54284
.56163
.57893
.59491
-60973
.62350
.63633
-64832
-65954
.67007
-67997| |tt||-68929|| tt||.69808
.70639
.71425
.72171
.72878
.73550
.74190||tt ||.74800
.75381
.75937
.76468
.76975
.77462
.77928||tt| |.78375
.78 805
.00000
-05613
.12579
.23939
.28589
-32704
.36371
.50000
.52054
.53946
155695
.57315
.60225
.61536|| tt||.62764||tt ||.63915
.64997
.66017
.66978
.67887
.68747
.69562||tt| |.70336
.71072
.71771
.72438
.73074
.73681
.74262
.74817
.7534 9
.75859
.76349
.76819
.00000
-05192
.11702
.17432
.22474
.26940
.30921
.34491
.37711
: 40629
.43286| |tt||.45716
.47946
.50000
.51898
.53658
.55293
.56817
.58240
. 59573
.60823
.61998
.63105
.64149
.65135
.66069
.66954
.67794| |tt||.68593
.69353
.70076
.70767
.71426
.72056
.72660|| tt||.73237
.73791
.74322
.74832
.00000
.04830
-16365||tt ||.21178
.2 5471
.35943
.38810
.41431
.43837
.46054
·48102
.50000
.51764
.53408
.54944
.56382
.57731
.58999
.60193| |tt||.61319||t t||, 62384
.63391
.64346
-65252
.66114
.66934
.67715||tt ||.68460
-69171
.69851
.70502
.71125
.71722
.72295||tt| |-00000
-045 16
.10270
.15422
.20024
.24154
.27880
.31258
.34335
.37147
.39729
.42107
.44305
.46342
.48236
.50000| |tt||.51648||tt| |.53191
.54638
.55999
+57280
.58489
.59632
-60713
.61738
.62710
.63635
.64514
.65353
.66152
.66916
. 67645
.68344
.69653
.70269
.70859
.00000
.04240
.09678
.14581| |tt||.18989
.22967
.26574
.29859
.32863
.35621
.38161|| tt||.40509
.42685
-44707
.46592
.50000
.51546
.52999
.54368
.55660
.56880
.58035
.59129
.60168
.61156
.62095
.62991| |tt||.63845|| tt||.64660
.65440
.66186
.66900
.67585
.68242
.68873||tt ||4087.3-85
.00000
.03995
.09151
.13827
.18055
.21891||tt ||.25384
.28580
.31513
.34215
.36713
.39027
.41178
-43183
: 45056
.46809
.48454
.50000
.51456
.52830
.54128
.57626
.58677| |tt||.59676
.60629
.61537
.62405
.63234
.64028
.64787|| tt||.65516
.66215
.66886
.00000
.03778
.08678
.13147||tt ||.17209
-2 0911
.24297
.27406
.30270
.32916
.35370
.37650
.39775
.41760
.43618
.45362
.47001
.51376
.52678
.53913| |tt||.55084||t t||.56198
.57257
.58267
.59230
.60149
.61028
.61869||tt ||.62675
.63447
.64188
.64900
.00000
.03582
.08251||tt| |.12531
.164 39
.20015
.23299
.26324
.29120
.31712
.34122
.38464
.40427
-42269
.44001
.45632
.47170
.48624
.50000| |tt||.51304||tt| |.52542
.53719
.54838
.55905
.56922
.57894
.58823
.59711
.60563
.61378
.62161
.62913
.00000
.03406
. 07864
.11970
.15734
.19192
.22379
.25325
.28055
.30593
.32959| |tt||.35168
.37236
.39177
.41001
-42720
.44340.
