Statistical interpretation of data - One-sided confidence lower limit of reliability for binomial distribution
Some standard content:
ICS03.120.30
National Standard of the People's Republic of China
GB/T 40872009
Replaces GB/T 4087.3—1985
Statistical interpretation of data-One-sided confidence lower limil of reliabililyfor binomial distribution
Published on October 15, 2009
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China Administration of Standardization of the People's Republic of China
Implemented on December 1, 2009
GR/T 40872009
Normative references
3 Terms, definitions and symbols
3. 1 Terms and definitions
3.2 Symbols
1 Determination of the lower confidence limit of a single reliability test
4.! Calculation formula for one-sided lower confidence limit of reliability Table 4.2 Determination of one-sided confidence limit of reliability by set of tables (see Table A.1 in Appendix A) Appendix A (Normative Appendix) One-sided lower confidence limit R of reliability of binomial distribution Tables Appendix B (Informative Appendix) Approximate formula for one-sided lower confidence limit of reliability of binomial distribution 3 "Statistical processing and interpretation of data" includes the following national standards: Statistical processing and interpretation of data GB/T 3359 Determination of statistical tolerance interval GB/T 3361 GR/T 4087 GB/T 1088 GB/T 4089 GB/T4882 GB/T 4883 --- GB/1 4885
----GB/T 4889
GB/T 1890
GB/T 8055
--.-GB/T 8056
GH/T 6380
GB/T 10092
Statistical Processing and Interpretation of Data
Statistical Processing and Interpretation of Data
Statistical Processing and Interpretation of Data
Statistical Processing and Interpretation of Data
GB/T 4087—2009
Comparison of two means in the case of paired observationsOne-sided lower confidence limit for reliability of binomial distribution
Estimation and test of binomial distribution parameters
Estimation and test of Poisson distribution parameters
Statistical processing and interpretation of data
Test of normality
Statistical processing and interpretation of data
Determination and treatment of outliers in normal samples
Lower confidence limit for reliability of complete samples of normal distributionStatistical processing and interpretation of data
Statistical processing and interpretation of data
Statistical processing and interpretation of data
Statistical processing and interpretation of data
Statistical processing and interpretation of data Statistical processing and interpretation of data
Statistical processing and interpretation of data
Estimation and test of mean and variance of normal distributionTest of mean and variance of normal distributionParameter estimation of Pearson distribution (Pearson distribution)Judgment and treatment of outliers in samples from exponential distributionJudgment and treatment of outliers in samples from Pearson distributionStatistical processing and interpretation of dataComparison of test results - GB/T10094
Confidence limits of quantiles and coefficient of variation of normal distributionThis standard replaces GB/T4087.3-10854Statistical processing and interpretation of data"One-sided lower confidence limit for reliability of item distribution"This standard replaces GB/T Compared with 4087.31985, the main changes are as follows: the standard format has been revised according to the requirements of GB/T11.1--2000 Standardization Guidelines Part 1: Structure and Writing Rules of Standards; the terminology has been modified according to GB/T3358.1--2009 Statistical Terms and Symbols Part 1: General Statistical Terms and Terms Used in Probability, and additional terms, symbols and definitions have been added; ... the number of significant figures in Appendix A has been increased from 5 to 7; the calculation program in Appendix B has been changed from BASIC language to SP1.US language. Appendix A of this standard is a normative appendix, and Appendix B is an informative appendix. This standard was proposed by the National Technical Committee for Standardization of Statistical Methods (SACTC21) and drafted by: Northeast Normal University, Peking University, China National Institute of Standardization. The main contributors to this standard are: Zhang Baoxue, Fang Xianghuan, Li Dan, Ding Wenxing, Yu Zhenfan. The previous versions of the standards replaced by this standard are: -G3/T 4087. 3-1985.
