CN113567795A - Step-back stress acceleration reliability test method based on Weibull distribution - Google Patents

Step-back stress acceleration reliability test method based on Weibull distribution Download PDF

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CN113567795A
CN113567795A CN202111132214.0A CN202111132214A CN113567795A CN 113567795 A CN113567795 A CN 113567795A CN 202111132214 A CN202111132214 A CN 202111132214A CN 113567795 A CN113567795 A CN 113567795A
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stress
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weibull distribution
failure
reliability
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CN113567795B (en
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周天朋
刘德军
雷霆
呼东亮
张晓鹏
杨立伟
胡绍华
宁薇薇
刘福江
周洁
吴嫄嫄
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Tianjin Aerospace Ruilai Technology Co Ltd
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Abstract

The invention discloses a step-annealing stress acceleration reliability test method based on Weibull distribution, which comprises the following steps: selecting an accelerated life test physical model according to a product failure mode; determining the relation between an acceleration factor and a model parameter of a Weibull distribution acceleration reliability test; determining a step-annealing stress acceleration reliability scheme based on Weibull distribution; carrying out a test; and (4) processing test data and calculating reliability. The invention provides a mathematical model for accelerating a reliability test, a constraint relation acceleration factor calculation formula of model parameters, a test implementation step and a test data processing method when the product reliability obeys Weibull distribution, and provides a test case to explain the solving process.