.45872| |tt||.47322
.48696
.50000
.51240
.52419
.53543
.54615
.55639
. 56617
.57553
.58450
.59310
.60134
.60926
.00000
.03247
.07512| |tt||.11458
.15088
.18435
.21529
.24398
.27065
.29550|| tt||.31872
.34046
.36085
.38002
.39807
.41511
.43120||tt ||.44644
.4 6087
.47458
.48760
.50000
.51181
.52307
.53383
.54411
.55395
.56337
.57241
.58107
.58940
.98623
.98650| |tt||.98676||t t||.98701
.98725
.98748
.98770
.98791
.98812
.98832||tt ||.98851
.98870
.98888
.98906
.98939
.98955
.98971||tt| |.98986
.990 00
.99015
.99080
.99137
.99188
.99233
.99273
.99309
.99372
.99424
.99468
.99506
.99568
.99616
.99654| |tt||.99723||tt| |.99802
.99827
.99846
.99861
.99874
.99885
.99893
.99901
.99908
.99913
.99923
.99931
.96666
.96731
. 96793
.96853
.96911
.96967
.97021
.97073
.97123
.97172
.97219| |tt||.97264
.97308
.97350
.97391
-97431
.97470
.97508|| tt||.97544
.97580
.97614
.97772
.97911
.98033
.98142
.98240
.98327
.98479
.98605
.98712
.98804
.98953
.99069
.99162| |tt||.99330|| tt||.99441
.99581
.99627
.99665
.99695
.99720
.99742||tt ||.99760
.99776
.99790
.99803
.99814
.99823
.99832||tt| |GB4087.3--85||t t||.94688
.94791
.94891
.94987
.95079
.95168
.95254||tt ||.95336
.95416
.95493
.95568
.95640
.95710
.95778||tt| |.95844
.959 07
.95969
.96029
.96087
.96143
.96198
.96451
.96671
.96866
.97040
.97195
.97335
.97576
.97778
.97948| |tt||.98095||tt| |.98332
.98517
.98665
.98932
.99110
.99237
.99332
.99406
.99466
.99514
.99589
.99618
.99644
.99666
. 99686
.99703
.99719
.99733
.92705
.92847
.92984
.93115
.93242| |tt||.93364
.93482
.93596
.93705
.93811
.93914
.94013|| tt||.94109
. 94202
.94292
.94380
.94465
.94547
.94627
.94704
.94779
.95126
.95429
.95697
.95935
.96148
.96340
.96672| |tt||.96949|| tt||.97183
.97383
.97710
.97964
.98167
.98533
.98777||tt ||.98952
.99083
.99185
.99266
.99333
.99388
.99435||tt| |.99476
.995 11
.99541
.99568
.99592
.99614
.99633
.90721
.90901
.91075
.91243
.91404
.91559
.91709
.91853
.91993| |tt||-92128||tt| |.92259
.92385
.92507
.92625
.92740
.92851
.92959
.93063
.93165
.93263
.93359
.93800
.94186
.94526
. 94829
.95101
.95345
.95767
.96118
.96416
.96672
.97087
.97410| |tt||.97668
.98134
.98445
.98667
.98833
.98963
.99066|| tt||.99151
. 99222
.99282
.99333
.99377
.99416
.99451
.99481
.99508
.99533
.88735
.88955
.89166
.89369
.89565
.89753| |tt||.89935|| tt||.90280
.90444
.90602
.90756
.90904
.91047
.91187||tt ||.91321
.91452
.91579
.91702
.91822
.91938
.92473||tt| |.92942
.93 355
.93723
.94052
.94349
.94861
.95288
.95650
.95960
.96856
.97170
.97735
.98112
.98382
.98584
.98741| |tt||.98867||tt ||.98970
.99056
.99128
.99190
.99244
.99292
.99370||tt| |.99403
.99433
.86750
.87008
.87256
.87495
.87725
.87947
.8816 1
.88367
.88567
.88759
.88946
.89126
.89300
.89469
.89633
.89792
.89946
.90095
.90240
.90381
.90517| |tt||.91147
.91698
.92184
.93004
.93353
.93955
.94457
.94883
.95247
.95840
.96302
.96671
.97336
.97779
.98096
.98334| |tt||.98519|| tt||.98667
.98788
.98889
.98974
.99048
.99111
.99167||tt ||.99216
.99259
.99298
.99333
.84764
.85061
.85346||tt| |.85621
.858 85
.86140
.86386
.86624
.86853
.87075
.87496
.87697
.87891
.88079
.88262
.88439
.88610
.88777
.88939| |tt||.89096||tt| |.89820
.90453
.91013
.91510
.91955
.92356
.93049
.93627
.94116
.94535
.95217
.95747
.96172
.96936
. 97446
.97811| |tt||.98084
.98297
.98467
.98606
.98821
.98905
.98978|| tt||.99042
.99098
.99148
.99193
.99233
.82778
.83113||tt ||.83436
.8 3746
.84045
.84334
.84612
.84880
.85139
.85390
.85632
.85866
-86093
.86313
.86525
.86732
-86932
.87126| |tt||.87314||tt ||.87497
.87675
.88493
.89209
.89841
.90404
.90907||tt| |.91360
.92143
.92796
.93349
.93823
.94593
.95193
.95673
.9653 7
.97114
.97526
.97835
.98075
.98267
.98425
.98556
.98667
.98762
.98845
.98917
.98981
.99037
.99088| |tt||.99133
. 80791
, 81166
.81525
.81872
.82205
.82527
.82837
.83136
.83426
.83705
.83975
.84236
.84734
.84971
.85201| |tt||.85424|| tt||.85641
.85851
.86055
.86253
.87166
.87964
.88670||tt ||.89297
.89858
.90364
.91237
.91965
.92582
.93110||tt| |.93970
.946 38
.95174
.96138
.96781
.97240
.97585
.97853
.98068
.98243
.98389
.98513
.98619
.98711
.98792
.98863| |tt||.98926||tt| |.98983
.99033
.78805
.79218
.79615
.79997
.80365
.80720
.81062
.81393
.81712
.82020
.82318
.82606
. 82885
.83155| |tt||.83417
.83671
.83917
.84156
.84388
.84613
-84832|| tt||.85839
.86720
.87498
.88190
.88809
.89367
.90331||tt ||.91134
.9 1815
.92398
.93346
.94084
.94675
.95738
.96448
.96955
.97335
.97631
.97868
.98061
.98223
.98360
.98477| |tt||.98578||tt ||.98667
.98745
.98815
.98877
.98934
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