This standard specifies the procedures and methods for simple linear unbiased estimation methods for constant stress life tests and accelerated life tests. GB 2689.3-1981 Simple linear unbiased estimation methods for life tests and accelerated life tests (for Weibull distribution) GB2689.3-1981 Standard download decompression password: www.bzxz.net

National Standard of the People's Republic of China
Simple linear unbiased estimation method for life test and accelerated life test (for Weibull distribution) 1 Scope of application
GB 2689.3 - 81
This standard specifies the procedures and methods for simple linear unbiased estimation method for constant stress life test and accelerated life test. It is applicable to the data processing of life test and accelerated life test of electronic component products (hereinafter referred to as products) whose life follows Weibull distribution, whose shape parameter m>0, characteristic life n>0, position parameter=0, and the number of test samples in each group is n>25. ​​
2 Symbols and meanings
Number of test samples;
Number of truncated failures, r=1,2,….n;
Serial number of failed samples, =! ,2..
Stress level sequence number, i=1,2,…………; Number of test samples under the i-th stress level; Number of truncated failures under the 1st stress level, Failure time of the j-th failed sample;
Failure time of the r-th failed sample;
Shape parameter of Weibull distribution;
Characteristic life of Weibull distribution;
Location parameter of Weibull distribution,
Location parameter of logarithmic Weibull distribution;
Scale parameter of logarithmic Weibull distribution;
Absolute temperature (K),
Electrical stress,
Boltzmann constant, k=0.8617×10㎡1eV/°K, Activation energy:
Scale parameter of logarithmic Weibull distribution under the i-th group of stress levels, i=1.2, (, Location parameter of logarithmic Weibull distribution under the i-th group of stress levels, i=1,2 ,…,! , shape parameter of Weibull distribution under the i-th group of stress levels, i=1,2…, ", characteristic life of Weibull distribution under the i-th group of stress levels, i1,2,, mean of the r-th order statistic of standard extreme value distribution, Kr.n
when the number of samples is r, unbiased coefficient of ①; m
m; weighted average, bZxz.net
A(t) instantaneous failure rate at time t; ||tt ||(t) Average failure rate from 0 to 1; th:
Average life;
Reliable life with reliability R:
Issued by the Bureau
Proposed by the Fourth Machine Industry Ministry of the People's Republic of China
Trial implementation on October 1, 1981
Standardization Institute of the Fourth Machine Industry Ministry
Intercept of the acceleration equation;
Slope of the acceleration equation;
GB2 689.3-81
The inverse of the variance of u;/α in the i-th test with n samples and r truncation failures; the inverse of the variance of ;/ in the i-th test with n samples and r truncation failures; the inverse of the variance of m;/m in the i-th test with ni samples and r truncation failures; the correction factor of m;
Temperature 7: For temperature 7. The life acceleration factor of electrical stress is the life acceleration factor of electrical stress Vo. 3 Methods and procedures for life test data processing 3.1 Test truncation and processing of failed samples
In general, the test truncation time should make the number of failures r≥30%n; when the number of failures 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 in accordance with GB2689.1-81 Chapter 6 of the General Rules for Constant Stress Life Test and Accelerated Life Test Methods (hereinafter referred to as the General Rules) is determined. Arrange the failure times in order from small to large and process them according to the format of Table 1.
Sample model
Number of samples
Test time
Failed sample serial number
3.3 Calculation of shape parameter m and characteristic life n 3.3.1 Calculation procedure of shape parameter m
Stress conditions
Failure criteria
Production time
Failure time
3.3.1.1 Calculation of the scale parameter rX,-M
0.4343nKr.n
(2Sr-1）X,-
0.4343nK.n
A: X, (i1, 2r) and M are given in Table 1: 22
X,- Igti
When r/n<0.9
（１）
When r/n0.9
GB 2689.3-81
nKr.n, refer to Table 2 of the Reliability Test Table (hereinafter referred to as the Test Table); S=the integer part of [0.892n+1], or refer to Table 2 of the Test Table. 3.3.1.2 The shape parameter m is calculated as follows: m=
Where: 9rn Refer to Table 2 of the Test Table. 3.3.2 Calculation of characteristic life n
3.3.2.1 The location parameter μ of the logarithmic Weibull distribution is calculated as follows: u
Where: X, given in Table 1 of Article 3.2;
2.3026 X,E(Zr-n ) C
t2.3026X,-F( Zs.n )o
E (Zr) Refer to Table 2 of the Test Table;
α is given by formula ().
3.3.2.2n is calculated as follows:
Where: Given by formula (3).
