GB 2689.2-1981 Graphical estimation method for life test and accelerated life test (for Weibull distribution)
Some standard content:
National Standard of the People's Republic of China
Graphical Estimation Method for Life Test and Accelerated Life Test (for Weibull Distribution)
1 Scope and Purpose
GB 2689·2 --81
This standard specifies the procedures for the graphical estimation method for constant stress life test and accelerated life test. It is applicable to the case where the life of electronic component products (hereinafter referred to as products) obeys the Weibull distribution, with shape parameter m>0, characteristic life n>0, and location parameter = 0. It can be used to estimate the product life characteristics; to determine whether there are abnormalities in the entire test data or to determine whether the test results meet the test assumptions of the numerical analysis method.
2Symbols and meanings
Number of test samples;
Number of truncation failures, r=1,2…n,
Failure sample serial number, j-1,2..r,
Stress level serial number, i=1.2.,
Number of test samples at the ith stress level;
Number of truncation failures at the ith stress level;
Failure time of the jth failed sample,
Failure time of the rth failed sample;
Shape parameter of the Weibull distribution Number;
Characteristic life of Weibull distribution;
Location parameter of Weibull distribution:
Absolute temperature (°K):
Electrical stress;
Boltzmann constant, =0.8617×10-4eV／K, activation energy;
m; weighted average;
Average life,
Reliable life with reliability R;
Intercept of acceleration equation;
Slope of acceleration equation;
Constant of inverse power law.
3 Graphic estimation procedure for life test
3.1 Test truncation and handling of failed samples
Generally, 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 Handling of failure time The failure time of the failed sample shall be determined in accordance with Article 6 of GB2689·1-81 "General Rules for Constant Stress Life Test and Accelerated Life Test Methods". The failure time shall be arranged in ascending order and handled in accordance with the format of Table 1. Issued by the General Administration of Standards of the People's Republic of China Proposed by the Fourth Ministry of Machine Building Industry of the People's Republic of China for trial implementation on October 1, 1981 Standardization Research Institute of the Fourth Ministry of Machine Building Industry Sample Model Sample Quantity Test Time Iron Effect Sample Serial Number GB 2689.2- 81
Product failure time
In the table: F(（，）value is calculated according to the number of test samples as follows:n+1
F(t,)=
3.3 Estimation procedure
(11,2......r)
3.3.1 Configuring the distribution straight line When configuring the distribution straight line, the following principles must be observed: a. The distribution straight line must make the data points staggered on both sides of the true line: b. The data points on both sides of the distribution straight line should not be too different; stress condition
Failure standardwww.bzxz.net
Production time
n≥50
c. The deviation of the data points near F(t)=0.5～0.6 from the distribution straight line should be as small as possible. 3.3.2 Estimation of distribution parameters
3.3.2.1 Estimation of shape Parameter m value
3.3.2.2 Estimation of characteristic life n value
3.3.3 Estimation of product reliability characteristic quantity
3.3.3.1 Estimation of cumulative failure probability F(1) value at any time3.3.3.2 Estimation of reliability R(1) value at any time3.3.3.3 Estimation of reliable life value
3.3.3.4 Estimation of average life value,
4 Intuitive judgment of abnormal data of life test
R(t）1(t)
4.1 Judgment of suspicious data points at the lower end of the distribution line, F(t) ≤ 0.3)
Cumulative failure probability
(1)
(2)
As shown in Figures 1 and 2, the data points at the lower end of the distribution line deviate far from the straight line. These data points that deviate from the straight line can be regarded as abnormal data points. They are classified as follows:
GB2689.2-81
a. Reasons other than the product itself. Combined with physical analysis, it is judged that the abnormal data points generated are caused by reasons other than the product itself. These abnormal points should be deducted from the total number of test samples n and the number of failures r, and the cumulative failure probability should be recalculated. b. According to the physical analysis of failure, the life distribution of the product belongs to the early failure type. This situation can be fitted with a composite Weibull distribution. If the failure number r<5%n (or r≤4), it can be treated as a single distribution: otherwise it can be treated as a composite distribution. When treated as a composite distribution, only the previous data is used as the order statistic for analyzing the product life characteristics. At this time, the total number of samples n remains unchanged. c. Location parameter ≠0. When there is sufficient reason to determine that the location parameter of the product is 0, it is treated as ≠0; otherwise, it is treated as the second case. 4.2 Suspicious data points are at the upper end of the distribution line, that is, judgment of F(t)>0.30.3
As shown in Figures 3 and 4, the data points at the upper end of the distribution line deviate far from the line. These data points that deviate from the line can be regarded as abnormal data points. They are divided into:
a. The reason is not the product itself.