GB/T40872009
This standard is applicable to the estimation of the one-sided lower limit of 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. Ten individuals are randomly and independently selected from the product population as samples. This standard specifies the method for determining the one-sided lower limit of product reliability based on such samples. The main contents of this standard are listed in the form of a table, but the parameters of some occasions may not be in the table. In this case, they can be calculated by the approximate formula in Appendix B, or directly calculated by the S PLUS program in Appendix B. Scope
Statistical processing and interpretation of data
One-sided confidence lower limit of reliability of binomial distribution
GB/T 4087—2009
1-2 individuals are randomly and independently selected from the product population as samples. This standard specifies the method for determining the one-sided confidence lower limit of product reliability based on such samples. For a finite population, let its size be N and the sample size be n. When the sampling is random sampling or when the sampling is random sampling, but n/N<0.1, the n samplings can be considered independent. This standard is applicable to the estimation of the one-sided confidence lower limit of reliability of products with test results in the two states of success and failure, and can also be used in other occasions that can be transformed into such situations.
Normative referenced documents
The clauses in the following documents become the clauses of this standard through reference in this standard. For any dated referenced document, all its accompanying amendments (excluding errata) or revisions are not applicable to this standard. However, all parties that have reached an agreement based on this standard are encouraged to study whether to use the latest versions of these documents. For undated referenced documents, their latest versions are applicable to this standard. GB/T2900.13 Telecommunications terminology Credibility and service quality (GB/T2900.13--2008, IECG0050 (191): 1990Amd.1: 1999 and Anmd.2.2002, IDT)
GB/T3358.1 Statistical vocabulary and symbols Part 1: General statistical terms and terms using probability (GB/T3358.12009, IS03534-1: 2006, 10)
(R/T3358.2 Statistical terms and symbols Part 2: Applied statistics ((R/T3358.2-2009, IS03534-2: 2006, IDT)
3 Terms, definitions and symbols
3. 1 Terms and definitions
GB/T 2900.13, the terms and definitions established in GB/T 3358.1 and GB/T 3358.2 apply. For reference, some terms are directly quoted from the above standards.
3.2 Symbols
The symbols established in GB/T 3358.1 and GB/T 3358.2 and the following symbols apply to this standard. Sample size
Confidence level
One-sided lower confidence limit of reliability
Number of test results with failures
4 Determination of one-sided lower confidence limit of reliability
4.1 Calculation formula for one-sided lower confidence limit of reliability For sample size n, number of failures F. At the confidence level, the one-sided lower confidence limit R of the reliability R is calculated according to the following formula: F.-- 0, R.. --VI -.Y
F - - 1, RL - 1--
. (3)
GB/T 4087-2009
Formula (1), (3), and (4) directly give the calculation formula for R:. The calculation method of (2) can be found in the recommended method in Appendix B. 4.2 Determine the one-sided confidence limit of reliability by table lookup method (now Table A in Appendix A, 1) 4.2.1 Parameter range of the table and the table
--0. 50 (0. 10) 0. 90, 0. 95, 0,99n=1(1)70(3)100(10)4G(20)20C(50)1000F—0(1)20