Description

Step-back stress acceleration reliability test method based on Weibull distribution
Technical Field
The invention relates to the technical field of acceleration reliability tests, in particular to a step-annealing stress acceleration reliability test method based on Weibull distribution.
Background
High-reliability long-life assessment has long been a technical problem in the field of reliability engineering. The defects of the long-life evaluation means cause adverse effects on the development and the use of products, and firstly, the life index of a newly-developed product cannot be fully verified in the development stage, so that serious hidden life danger can be caused; secondly, some products are scrapped in advance, the service life potential of the products cannot be fully exerted, and huge resource waste is caused. The application of accelerated reliability (life) test technology becomes a necessary means for developing products with high reliability and long service life. The accelerated reliability test is a rapid reliability evaluation test technology which shortens the test period by increasing the test stress level under the condition of keeping the failure mechanism unchanged. The accelerated reliability test technology meets the engineering requirements of high-reliability long-life evaluation, and is widely regarded in the field of reliability engineering. The method is widely applied to various fields of machinery, electronics, electromechanics, materials and the like of high-end equipment at present.
The accelerated reliability test is divided into four types, namely a constant stress test, a stepping stress test, a sequential stepping stress test and a stepping stress relief test, according to a stress loading mode. Theoretical analysis and numerical simulation prove that the step-annealing stress test has the highest test efficiency and the shortest test time in four acceleration reliability test modes. However, at present, the acceleration reliability test research mainly focuses on the constant stress test and the step stress test, and no published literature reports a step-annealing stress acceleration reliability test method based on the weibull distribution.
Disclosure of Invention
The invention aims to provide a step-annealing stress acceleration reliability test method based on Weibull distribution, aiming at the technical problem of reliability evaluation of products with high reliability and long service life.
The invention is realized by the following steps:
a step-annealing stress acceleration reliability test method based on Weibull distribution comprises the following steps:
firstly, selecting an accelerated life test physical model according to a product failure mode;
the accelerated life test physical model adopts an Allen-nier model or an inverse power rate model;
secondly, determining the relation between an acceleration factor and a model parameter of a Weibull distribution acceleration reliability test;
the accelerated reliability test is the acceleration of the failure process, and the failure characteristics of the tested product are consistent with the failure characteristics of the product under the action of long-time low stress under the action of short-time high stress; the relationship between the acceleration factor and the model parameter should satisfy the following relationship to ensure the consistency of the failure characteristics:
(1) regular consistency of failure process: the method is characterized in that the same determined function model exists between the service life of a product and stress; the function forms of the service life distribution under different stress levels are the same, and only the parameters of the functions are different;
(2) consistency of failure mechanism: the failure mode is unchanged, for Weibull distribution, the shape parameters reflect the failure mechanism of the Weibull distribution, and the same shape parameters are the essential conditions for the consistency of the failure mechanism of the Weibull distribution accelerated life test;
thirdly, determining a step-annealing stress acceleration reliability scheme based on Weibull distribution;
the step-annealing stress acceleration reliability test scheme can set at least 2 stress gradients, the stress applied in the 1 st stage is usually the ultimate stress of the product, and the stress in the 2 nd stage is lower than that in the 1 st stage, but is far greater than the normal working stress;
selecting N samples, and setting test stress S causing sample failure2,S1,S2 >S1,S2The ultimate stress of the product is that the two groups of test stresses are both larger than the normal working stress S of the product0
Stress S for N samples2The test is carried out, and the first stage test is stopped until the N/2 samples fail;
for the remaining N/2 samples, at stress S1And (5) performing the next test until the N/4 samples fail, and finishing the test.
Fourthly, carrying out a test;
and (5) carrying out a test according to the third accelerated reliability scheme, and recording the failure stress and the failure time of each sample.
Fifthly, processing test data and calculating reliability;
to stress S2Carrying out distribution inspection on the failure data, and judging whether the failure data accords with Weibull distribution; by means of stress S2The test data is subjected to Weibull distribution parameter fitting to obtain stress S2Characteristic life η of2And a shape parameter m2
Under stress S1Lower weibull distribution shape parameter m1=m2By means of stress S1Characteristic lifetime η of fitting Weibull distribution to lower test data1
According to characteristic lifetime η2And characteristic lifetime η1Obtaining the stress S2With respect to stress S1Acceleration factor for lower product life
Figure 591778DEST_PATH_IMAGE001
If the product stress is mechanical stress or electrical stress, the relationship between the characteristic life and the stress satisfies the inverse power-law model, stress S2With respect to stress S1Acceleration factor for lower product life
Figure 774498DEST_PATH_IMAGE002
According to
Figure 350972DEST_PATH_IMAGE001
And
Figure 11761DEST_PATH_IMAGE002
solving to obtain an inverse power rate model index n;
stress S under inverse power rate model1With respect to stress S0Acceleration factor for lower product life
Figure 419609DEST_PATH_IMAGE003
And stress S expressed by Weibull distribution characteristic lifetime1With respect to stress S0Lower product life acceleration factor
Figure 74362DEST_PATH_IMAGE004
According to Q
Figure 934870DEST_PATH_IMAGE003
And
Figure 602612DEST_PATH_IMAGE004
calculating to obtain normal working stress S0Lower characteristic life
Figure 333808DEST_PATH_IMAGE005
Normal working stress S0Shape parameter m of Weibull distribution0=m1=m2