b. The distribution of the product is a composite distribution or a mixed distribution type. Regardless of whether it belongs to the a or the type, when processing the data, the previous data is used as the order statistic when analyzing the product life characteristic quantity. At this time, the total number of samples n remains unchanged.
4.3 As shown in Figures 5 and 6, it should be judged that the test is abnormal, or the test sample is not a test batch. F(t)
5 Graphical estimation procedure for temperature stress accelerated life test 5.1 Test assumptions
a. The shape parameter m is independent of temperature stress.
b, the relationship between characteristic life n and temperature T (°K) conforms to the Arrhenius equation; n = 10g +6/7
c. - In general, the number of truncated failures should have r ≥ 30% n; when the number of failures cannot reach 30% n, at least r ≥ 4. 5.2 Estimation procedure
5.2.1 Configure the distribution straight line for each temperature level. 15
GB2689.2-81
5.2.2 Estimate the shape parameter m and characteristic life n for each temperature level and list them in Table 2. Stress level T
Shape parameter
Characteristic life
103/T2
5.2.3 Configure the accelerated life straight line (using single-sided logarithmic paper) as shown in Figure 7. Small
.. 0*/ T2 0+ /T
Accelerated life straight line diagram on single-sided logarithmic paper?
5.2.4 Estimation of distribution parameters under normal temperature stress level T5.2.4.1 The weighted average value of the shape parameter is calculated as follows: n mi+ nzm2+.....nym!
ni+ n2+......n.
Where m (i=1,2,..，1) is given in Table 2 of 5.2.2. 5.2.4.2 The slope b of the acceleration equation is calculated as follows: T
10 \/ T
（3）
b=（Ign'-Ign\）·T\T\/(T\-7)（4）
Where; T' and T\ are two stress levels arbitrarily selected on the accelerated life straight line; n and n\ are the characteristic lives corresponding to T' and T\. 5.2.4.3 The intercept α of the acceleration equation is calculated as follows: a = Ign'-b/T
Where: T and ㎡ are the characteristic life corresponding to any temperature; the b value is given by Item 5.2.4.2 5.2.4.4 The activation energy E is calculated as follows:
Eb.k/0.4343
Where: the b value is given by Item 5.2.4.2; k = 0.8617×10-4eV/°K. 6 Graphical Estimation Procedure for Electrical Stress Accelerated Life Test 6.1 Test Assumptions
a. The shape parameter m is independent of electrical stress;
b. The relationship between the characteristic life n and the electrical stress conforms to the inverse power law equation n = 1/kVc\ or n = 10α+blkh
c. --Generally, the truncated failure number should be r30%n. When the truncated failure number cannot reach 30%n, it should be at least r4. 6.2 Estimation procedure
6.2.1 Configure the distribution straight line for each electrical stress level. 16
（5）
（6）
GB 26892- 81
6.2.2 Estimate the shape parameter m and characteristic life n of each electrical stress level and tabulate them. Stress level V
Shape parameter m;
Characteristic life n;
6.2.3 Configure the accelerated life straight line (using double-sided logarithmic paper) as shown in Figure 8. n
Accelerated life straight line diagram on double-sided logarithmic paper 8
6.2.4 Estimate the distribution parameters under the normal stress level V6.2.4.1 Estimate the weighted average m of the shape parameter m, see formula (3). 6.2.4.2 Estimate the characteristic life n
6.2.5 Estimate the slope b of the accelerated life equation, and the b value is calculated as follows: b=
Ign'-Igm
Igw\_- igv
Where: V' and V\ are two stress levels arbitrarily selected on the accelerated life straight line, and n\ and n\ are the characteristic lives obtained on the accelerated life straight line corresponding to the V' and V\ values. 6.2.6 Estimated constant c
cm—b
Where: b value is given in 6.2.5.