4. 2. 2 Application of tables
Given the confidence level 7, sample size n and number of failures F, the table (Table A.1) listed in Appendix A of this standard can be used to obtain the one-sided confidence lower limit R. of product reliability. The R. value not given in Table A.1 can be calculated using the data provided in this standard, or can be calculated by referring to the approximate formula given in Appendix B of this standard. Appendix B also provides the SP.1S program for approximate calculation. 4.2.3 Application examples
Example 1:
A coal-fired snail light test tested 15 pieces, and none of them failed. The confidence level was specified to be 0.90. The one-sided confidence lower limit of reliability was calculated. Corresponding to n-100, F-1, 7-0. 53, check Table A. [ and get: R.. - : 0. 961 66o 4
Example 2:
The user of the electronic equipment obeys the index distribution. Its task time is tm253. The number of tests is 80, the number of failures is F: -2, and the effective time is not recorded. Set the average to G.90, and find the upper limit of the failure rate of the equipment. According to the index distribution, the reliability estimation theory is; R. - e
Ke becomes 80, F -2, 0. 90, clear Table A. 1 and get ta
R: 0.934 840 C
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Appendix A
(Normative Appendix)
Reliability lower limit of binomial distribution R. Table A.1 Reliability lower limit of binomial distribution R. Table y-0. 50 | |tt | 3
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Table A.1 (continued)
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0.0000000
0,0000000
o .cCCooD0
0.coc0000
o.c660000
9.C483049
0109280| |tt||0.1636165
o,2t17664
6.2547022
0.2932144
0.3279183
0.3594317
0.3881005
0.4113133| |tt||0,4383744
0.4605370
0.4810176
0.5176 429
0.5345838
0.5494413
0.5638181
0.5773067
0.5899858
0,6019263
0.6131909
0.6238357
0.6339135
0,6434595
0.6525236
$, 6611377
3.6693354
9.6771457
0.6845957
9.6917093
0.6985100
D.7C50160
0.7112479
0.7172217
9.7284571
GB/T 4087—2009
0.8506063
0.8534610
0.8562084
0.8588549
0.8614056
9.8638660
3.8662398
0.8685326
0.8707483
0.872890 5
0.8749633
0.8769651
0.8789115
0.8807933
0.8826176
0.8843877
0.8861322
0.8877711| |tt||0.8893887
0.8909625
0. 8981291
0.9045352
0,91G1286
0,9151028
G.9195657
G.9235642
c.9364916||tt ||C.9362664
0.9411577
0.5453510
0.9521673
.3574730
0.9617 182
9.0653511
0.9744544
0.9781090
0.5805432
(.6829700
0.9845720
e9850546
0.98722.1
0.9882072
e.5830489
6.9897789
Q.99C4172| | tt |
0.8161155
0.8488035
0.8513559
0.8538995||tt ||0.8563208
C.8586637
0.8609308
C8631270
6.8652538
6.5573165
C.8712574
C. 8731415
0.8749709
0.8767485
G.884929E
G.5520309
0. 8584135
0.9940359
Q.9903691
0.5136000
0.9211312
D.9279603
0.9334875
0.5382272||tt ||0.9459323
0.9519250
0.9567281
0.9653795
0.9711356
0.9752h57| | tt | ||0.9891687
0.5898950
0.9903714
0.9908781
0,9913343
Table A.1 (continued)
0.6116561
U,8152550
0.8187130
0.8220551
0.8252708
0.8283722
C.8313657| |tt||0.8312566
C.8370499
0.8397502
0.842363 4
0.8418918
C,8473409
0.8497135
0.8520143
0.8542449
o.85h409t
0.8585104||tt ||0.8695514
0.8625338
0.8716576
0.8796451|| tt | ||0.9396968
0.9463848
0.9517372||tt| |0.9613773
0.9678069
0.9724016
0.9758486
n.9785301
U,9806769
0.9824312
0.9838918|| tt||0.9851326
0.9861941
0.9871146
0.9886293
0.989261heart
n.9898263
0.99033-3
0.7921795
0.7961501
0.7999724
n.8036533
0.8072019
0.8106211
0.8139271
3.8171167
.821992
0.8231785
9.8260622
5.8288521| |tt||5. 831541
0.8317241
0.8367105
0.8391720
0.8415658
0.8438793
0.8461311
0.8183183
0.85 83860| |tt||0.8971993
0.8719810
0.8319007
0.8880943
G.8936710
C.9C33082
9113432
C.9181155
C.923973!