3.4 ​​Failure rate A (t) is calculated as follows: n=e
When r/n<0.9
When r/n≥0.9
2(t)=mtm-l/nm
Where: m and n are given by formulas (2) and (4); the value of t is given in advance. 3.5 Average failure rate A (t) is calculated as follows: A(t)=tm-1/nm
Where: m and n are given by formulas (2) and (4); the value of t is given in advance. 3.6 The average life tE is calculated as follows:
te=n(1+-
wherein: m and n are given by formulas (2) and (4); "(1+1/m) is shown in Table 4 of the "Test Table". 3.7 The reliable life tR is calculated as follows:
tr=n(-2.3026lgR)1/m
wherein: m and n are given by formulas (2) and (4); the R value is given in advance. 4 Data processing procedures and methods for temperature stress accelerated life test 4.1 Test assumptions
(1) The shape parameter m is independent of temperature stress; (2) The relationship between the characteristic life n and the temperature T (°K) conforms to the Arrhenius equation. That is:
n = ea+b/
（3）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 For each stress level, mi,;,ui,n (i1.2,.!), calculate according to the formula specified in Chapter 3. 4.3 Calculation of the accelerated life equation n=ea+b/T 4.3.1 In the accelerated life equation, a and b are calculated according to the format specified in Table 2. (2)
（4）
（5）
（6）
（7）
（8）
Temperature water
Level
GB2689.3-81
Table: Check Table 2 of the "Test Table"; u is given by Article 4.2. Calculate ab
GH- according to the following formula IM
b=BM-IH
4.3.2 The characteristic life n of the product under a certain temperature stress T is calculated as follows: Nmeu+h.
Wu Zhong: a and Jie Gong Wu (9) and (10) are given. 4.4 The weighted average value m of the shape parameter m is calculated in the format of Table 3: Stress level shore number
Table: (deaf "Test Table" Table 2, U; value is given by Article 4.2. m is calculated as follows:
1.5 Excitation energy E is calculated as follows:
m=(L-1)/Q
（9）
（10）
GB 2689.3—81
Where: is the Boltzmann constant; b is given by formula (10). 4.6 Acceleration factor - calculated as follows:
W: The value is given by formula (10).
T -7:=eb1/7u-1/7; ,
4.7 The failure rate of the product under a certain temperature 7 condition is calculated as follows: a(t)=m.qm-l/n
Where: m and n are given by (12) and (H), and the value is given in advance. 4.8 The average failure rate of the product under a certain temperature 7 condition (1) is calculated as follows: T(t)-tm-/mm
Where: m and n are given by formulas (12) and (11); the value is given in advance. 4.9 The average life of the product under a certain temperature condition is calculated as follows: t#=ml(1+1/m)
Where: n and m are given by formula (11) and (12); the value of 1(1+1/m) is found in the "Test Table". 4.10 The reliable life of the product under table temperature condition is calculated as follows: t+=n(-- 2.30261gR)/m
Where: n and m are given by formula (11) and (12), and the R value is given in advance. 5 Electrical stress accelerated life test data processing procedures and methods 5.1 Test assumptions
a. Shape parameter m! j is independent of electrical stress;
b, the relationship between characteristic life n and electrical stress conforms to the inverse law equation:
（13）
（16）
（17）
（18)
n =1/kl\orn =ea+bhgl
Under normal circumstances, the number of truncation failures should be r≥30%n; when the number of truncation failures cannot reach 30%n, at least r≥4. 5.2 m, (, ui, m (i=1, 2..1) for each stress level is calculated according to the formula specified in Chapter 3. 5.3 Calculation of the accelerated life equation m=1/V
5.3.1 α and b in the accelerated life equation are calculated according to the format specified in Table 4. Electrostress level number
Electrostress level number
rn,(igt'i)
deh-(gg?
h.μr igl;
GB 2689.3— 81
h in the table, check Table 2 of the "Test Table", u is given in Article 5.2. Calculate a and 6 according to the following formula
5.3.2 Constants c and are calculated according to the following formula
Where: α and 6 values ​​are given in formulas (19) and (20). k=e-α
C= - b
5.3.3 The product's n under a certain table electrical stress V condition is calculated according to the following formula: n= ea+ blgl
Wu Zhong: α and 6 are given by formulas (19) and (20). 5.4 The weighted average value m of the shape parameter is calculated according to the format of Table 5. Stress level serial number
Table: (check "Test Table" Table 2: The value is given by Article 5.2. m is calculated according to the following formula
5.5 The acceleration factor ~ is calculated according to the following formula:
m(L-1)/Q
tr,=(V/V0)
Where: The c value is given by formula (22); V; and V, are given in advance. 5.6 The failure rate element (t) of the product under a certain electrical stress V condition is calculated according to the following formula: a(t)=m/m-/nm
Wu Zhong: nli m is given by (23) and (24). 5.7 The average failure rate (t) of the product under a certain electrical stress V condition is not calculated according to the following formula: X(t)= tm/nm
Where: n and m are given by (23) and (24); t is given in advance. 5.8 The average life t of the product under a certain electrical stress V is calculated as follows: tE=n/(1+1/m)
（J9）
（20）
（22）
（23）
（24)
（26）
（27）||t t||（28）
GB2689.3—81
武：n and m values ​​are given by formulas (23) and (24); the factory (1+1/m) value is given in 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（-2.30261gR)t/m
Where: n and m values ​​are given by formulas (23) and (24); the R value is given in advance. (29)
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