6.2.7 Estimate the intercept α of the accelerated life equation, and the a value is calculated as follows: a=lgnbligV
Where: b value is given in 6.2.5, and n is the characteristic life corresponding to the V value obtained on the accelerated life straight line. V
（7）
（8）
（9）
GB 2689-2- 81
Data processing method for life test and accelerated life test Drawing method for graph estimation 1 Arrange the distribution straight line
1.1 Make a data table. Arrange the failure times t; in ascending order and calculate the corresponding cumulative failure probability F(t,) and make a data table. Table 1
Sample model
Number of samples
Test time
Failed sample serial number
Sample failure time
(Attachment)
Stress condition
Failure standard
Production time
Cumulative failure probability
F(t/)%
1.2 Plotting points Plot the data points in Table 1 [t, F (t,)] (=1.2,) on the Weibull probability paper. 1.3 Configuring straight lines If the plotted points are roughly on a straight line, configure a straight line by force so that the plotted points are staggered and evenly distributed on both sides of the straight line. The configured straight line is the product life distribution line. For precautions for configuring the life distribution line, see GB 2689-2--81 Clause 3.3.1.
2. Estimate the value of shape parameter m. Draw a parallel line through the "estimation point" to the distribution line and intersect the Y axis. Then draw a horizontal line to the right of this intersection and intersect the Y ruler. The absolute value of the scale value on the Y ruler at the intersection is the m value, see Figure 1. 18
GB2689.2-81
Distribution line
m estimation point
3 Estimate the value of characteristic life n. The distribution line intersects the X axis, and a vertical line is drawn from the intersection to intersect the t axis. This intersection is at ! The scale value on the axis is the 7 value, see Figure 1.
4 Estimate the F(t.) value at any time t., determine any time ta, and find the scale point of t. on the t axis, draw a vertical line to intersect the distribution line, and then draw a horizontal line from the intersection to the left to intersect the F() axis. The scale value of this intersection is the F(t.) value, see [Figure 2. F()
5 Estimate the reliable life R, the reliability R is given in advance, and the value of F1-R is calculated from this. Draw a horizontal line from the F scale point on the F() axis to the right to intersect the distribution line , and then draw a vertical line from this intersection to intersect the t axis. The scale value of this intersection on the t axis is! See Figure 2.
6 Estimate the average life span. Draw a parallel line from the "m estimated point" to the distribution line and intersect the Y axis. Draw a horizontal line from this intersection to the right and intersect with the / (u) scale. The scale value at this intersection is J. Then find the value of / on the F () axis, and draw a horizontal line to the right to intersect the distribution line. Then draw a vertical line from this intersection to intersect the t axis. The scale value of this intersection is the t value. See Figure 3. Fn
m estimated point
GB 2689.2-81
7 Configure the accelerated life straight line of temperature stress according to the data of Section 5.2.2 of the standard to make Table 2, and use the data points in the table (10/7, n) (i=1, 2...) to draw points on a single-sided logarithmic paper. ni takes values on the logarithmic axis, and 10\/7, takes values on the other side of the axis. Configure a straight line based on the output, which is the accelerated life straight line (see Figure 4). Table 2
Stress level
Characteristic voucher n;
10\/T,
10/ T10/7
Figure 4 Draw a temperature accelerated life straight line on a single-sided logarithmic paper 10\/T
8 Configure the accelerated life straight line of electrical stress according to the data of Section 6.2.2 of the standard to make Table 3, and use the data points in Table 3 (, m) (i=1.2.! ) Draw points on the double-sided logarithmic paper and visually configure a straight line, which is the accelerated life line (see Figure 5). Table 3
Stress level V
Shape parameter m;
Characteristic life n:
Figure 5 Draw the voltage accelerated life line n on the double-sided logarithmic paper2—81
Distribution line
mEstimation point
3Estimate the characteristic life n value. The distribution line intersects the X axis, and the vertical line drawn from the intersection intersects the t axis. The scale value of this intersection on the axis is the 7 value, see Figure 1.