c.9334613 | | tt | |tt||00822289
0.9835957
0. 9847663
0.9857820
0.9874536
0.0881507
0.9857735
Q.0893350
0.7727021
0.7770452
0.7812257
3.7852515
0.7891330
9.7928761
0. 7964885 | 8414068
0.2240999
Q.8267117
0.8292474
c. 5317101
c.$311027
.8151138
C.8547534
e.8532536
0.8708323
0.5776068
0.8837961
0.8912162
0.9333343
0.9104739
0.9168536
0.9272251
0.9352958
0.9117555
0.9533888|| tt ||0.9611486
0.9666934
0.9708535
0.9740895
0.9766785
0.9787979
0.9805638
0.9820580
0.9833393
0.9846494
0.985-210
0.9862770
0.9870403
0.9877218
0.9883358
0.7532247
.7579396
0.7621781
C.7668498
0.7710634
0.7751265
0.7790492
0.7828361
0.7900348 | | tt | .814 G15G
0.8172851
0.8198872
0.8318107
0.8423068
0.8515465
0.8597632
0.8671187
8737404
t.8851836
C.2947254
G.9028022
e,9097282
0.9209888
0.9297517
0.5367617
. 9493949
0.9578198
0.9538393
0.9653562
6.9715695
0.9746804
0.9759805
0.5728979
0.5 805203| |tt||0. 9819114
.9831168
0.9841710
0.9851022
0, 9859292
0.9566600
0.9873358
0.7337466
0.7388339
0.7437310
0.7484472
0.7529923
.75 73777
u,761Ge91
0. 7656555
0.76HE447
0.7734627
0.7771558
0.7807305
0.7841933
0.7875469
0.7907993
. 7939524
0.7970128
C.7 999829
(.8028680
0.8056709
C.8185684
C.8298603
6.8398295
C.8485918
C.8366297
0.8637747
0.8761203
0. 8864137
C.8951305
0.9026937
0.5147525
0.9242068
0.0317739
0.4454992
0.9544903
0.9609852
0.9658585
0. 4696489
0.0726820
0.9751639
0,9772327
0.5789833
0.9804836
0.58178-3
0.9829218||tt ||0.9848189
0.9856173
0.9863366
0.5099560
0.0000900
0.0000000
0.0000000
t.0000000||tt ||0.0000000
0.0000000
o,0cog0o
o.co00060
0.000c0co
0.0000000
0.0000000
0.0000005|| tt||0,0451584
C.1026103
c.t541816| |tt||6.20022ng
0.2415327
0.2787990
0.3125862
0.3433425
0.3714721
0.3972914
U.4210741
t.4430528
0.4534230
0.4 823566
0.5000000
0.5154803
0.5319095
0.5163845
0.5599902
0.5728011
0.5818934
0.59 63173| |tt||3.6071292
0.6173764|| tt||0.6271031
0.6363475
.6451450
C.6535269
c.6615214
0.6691550
0.5761533||tt| 0.6834363
0.6901239
0.6965348
0.702 6855
.7085921
.0000000
0.0000000
0.0000500
0,0000093
0.0000099
0.0000000||tt ||0,0000000
0.0000000
0.0000000||tt| |0.0000000
0.0000000
G.G0OUOCC
0.o0ccc00
,u423967
9.0966912
0.1157754
0.1898685| |tt||U.2296581
C.2657340
Q.298588 3
c.3286316
0.3562099
0.3816127
0.4050879
0.4268468
0.4470703
0.4659163
0,4835193
0.5154613
3.5299954
0 .5436826
0.5565958
0.5687981
.5903470
0.5912933
0.6016833
0.6115573
D.6299073||tt ||0.6384430
0.646G027
C.5513974| |tt||0.6618559
0.6659591
0.6758472
0.6824178
0.6887264
Table A.1 (continued)
0.0000000||tt ||0.0000000
0.0000000
0.0000000
0.08 01000
0,c006000
0.0000000
0.0000000
0.0900000
0.0000000
0.0000000
D.0000000||tt ||0.0000990
