標準解讀
《GB/T 4885-1985 正態(tài)分布完全樣本可靠度單側(cè)置信下限》是一項國家標準,主要針對的是基于正態(tài)分布的數(shù)據(jù)集,在給定的置信水平下計算可靠度(即生存函數(shù)值)的單側(cè)置信下限。該標準適用于具有已知均值和方差或可估計這些參數(shù)的情況下的產(chǎn)品質(zhì)量控制、可靠性分析等領(lǐng)域。
在實際應(yīng)用中,當處理一批產(chǎn)品時,如果其壽命遵循正態(tài)分布,則可以通過本標準提供的方法來評估這批產(chǎn)品的最低預(yù)期性能水平。具體來說,它定義了一系列步驟和技術(shù),包括但不限于確定樣本大小、計算統(tǒng)計量以及查找相應(yīng)的臨界值表等,用以構(gòu)建出一個合理的區(qū)間估計,從而幫助決策者了解在特定置信水平下產(chǎn)品至少能夠達到的性能標準。
如需獲取更多詳盡信息,請直接參考下方經(jīng)官方授權(quán)發(fā)布的權(quán)威標準文檔。
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中華人民共和國國家標準
UDC引9.28
正態(tài)分布完全樣本可靠度單側(cè)置信下限
GS4885一[1b
One一sidedreliabilityconfidencelowerlimit
(Normaldistributioncompletesample)
1引言
1.1本標準所用統(tǒng)計學名L及符號見GB3358-82《統(tǒng)計學名詞及符號》,可靠性名詞術(shù)語見國標
GB3187-82《可靠性墓本名詞術(shù)語及定義)))o
1.2本標準適用于產(chǎn)品特性值h可合理地認為服從正態(tài)分布的情形。其分布密度函數(shù)為
f(x)二甲二1_rexp
uV乙Jt
r1rx一u\2-)
l一二r、-一戶一一夕J,一。。久x久+‘.
Zu
式中拜為總體期望值,a為總體標準差。
1.3本標準基1'產(chǎn)品特性值X來自同一總體的樣本大小為,的獨立隨機樣本XIsx2,.....,X.及給
定的置信水、}
的方法。
,,當N,"未知時,對于給定的特性值上(或下)限給出了確定可靠度單側(cè)置信下限R,
2可靠度單側(cè)皿信下限的確定
本標準給出兩種確定可靠度下限的方法,查表法和直接法。查表法簡便易行,但精度較低。在精
度要求較高的場合應(yīng)采用直接法。
2.,查表法
2.1.1
2.1.2
2.1.3
由樣本觀察值x1,X2,??,x計算樣本均值x,樣本標準差:
x=告全:
‘孫件1.(二一x)2
V幾一1.刁
據(jù)特性值七(一卜)限計算系數(shù)K.
當規(guī)}Lh限U時,K=we.U-x.r
當規(guī)定下限L時,K
x一L
s
X
由給定的置信水平Y(jié),樣木大小。及算得的K值,反杏本標準附錄A的K系數(shù)表,即得特州
國家標準局1985-01-2,發(fā)布
1985一10一01實施
GB4885一85
泊x的可靠度單側(cè)置信卜限R,,。
2.1.4杏表,J<例
某壓力容器承受內(nèi)壓,其抗壓強度服從IF杰分布。該種容器10次旅力試驗的破壞應(yīng)少}分別為:2565,
2960,12685,2755,2790,2720,2634,2860,2905,2825kg/cm'a容器抗壓強度的下限規(guī)定為l=2200
kg/cm2。給定置信水平v二0.90,要求估計該容器可靠度單側(cè)置信下限。
根據(jù)破壞應(yīng)力的10個試驗數(shù)據(jù)計算樣本均值萬和樣本標準差,:
x二2769.9.s二123.1
K二x-蘭
2769.9一2200
二二一二:
123.1
4.6300
根據(jù)v=0.90,。二10,K=4.6300杏附錄A,},的K系數(shù)表得:
Ri--0.9990
即該容器在置信水、I'v=0.90之卜的可靠度單側(cè)置信下限為。.9990.
