GB 2689.4-1981 Best linear unbiased estimation method for life test and accelerated life test (for Weibull distribution)
Some standard content:
National Standard of the People's Republic of China
Best linear unbiased estimation method for life test and accelerated life test (for Weibull distribution) GB 2689·4-81
1 Scope of application
This standard specifies the procedures and methods for the best linear unbiased estimation method for constant stress life test and accelerated life test. It is applicable to the data processing of the fixed number truncated life test and accelerated life test of the life of the electronic component products (hereinafter referred to as products) obeying the Weibull distribution, shape parameter m>0, characteristic life n0, location parameter? =0, and the number of test samples in each group is n≤25. 2 Symbols and meanings
Number of test samples;
Truncation failure number r=1, 2.n
Failure sample number j1.2
Stress level number i1, 2,
Number of test samples under the ith stress level; Truncation failure number under the ith stress level; Failure time of the ith failed sample;
Failure time of the rth failed sample:
Shape parameter of Weibull distribution;
Weibull Characteristic life of the distribution,
Location parameter of Weibull distribution;
Location parameter of log-Weibull distribution;
Scale parameter of log-Weibull distribution;
Absolute temperature (K);
Electrical stress:
Boltzmann constant, k=0.8617×10-4eV/°K; Activation energy;
Scale parameter of log-Weibull distribution under the i-th group of stress levels, i1.2; Location parameter of logarithmic Weibull distribution, i=1,2…|; shape parameter of Weibull distribution under the i-th group of stress levels, i=1,2….1; characteristic life of Weibull distribution under the i-th group of stress levels, i=1.2…1; C(n,r,i) coefficient of the best linear unbiased estimate of α when the number of samples is n and the number of truncated failures is r; D(n,r,j) coefficient of the best linear unbiased estimate of uμ when the number of samples is n and the number of truncated failures is r; modification of gr.n
m Positive coefficient;
m; weighted average;
Λ(t) instantaneous failure rate at time t;
(t) average failure rate from 0 to time t; tEwww.bzxz.net
average life
reliable life with reliability R;
issued by the Bureau
The Fourth Ministry of Machine Building Industry of the People's Republic of China 28
October 1, 1981
Drafted by the Standardization Institute of the Fourth Ministry of Machine Building
TT; ~ T.
Intercept of the acceleration equation;
Slope of the acceleration equation;
GB 2689.4—81
The inverse of the variance of ;/α in the i-th test with n samples and r truncated failures; The inverse of the variance of ui/r in the i-th test with ni samples and r truncated failures; Temperature T; Life acceleration factor for temperature T; Electrical stress V: Life acceleration factor for electrical stress V.; The inverse of the variance of m;/m in the i-th test with ni samples and r truncated failures. 3 Procedures and methods for life test data processing 3.1 Test truncation and processing of failed samples
…-Under normal circumstances, the test truncation should make the failure number r≥30%n. When the failure number cannot reach 30%n, at least r≥4. Failed samples caused by reasons other than the product itself should not be included in the number of test samples n. 3.2 Processing of failure time The failure time of failed samples shall be determined in accordance with Chapter 6 of GB2689.1-81 "General principles for constant stress life test and accelerated life test methods" (hereinafter referred to as "General principles"). The failure times shall be arranged in order from small to large and processed according to the format of Table 1.
Failure sample number
Failure time
Sample model
Sample quantity
Test time
C(n, r,1)
(n, r,2)
(n, t, r)
Stress condition
Failure standard
Production time
C(n, r, j) Igtj
C(n, r,) Igt
C(n,r,2) Igt2
C'en,r, r) Igt,
Din,r,i
n,r,2)
D(n, r, r)
(n, r, j) lgtj
D(n, r,1) Igt
D(n, r,2) Igt:
D(n, r, r) Igt.
In the table: C(n, r,), D(n, r, i) values can be found in Table 1 of the Reliability Test Table (hereinafter referred to as the Test Table). 3.3 Calculation of distribution parameters
3.3.1u is calculated as follows:
μ=2.3026M2
Where: M2 is given in Table 1.
3.3.2m is calculated as follows:
m = 0.43439r, n/ M
Where: Mi is given in Table 1, 9r, can be found in Table 1 of the Test Table. 3.3.3n is calculated as follows:
Wu Zhong: Qu formula (1) is given.
