GB 12282.2-1990 Life test tables Simple linear unbiased estimation tables (extreme value distribution, Weibull distribution)

GB 12282.2-1990 Life test tables Simple linear unbiased estimation tables (extreme value distribution, Weibull distribution) GB12282.2-1990 standard download decompression password: www.bzxz.net

National Standard of the People's Republic of China
Tables for life testing
Tables for good linear unbiased estimate(CLUE)(Extreme-yalue distribution, Weibull distribution)
Tables for life testing
Tables for good linear unbiased estimate(CLUE)(Extreme-yalue distribution, Weibull distribution) 1 Subject content and scope of application
1.1 Subject content
GB 12282.2—90
This standard gives the numerical tables required for the simple linear unbiased estimate of the parameters of the extreme value distribution (or Weibull distribution) in the constant-number truncated life test. 1.2 Scope of application
This standard can be used in conjunction with the national standard GB2689.3 Simple linear unbiased estimate method for life testing and accelerated life testing (for Weibull distribution, 26≤≤200) or it can be used alone. 2 Reference standards
GB 3187 Basic terms and definitions of reliability
CB 2689 Life test and accelerated life test methods 3 Tables for simple linear unbiased estimation
3.1 Terms and symbols
The terms used in this standard conform to the provisions of GB3187. Simple linear unbiased estimate of the location parameter of the extreme value distribution. Simple linear unbiased estimate of the scale parameter of the extreme value distribution: Estimation of the shape parameter of the Weibull distribution: Estimation of the characteristic life of the Weibull distribution; other symbols are the same as GB2689.3.
3.2 Weibull distribution and extreme value distribution
The distribution function of the one-parameter Weibull distribution is F(e)
Where, ≥0 is the shape parameter, >0 is the characteristic life. robzxz.net
Now X=lnt, where t is the product life, x is the logarithm of the life, and it obeys the extreme value distribution. Its distribution function is approved by the State Technical Supervision Kitchen on February 27, 1990 and implemented on October 1, 1990
where =1,
GB 12282. 2—90
Fa(x) - 1 - exp[- exp
8AXAα
+are respectively called the location parameter and scale parameter of the extreme value distribution. When &=0, =1, it is called the standard extreme value distribution. 3.3 Simple linear unbiased estimation
When the product life obeys the Weibull distribution, randomly insert pieces from this batch of products and conduct a fixed number tail life test. When there are failures, stop the test. The failure time of the failed product is tst.t(rn)
When the number of samples is ≥25, use GI.UE to find the parameters in the extreme value distribution. The estimation formula of and p is: Erx, -Mi
where,X,=lgt,M,=
(2S -r- 1)x.
0.4343mr,
2.3026X, - E(Z...)
2.3026XE(Z...)\
X,n..,E(Z..>and S see Figure 2.
From and i, we can get the estimation of shape parameter m and characteristic life in Weibull distribution m = gr.a/ g
where gr is the correction factor,
3.4Number table
In the table, t.. is the inverse of the variance of a/, and A is the inverse of the variance of /. (2)
GB12282.2--90
Application example
Example: The life of an electronic product follows the Weibull distribution. Now 30 samples are drawn from a batch of products and the life is tested under a certain stress. The test was stopped when 10 samples failed. The failure time of each failed sample is listed in the table below. Based on the 10 failure times, GLUE was used to find the estimated value of the sum.
Number of samples n=30
Number of failed samples
Time of peak effect
Since r0.9n, the truncated number - 10
Number of failed samples
rX is obtained from formulas (1) and (2). M1
c.4343 X nk...
Where: M,=
34- 191 --- 25, 7482
0. 4343 X 9. 9128
Failure time
X,=lgti
M1=25.7482
= 2. 3026X, E(Z,)6 = 2. 3026 X 3. 4191 ( 0. 9746) X 1. 9611 - 9. 7841From formulas (3) and (4), we get
= e = e. i9 = 17 719
—3.8353
—2, 8156
—1. 9407
—1.6687
—1.2556
—1.0880
—0. 6704
— 0. 2164
—0.1112
—3. 8731
—1.7098
—1.1323
GB12282.2—90
Table for simple linear unbiased estimation
Du Qi,
2,0282
0, 8459
..-0.7190
—0.5998
.-0.4866
—0.3782
—0.1709
—0.0701
—2.3723
—2. 0194
-1, 5284
—0. 7652
—0, 6475
—0.4298
GB12282.2—90
12-6213
16-8574
3,1145
4,1895
0, 9450
—0.1289
—0. 0321
—3. 9445
—2. 9269
—1,3797
-·1.0680
—0.9336
—0, 4752
—0. 3774 | | tt | 8847
—2.0924
—1.4179
-1, 2544
—1.1080
—0.9746
—0.2360
GB 12282.2—90
3, 1169 ||tt | 8919
—0.5687
—0. 2851
—0.1074
GB 12282.2—90
1,u165
—3,0270
—2.1604
—1. 3281
—1.1834
—1.0519
—0. 9307
—0.8178
—Q.5144
—0.4217
—0.1579
—2. 5124
GB12282.2—90
23,7199
38-1762
—1. 9260
—1.5212
—1.3630
--1. 0B83
— 0.7509
—0.6512
—0.5560
—0.3761
—0. 2900
—0.2057
—0.1227
: 0. 0404||tt ||—1.9578
—1.7411
GB 12282.2—90
12,2082
3,1661
25. 60-11||tt| |：1.5573
--1. 3967
(—1.0040
—0.8929
—0.5958
—0.5056
—0, 4184
—0.3338||tt| |—0. 2511
—0.1698
E<7r,)
—4.1326
—2.6031
—1.9887
—1.7725
—1. 5893
12282.2—90
n· bra
—1.2867
—1.1574
—1. 0386
—0.9283
—0.8249
—0.7271
0, 6341
—0.5449
—0.2147
0,1745
—4.1607
—2.0187
—1. 4609|| tt||GB 12282.2—
35-7369
28-3087
Liu=36
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