2.2直接法
2.2.1求非線性方程
了
cPW-nXi+Jn下
n-聲,“)了竺-,
v)—h
廠件掃
一專(·
I),:^dh二1一v··?(1)
解X,。式
v二
少(
些,
x,
給定特性值上限時
給定特性i&ir限時
卜-工
·)—標準正態(tài)分布函數(shù)
rtn子)一參數(shù)為
刀一I
的伽瑪函數(shù)
2.2.2計算可靠度單側(cè)置信下限RL
凡二0(XL)·········,······················?!ぁぁぁぁぁぁひ?2)
木標準附錄B(參考件)給出了直接法的一種計算機程序。
GB4885一85
附錄A
確定正態(tài)分布可靠度單側(cè)置信下限的K系數(shù)表
(補充件)
本系數(shù)農(nóng)的參數(shù)范圍與表距:
1`0-01-0.05,0.10,0.20,0.40(0.10)0.90,0.95,0.99
RL=0.50,0.60(0.05)0.95,0.99,0.9'5,0.9',0.9'5,0.9',0.9'5,0.9',0.9',0.9
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3.30548
3.31538
3.59331
3.60798
3.62207
3.63560
3.64862
3.66115
3.67324
3.68490
3.69616
3.70704
3.94038
3.9562分
3.97155
3.98622
4.00033
4.01392
4.02702
4.03966
4.05187
4.06367
n八計n比nn曰nll門曰nll
肚犯3334腸363738
2.53738
2.54484
2.55207
2.55908
2.56588
2.57248
2.57889
2.58512
2.59118
2.59707
2.88464
2.89289
2.90088
2.90862
2.91613
2.92342
2.93051
2.93739
2.94408
2.95060
3.02326
3.03182
3.04011
3.04816
3.05596
3.06353
3.07089
3.07804
3.08499
3.09175
3.32495
3.33421
3.34319
3.35189
3.36033
3.36852
3.37648
3.38422
3.39174
3.39906
3.71757
3.72776
3.73764
3.74721
3.75650
3.76552
3.77428
3.78279
3.79107
3.79913
4.07508
4.08613
4.09684
4.10722
4.11.729
4.12707
4.13657
4.14580
4.15478
4.16351
41042.043.044045.(]46.047048.0490500
2.64842
2.68932
2.72295
2.75126
2.7755.1
2.79669
2.81532
3.00736
3.05258
3.08977
3.12109
3.14796
3.17136
3.19149
3.15071
3.19769
3.23633
3.26888
3.29680
3.32112
3.34256
3.46288
3.51374
3.55557
3.59081
3.62106
3.64740
3.67062
3.86937
3.92536
3.97142
4.01023
4.04354
4.07255
4.09813
4.23968
4.30040
4.35037
4.39247
4.42860
4.46008
4.48784
刁:0泊為川川
的708090剛11012D
40
GB1885一85
n
.5000000.6000000
丫_.05
65000007000000
7500000.8000000
一4.46450
一1.68585
一1.17668
一95339
一.82264
一,73445
一66983
一61985
一57968
一2.71769
一1.08959
一74556
一。58284
一,48284
一41311
一36073
一。31943
一28574
一2.02205
一。82575
一。54681
一40819
一。32046
一25806
一21052
一。17264
一.14147
一1.43100
一,58033
一,35547
一。23707
一15961
一10333
一05980
一,02473
.00437
.93469
.34938
.16799
.06600
.00313
05449
.09482
.12768
.15518
.52144
.12736
.02072
11001
.17273
22037
.25834
.28962
31602
.54648
.51843
.49432
.47330
.45477
.43826
42344
41003
.39782
.38665
25754
.23347
21260
.19427
.17799
.16341
.15025
.13828
.12734
.11729
11521
.09267
07303
.05570
.04027
.02640
.01385
0024#
.00807
01772
02906
.05038
06904
.08557
.10035
.11367
.12576
.13680
.14694
15630
.17868
.19909
21704
23299
.24731
.26025
.27203
.28282
29275
.30193
.33872
.35854
.37606
39169
.40576
41851
.43016
.44084
.45069
.4.5982
.37636
.36686
.35805
34984
34218
.33499
.32825
.32189
.31589
.31022
10801
.09940
.09140
.08392
07692
.07034
.06415
.05831
.05278
.04754
.02655
03494
04267
.04989
05666
06303
.06904
.07471
06009
.08518
16497
.17304
18057
.18762
.19424
.20047
.20635
21191
.21719
.22220
.31045
.31838
.32580
.33276
.33930
.34547
.35129
.35681
.36204
36702
.46830
.47622
.48363
.49059
.49714
50332
.50917
.51471
.51997
.52498
11.012013014015.016.0洲18.019.0翻21.022023.024.025J26.027.0280290300
31.0
32.0
33.0
34.0
35.0
36.0
37.0
38.0
39.0
40.0
30484
29973
.29487
.29024
28582
.28160
.27755
.27368
.26997
.26640
.04257
03783
.03333
.02902
.02491
02098
.01720
.01359
01011
00677
.09003
09464
.09904
.10324
.10726
.11110
.11479
11833
.12173
12501
22696
.23150
.23583
23997
24393
.24773
.25137
.25487
26823
.26147
.37175
.37627
38058
.38471
.38866
.39245
.39609
.39958
.40294
.40618
52975
53430
53865
54282
54681
.55064
.55432
.55785
.56126
.56454
26297
25967
.25650
.25343
.25047
24762
24486
.24219
.23960
23710
.00356
.00046
.00252
.00541
.00819
.01088
.01348
.01600
.01844
.02081
.12816
.13120
.13413
13696
.13969
.14234
.14490
.14738
.14978
.15211
.26459
.26760
.27051
.27331
.27603
.27865
28119
.28365
.28604
.28836
.40931
.41232
.41523
.41804
.42076
.42339
.42595
.42842
.43081
.43314
.56771
.57076
.57371
.57657
57933
.58200
.58460
.58711
58955
59192
八JCIJn”nn幻﹄八UonU們
41424344454647銘49邪
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.19927
18608
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16604
.15818
15133
.04108
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06944
.07991
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09637
10301
.17211
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20019