（3）
3.4 The failure rate (t) is calculated as follows:
GB2689-4—81
1(1)=m.tm-/nm
Where: m and n are given by formulas (2) and (3); the value of t is given in advance. 3.5 The average failure rate (t) is calculated as follows: (t)=tm-l/nm
Where: m and n are given by formulas (2) and (3); the value of t is given in advance. 3.6 The average life is calculated by the following formula:
te=nF(1+
wherein: n is given by (3);
[(1+1/m)] is given in Table 4 of the Test Method. 3.7 The reliable life tR is calculated by the following formula:
th=n(2.3026lgR)1/m
wherein: m and n are given by formulas (2) and (3); the R value is given in advance. A. Procedure and method for temperature stress accelerated life test 4.1 Test assumptions
a. The shape parameter m is independent of temperature
b. The relationship between the characteristic life n and the temperature T ('K) conforms to the Arrhenius equation. n=ea+b/not
c. -Under normal circumstances, the number of truncated failures should be r ≥ 30% n; when the number of failures cannot reach 30% n, at least r ≥ 4. 4.2 mi, ui (i-1, 2, 1) at each stress level shall be calculated according to the formula specified in Chapter 3. 4.3 Calculation of the accelerated life equation n = ea + b /. 4.3.1 In the accelerated life equation, a and b shall be in the format specified in Table 2. Stress level number
Stress level number
In the table: An, refer to Table 1 of the "Test Table", μi is given by Article 4.2. 30
(4)
(5)
(6)
A,:
Calculate α and
GB 2689.4-- 81
GH- IM
4.3.2 The characteristic life of the product under a certain temperature stress T condition is calculated according to the following formulan =ea+b/T
Where: a and b are given by formulas (8) and (99). 4.4 The weighted average value m of the shape parameter m is calculated in the format of Table 3. Stress level serial number
In the table: (check Table 1 (B) of the "Test Table"); Q; value is given by Article 4.2. The m value is calculated as follows:
m=(L-1)/Q
4.5 The activation energy E is calculated as follows:
Where: b is given by Gong Wu (9), and h is the Boltzmann constant. 4.6 Acceleration factor 7~7. Calculated as follows: Tia
Where: b is given by formula (9); T and To values are given in advance.eb(1/Ta1/Tr)
4.7 The product is in a certain The failure rate A(t) under temperature T is calculated as follows: a(t)=m.tm-1/nm
wherein: n and m are given by formulas (10) and (11), and t is given in advance. 4.8 The average failure rate A(t) of a product under a certain temperature T is calculated as follows: A(t)=tm-1/nm
wherein: n and m are given by formulas (10) and (11); t is given in advance. 4.9 The average life tE of a product under a certain temperature 7 is calculated as follows: tp=nr(1+1/m)
wherein: n and m are given by formulas (10) and (11): 7
（9）
（10）
th,· m
（12）
（14）
（15）
（16）
See Table 4 of the Test Table.
GB 2689.4—81
4.10 The reliable life tR of the product under a certain temperature T is calculated as follows: tR=n（-2.3026lgR)1/m
Where: n and m are given by formulas (10) and (11); R is given in advance. 5 Data processing procedures and methods for electrical stress accelerated life test 5.1 Test assumptions
a. The shape parameter m is independent of electrical stress;
b. The relationship between the characteristic life n and electrical stress conforms to the inverse power law equation n =1/kV° or n ea+blgv
Where: a=lgk; b=c.
c. In general, the number of truncated failures should be r ≥ 30% n. When the number of truncated failures cannot reach 30% n, at least r ≥ 4. 5.2 mi, Ui, ui, n for each stress level; (i = 1, 2.!) are calculated according to the formula specified in Chapter 3 5.3 Calculation of the accelerated life equation n = 1/kV° 5.3.1 α and b in the accelerated life equation are calculated according to the format specified in Table 4. Table 4
Electrical stress level number
Electrical stress level number
dzn,(lgvi)
n,igho)?
In the table: A, check Table 1 of the "Test Table"; u is given by Article 5.2. 32
(lga)?
ArhuilgV
Calculate a and b as follows:
5.3.2c and k as follows:
Where: a and b are given by formulas (18) and (19). GB 2689. 4-- 81
BM- IH
c=—6
5.3.3The characteristic life n of the product under a certain electrical stress V is calculated as follows:n; =ea+6igl,
Where: α and b are given by formulas (18) and (19). 5.4The weighted average value m of the shape parameter m is calculated in the format of Table 5. Stress level serial number
in the table; 1F, check Table 2 of the "Test Table"; (; value is given in Article 5.2. m is calculated as follows:
m=L-1/Q
5.5 The acceleration factor t~t is calculated as follows:
th-r.=(Vi/Vo)*
Where: the c value is given by formula (21), and the Vo and V; values are given in advance. 5.6 The failure rate (t) of the product under a certain electrical stress V condition is calculated as follows: A(t)=m.tm
Where: the n and m values are given by formulas (22) and (23) and the t value is given in advance . 5.7 The average failure rate element (t) of the product under a certain electrical stress V condition is calculated according to the following formula: T(t)=tm-1/nm
Wherein: the values of n and m are given by formulas (22) and (23): the value of t is given in advance. 5.8 The average life t of the product under a certain electrical stress condition is calculated according to the following formula: L
（23）
（24）
（25）
（26）
GB2689.4—81
t=n(+)）
Wherein: the values of n and m are given by formulas (22) and (23). Factory (1+1/m) Check Table 4 of the "Test Table". 5.9 The reliable life tR of the product under a certain electrical stress V condition is calculated as follows: tR=n(-2.3026igR)1/m
Where: n and m values are given by formulas (22) and (23); R value is given in advance. 34
（27)
（28）
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