4Estimate the F (t.) value at any time t. Determine any time ta, and find the scale point of t. on the t axis. Draw a vertical line to intersect the distribution line, and then draw a horizontal line from the intersection to the left to intersect the F () axis. The scale value of this intersection is the F (t.) value, see [Figure 2. F ()
5Estimate the reliable life R. The reliability R is given in advance. Calculate the value of F1-R from this. Draw a horizontal line from the F scale point on the F () axis to the right to intersect the distribution line, and then draw a vertical line from the intersection to intersect the t axis. The scale value of this intersection on the t axis is the 7 value, see Figure 2.
6 Estimate the average life. Draw a parallel line from the "m estimated point" to the distribution line and intersect the Y axis. Draw a horizontal line from this intersection to the right and intersect the / (u) scale. The scale value at this intersection is J. Then find the value of / on the F () axis, and draw a horizontal line to the right to intersect the distribution line. Then draw a vertical line from this intersection and intersect the t axis. The scale value of this intersection is the t value. See Figure 3. Fn
m estimated point
GB2689.2-81
7 Configure the accelerated life straight line of temperature stress. According to the data of Section 5.2.2 of the standard, make Table 2. Use the data points in the table (10/7, n) (i=1, 2...) to draw points on a single-sided logarithmic paper. ni takes the value on the logarithmic coordinate axis, and 10\/7, takes the value on the other side of the coordinate axis. Configure a straight line based on the output, which is the accelerated life straight line (see Figure 4). Table 2
Stress level
Characteristic life n;
10\/T,
10/ T10/7
Figure 4 Draw the temperature accelerated life straight line 10\/T on the single-sided logarithmic paper
8 Configure the accelerated life straight line of electrical stress. According to the data of Section 6.2.2 of the standard, make Table 3. Use the data points (, m) in Table 3 (i=1.2.!) to draw points on the double-sided logarithmic paper, and configure a straight line by visual observation. This is the accelerated life straight line (see Figure 5). Table 3
Stress level V
Shape parameter m;
Characteristic life n:
Figure 5 Draw the voltage accelerated life straight line n on the double-sided logarithmic paper2—81
Distribution line
mEstimation point
3Estimate the characteristic life n value. The distribution line intersects the X axis, and the vertical line drawn from the intersection intersects the t axis. The scale value of this intersection on the axis is the 7 value, see Figure 1.
4Estimate the F (t.) value at any time t. Determine any time ta, and find the scale point of t. on the t axis. Draw a vertical line to intersect the distribution line, and then draw a horizontal line from the intersection to the left to intersect the F () axis. The scale value of this intersection is the F (t.) value, see [Figure 2. F ()
5Estimate the reliable life R. The reliability R is given in advance. Calculate the value of F1-R from this. Draw a horizontal line from the F scale point on the F () axis to the right to intersect the distribution line, and then draw a vertical line from the intersection to intersect the t axis. The scale value of this intersection on the t axis is the 7 value, see Figure 2.
6 Estimate the average life. Draw a parallel line from the "m estimated point" to the distribution line and intersect the Y axis. Draw a horizontal line from this intersection to the right and intersect the / (u) scale. The scale value at this intersection is J. Then find the value of / on the F () axis, and draw a horizontal line to the right to intersect the distribution line. Then draw a vertical line from this intersection and intersect the t axis. The scale value of this intersection is the t value. See Figure 3. Fn
m estimated point
GB2689.2-81
7 Configure the accelerated life straight line of temperature stress. According to the data of Section 5.2.2 of the standard, make Table 2. Use the data points in the table (10/7, n) (i=1, 2...) to draw points on a single-sided logarithmic paper. ni takes the value on the logarithmic coordinate axis, and 10\/7, takes the value on the other side of the coordinate axis. Configure a straight line based on the output, which is the accelerated life straight line (see Figure 4). Table 2
Stress level
Characteristic life n;
10\/T,
10/ T10/7
Figure 4 Draw the temperature accelerated life straight line 10\/T on the single-sided logarithmic paper
8 Configure the accelerated life straight line of electrical stress. According to the data of Section 6.2.2 of the standard, make Table 3. Use the data points (, m) in Table 3 (i=1.2.!) to draw points on the double-sided logarithmic paper, and configure a straight line by visual observation. This is the accelerated life straight line (see Figure 5). Table 3
Stress level V
Shape parameter m;
Characteristic life n:
Figure 5 Draw the voltage accelerated life straight line n on the double-sided logarithmic paper
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