21059
.21940
.22698
23360
.30827
.32380
.33635
.34678
.35562
.36325
.36991
.45319
.46886
.48156
.49212
.50109
.50884
.51562
.61234
62836
.64136
.65219
.66141
.66937
.67635
8090如1020
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3.0
4.0
5.0
6.0
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.8500000
一17385
.09477
.21906
.29928
.35757
.40276
.43927
46965
.49550
9000000
.13802
.33448
.44389
51878
.57482
.61904
.65521
68557
.71157
.9500000
.47479
.63914
.74330
.81778
.87477
.92037
.95803
98987
1.01730
.9900000
.95381
1.12967
1.24616
1.33091
1.39644
1.44925
1.49310
1.53034
1.56253
.9950000
1.10789
1.29577
1.41979
1.50995
1.57968
1.63589
1.68258
1.72226
1.75657
.9990000
1,40923
1.62643
1.76807
1.87069
1.94994
2.01382
2.06690
2.11201
2.15103
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
.51786
.53748
.55489
.57048
.58456
59736
.60906
61983
.62978
.63901
.73419
.75412
77187
78782
80226
81543
.82749
83861
84890
.85846
1.04127
1.06247
1.08141
1.09848
1.11397
1.12812
1.14112
1.15311
1.16423
1.17458
1.59076
1.61579
1.63821
1.65845
1.67686
1.69371
1.70920
1.72352
1.73682
1.74920
1.78667
1.81337
1.83729
1.85889
1.87855
1.89654
1.91309
1.92839
1.94260
1.95584
2.18527
2.21565
2.24289
2.26750
2.28989
2.31039
2.32926
2.34671
2.36291
2.37802
26.0
.64760
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.66316
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1.18425
1.19330
1.20181
1.20982
1.21739
1.22455
1.23135
1,23780
1.24395
1.24981
1.76078
1.77164
1.78186
1.79149
1.80059
1.80921
1.81740
1.82518
1.83259
1.83966
1.96822
1.97983
1.99075
2.00105
2.01079
2.02002
2.112878
2.03711
2.04504
2.05261
2.39215
2.40540
2.41788
2.42964
2.44076
2.451311
2.46131
2.47083
2.47990
2.4RR56
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95106
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96299
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25540
26075
26588
27079
27551
28004
28441
28861
29266
29657
1.84642
1.85289
1.85909
1.86503
1.87074
1.87624
1.88152
1.88662
1.89153
1.89627
2.05985
2.06677
2.07341
2.07978
2.08590
2.09178
2.09744
2.10290
2.10816
2.11325
2.49683
2.50475
2.51234
2.51963
2.52663
2.53336
2.53984
2.54608
2.55211
2.55793
33.34.35.36
八“nnllnnnnlJ八
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41.0
42.0
43.0
44.0
45.0
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.75834
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76395
.76663
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77174
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.97367
97699
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98922
99205
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.99745
1.00003
1.30035
1.30399
1.30752
1,31094
1.31425
1.31746
1.320.58
1.32360
1.32653
1.32939
1.90085
1.90529
1.90957
1.91373
1.91775
1.92165
1.92544
1.92912
1.93269
1.93617
2.11816
2.12291
2.12750
2.13196
2.13627
2.14045
2.14452
2.14846
2.15229
2.15602
2.56355
2.56899
2.57425
2.57435
2.58429
2.58909
2.559374
2.59826
2.60265
2.60691
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02242
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09334
1.35412
1.37364
1.38959
1.40294
1.41433
1.42421
1.43289
1.96632
1.99018
2.00970
2.02607
2.04006
2.05220
2.06287
2.18836
2.21397
2.23492
2.25250
2.26753
2.28057
2.29205
2.64399
2.67336
2.69741
2.71760
2.73486
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1.75221
1.90117
2.00893
2.09212
2.15915
2.21483
2.26216
2.30310
1.76082
2.01747
2.18263
2.30176
2.39361
2.46758
2.52902
2.58123
2.62639
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2.12255
2.29431
2.41812
2.51352
2.59033
2.65111
2.70832
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2.53652
2.670611
2.77381
2.85693
2.92592
2.98454
3.03525
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2.64427
2.85016
2.99791
3.11157
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3.13463
3.29502
3.41831
3.51745
3.59973
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2.37092
2.39950
2.42533
2.44883
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2.50848
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2.54135
2.
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