0.0000905
0.0399533||t t | |tt||0.3671238
0.3902706
0.411 7840
0.4318325
0.4505591
0.4685907
0.4845386
0.5000000
0.$145607
.5282975||tt| |3.5112790
0.5535649
0.5652094||tt| |0.57G2620
0.58657671
0.5967636
C.6C62885
0.6153730
0.6243186
0.G323107
0.6402V54
0.6478744
Q.6551596
0.6621 492
0.6688614
0,0000000
0.0000000
0.0000000
o,00cc000
0.0c00000
0.0000000
0.0000000
0.0095500||tt| |0.0000000
0.0000000
0.0000000
0.0000000
0,0000000
.OUGGOC
0.000G0GG
0.$377762
5.086G958
0.1314426
0.1720711
0.2090975
0.2429629
G.2740530
C-302593l
0.3291612
0.3536051
0.3764985||tt| |0.3977488
0.4175980
0.4361820
0. 4536159 | | tt | | Q.4700G51 | 0.5510770
0,5725732
0.5826690
0.5922987
0.6014945
, 6l02841
0.6186950
0,6267503
0.6418807
0.6189957
0.0000000
0.5555030
0.0500000
0.0909990
0 .0500990
0.0000900
0.0990000
0.0000000
o.cocooco
0.0000600
9,0000 hearts
0.0000032| |tt||0.0358240
0.0824337 | ||0. 3412145
0.3636658
0.3846385
0.4042726
0.4226949
0.4100095
0.4563170
0.4717025
0.4 862407| |tt||0.500GGO0
0,5130417
0.5251205
0.5371860
0.5183821
C.5590494
.5692245
0.6882274
0.5971138
0.6056248
0.6137811
0.6216121
0.6 203292
GB/T4087——2009
0.0000000
0.0000000
0.c000000
G.GGGOCOO
c,cC9060|| tt||0.00G0000
0.0006000
0.000c000
0.00000 00 | |tt | | 0.0000000 | 500co0o0
2.0340637
0.0785711
0. 1196754
Q.1573286
0.1919160
C.2237856
0.2532429
0.2505488
0.3059305
0.3295836||tt ||0.3516799
0.3723647
0. 3917713
0.41G0147
9. 1271552
5,4434042
0.4587208
0.4732178
Q.4859579
.5000000
o.51zxyic
0.5241910
0.5354299
0.5451495
0.5563856
0.5661767
.5755334
0.5815060
0.60134 35
0.6092635
0.00G0000
6.0CC0000
0.0000000
0.0000000
0.0000000
0.0000000
0,0000000
0,0000900
0.0000500
0.0000000
0.0000000
0.0000900
0.0000000| |tt||0.0000003
0.0000000
0.0000000
0.0000000
0.00000C0
0.0324682
0.075054C
heart, on145477
0.1508650
0.1843418
0.21h2895
0,2439794
0.2706188
0.2955929||tt ||0.3187203
0.34c4565
D.3608193
0.3800199
.3980741
0.4151066
0.4312017
0.4464356| |tt||0.1508745
0.±745791
0.4876048
0.5000000
0.511809G
0.5230715
0. 5441111
0.5539522
0.5633753
0.5724084
0.5510750
0. 5893978
GB/T 4087-- 2009
5.7142684
9.7107283
.7249828
0.7300117
0.7349225
0.7396282
0.7441691
0.74855 48
0.7527925
0.7568899
0.7698532|| tt||0.7645899
0.7684054
0.7?20050
e.7754948
C.7788787
0.7821630
0.7853503||tt| |0.7881462
0.7914535
0.8052953
0.5174137
3. 8281114
0.8376256
0.8461416
0.8538091
0.8670599
0.8781555
0.8874589
0.8951784
0.0 186619| |tt||0.9267822
G.9414063
0, 9511608 | | tt | 00558
0. 9804517 | | tt | |0.7062347
0.711G413
.7168521
6.7218785
(.7267289
C.7314134
G.7359102||tt| |0. 7403171 | | tt | C.7707176
G.7740244
G.7772376
0.7920223
0.8049663
0.8163943
9.8265565
3.8356534
c8438426
0.8579953
0.8697971
0.8797853
0.8883531
0.9022800
0.9131170
0.92 17914| |tt||0.5374117
0. 9478321 | | tt | |0.0776280
0.9791184
0.9804233
0.9615713
0. 9825974
0. 9835135
0.9843373
Table A.1 (continued)
0.6753114
0.6815155
0.6874866
0.6932380
0.6987816| |tt||0.7341290
U.7092888
0.7142727
0.7190879
0.7237435
0.7282478
e,7326073
G.7 368287
G.7109158
0.7448850
0.7487305
0.7524623
0.7560850
0.759Gc25
0.7636205||tt| |0.7787492
0.7925197
0.80467GG
0.8151873
0.8351645
0.8338770
0.8485336
0. 8614874
0.8812278
e.8960130
0.9075722
0.5167998
0.59331178
0.9445025
0.9524229
5.9583653
0.9529876
0.9655865
G.9697131
Q.9722358
0.9743702
0.7620心2
0 .9777858
0.9791741
0.9803986
0.9814871
Q.9824601
0.9833381
0.6555325
o,GG24091|| tt||0.G687384
0.6748347
.6807112
0.6863787
0.6918487
0.6971313
9.7022357
0. 7119444
Q.7165661
:7210412
0.7253765
0.7255797
C.7335569
c,7376119
0 . 74518C8 | | tt | 98702
0.8531777
0.8614129
0.8858057
0.5920273
Q.9118082
0, 9294231
0.9411730
0.9495689
0.9558676
0.960767G
0.9646881
0.0678963
0.0705699
0.9 728325
0,9717724
0.9764532
0.9779248
0.9792223
6.1803767
0.0814090
G .9823381
0.6433019
0.6199595
0.6564314
0.G626400
6685284
0.6744078
e.6795891|| tt || 0.6853827 | 7185824
C.7227621
G.7268189
0.7307590
0.7345864
0.7522023
0.7676250
0.7812492||tt ||0.7033483
0.8041865
6.8139419
0.8308075
n.8448630
0,8567704
0.8669764
0. 8835657
0.8961824
0.9068173
9.0254285
0.5378135
0.5467148
0.9533699
0.9585469
0.9 626896| |tt||0.9660791
3.5685047
0.9712948
0.9733446
0.975120?
0.9766718
0. 9780-64
0.9792656
0.0803564
0.5813389
0.6168747
0.6241955
0.6312414
0.6380281
0.6508788
0.6569677
0.6528476
0.6685296
0.6710235
0.6793384
0.6844827
0.6894537
C.6912913
0.6989695
0.7035089
0.7079115
0.7121855
0. 7163365
.7263634
9. 738928
0.7551776
0.7695221
0,7822791
0.7936977
0.8339781|| tt |9214346
0.9:5-15140
0.9508722
0.4563262
996091
0.9642624
0,9672388
C. 5697579
0.9715168
0.5737881
0.9754256
0.9768707||tt ||0.9781553
n.9793045
0.9803389
c,5973958
0.605C883
0.6124925
0.6196240
0.6264984
0.6331285
0.6395265
0.6457062
0.6516774
0.6574499
0.6630345
0.6684406
0.6736754
0.6787479
Q.5336647
C.6884335||tt| |G.6930699
0.6975521
(1.7019147
0.7061523
0.7 256554
0.7427303
0.7578039
0.7832088
0.7940120
G.8726814
0.8282470
0.8412262
0.8527258
0710964
0.8853927
.9174395
C. 9311815 | ||0.9704899
0.9724555
0.9741764
0.97:6550
0.9770442
0.9782519
C.9793306
Tip: This standard content only shows part of the intercepted content of the complete standard. If you need the complete standard, please go to the top to download the complete standard document for free.