According to normal working stress S0Lower characteristic life
Figure 920647DEST_PATH_IMAGE006
And a shape parameter m0Calculating according to the cumulative failure probability distribution function of Weibull distribution to obtain the normal working stress S of the product0Cumulative probability of failure
Figure 143818DEST_PATH_IMAGE007
And degree of reliability
Figure 975770DEST_PATH_IMAGE008
The step-annealing stress acceleration reliability test method based on Weibull distribution provided by the invention provides a mathematical model of an acceleration reliability test when the product reliability obeys the Weibull distribution, a constraint relation acceleration factor calculation formula of model parameters, a test implementation step and a test data processing method, provides a test case and explains a solving process, is beneficial to saving test cost and test period through the application of the method, and has great practical significance for reliability evaluation of products with high reliability and long service life.
Drawings
Fig. 1 is a flowchart of a step-annealing stress acceleration reliability test method based on weibull distribution according to an embodiment of the present invention.
FIG. 2 shows stress S according to an embodiment of the present invention2Failure data histogram.
FIG. 3 shows stress S according to an embodiment of the present invention2Weibull probability distribution of failure data.
FIG. 4 shows stress S according to an embodiment of the present invention2Fitting graph of Weibull distribution of lower failure data.
FIG. 5 shows stress S according to an embodiment of the present invention1Weibull probability distribution of failure data.
Detailed Description
The present invention will be described in detail below in order to make those skilled in the art better understand the concept of the present invention.
Referring to fig. 1, a step-annealing stress acceleration reliability test method based on weibull distribution is implemented by the following steps:
firstly, selecting a proper accelerated life test physical model according to a product failure mode;
the basic idea of accelerated life testing is to use the life characteristic at high stress to extrapolate the life characteristic at normal stress levels. The key is to establish a relationship between life characteristics and stress levels, i.e., an acceleration model. The most common of the acceleration models are the arrhenius model and the inverse power rate model.
(1) Arrhenius model
The arrhenius model is a lifetime model based on temperature stress acceleration:
Figure 967997DEST_PATH_IMAGE009
(1)
wherein L is a certain lifetime characteristic, A is a constant,
Figure 991316DEST_PATH_IMAGE010
represents activation energy, k represents boltzmann constant, and T is absolute temperature.
Temperature T2With respect to temperature T1Acceleration factor for lower product life:
Figure 701783DEST_PATH_IMAGE011
(2)
the Arrhenius model is widely applied to accelerated life tests and accelerated storage life tests of electronic products.
(2) Inverse power rate model
Besides the temperature stress, mechanical stress and electrical stress are also frequently encountered, and a large amount of experimental data prove that the relationship between the life characteristic of a product under the action of the mechanical stress and the electrical stress and the stress meets an inverse power-law model:
Figure 242486DEST_PATH_IMAGE012
(3)
where L is a certain lifetime characteristic, A and n are constants, and S represents a stress level.
Stress S2With respect to stress S1Acceleration factor for lower product life:
Figure 682695DEST_PATH_IMAGE013
(4)
secondly, determining the relation between an acceleration factor and a model parameter of a Weibull distribution acceleration reliability test;
the accelerated reliability test is based on the accelerated life test, and further considers the reliability distribution characteristics of the life. The accelerated reliability test is the acceleration of the failure process, and the failure characteristics of the tested product are consistent with the failure characteristics of the product under the action of long-time low stress. The failure property consistency is embodied as:
(1) regular consistency of failure process: means that the same determined function model exists between the service life and the stress of the product. The life distribution under different stress levels has the same functional form, but the parameters of the function have differences.
(2) Consistency of failure mechanism: meaning that the failure mode is unchanged. For Weibull distribution, the shape parameters reflect the failure mechanism of the Weibull distribution, and the same shape parameters are the essential conditions for the consistency of the failure mechanism of the Weibull distribution accelerated life test.
The acceleration factor for the acceleration reliability test is defined as: if the product is under stress S1And S2Time of respective action t1And t2Has the same cumulative probability of failure, i.e.
Figure 611336DEST_PATH_IMAGE014
Then stress S2With respect to stress S1The acceleration factor of (a) is:
Figure 605837DEST_PATH_IMAGE015
(5)
the cumulative probability of failure expression for the weibull distribution is:
Figure 979924DEST_PATH_IMAGE016
(6)
in the formula, f (t) represents the cumulative uncertainty, η represents a scale parameter (characteristic lifetime, constant under the same stress), m represents a shape parameter (constant under different stresses), and t represents time.
Acceleration factor of the weibull distribution under two stress conditions:
Figure 946743DEST_PATH_IMAGE017
(7)
thirdly, determining a step-annealing stress acceleration reliability scheme based on Weibull distribution;
the step-annealing stress acceleration reliability test scheme can set 2 stress gradients at least, the stress applied in the 1 st stage is usually the limit stress of the product, and the stress in the 2 nd stage is lower than that in the 1 st stage, but is far greater than the normal working stress.
The smaller the weibull distribution shape parameter m is, the larger the number of test pieces is required, and when the shape parameter m =2.2, the characteristic lifetime accuracy is 10%, and the confidence level is 0.8, the number of test pieces is 12.
A total of 24 specimens were tested under a first set of stress S2The stress S can be fitted when the next 12 samples are failed2Shape parameters and characteristic lifetime parameters of the lower weibull distribution. In the second set of stresses S1The lower 6 failures were used to fit the stress S1Characteristic life parameter of the lower weibull distribution. At the end of the test 18 specimens failed, leaving 6 specimens. The protocol is shown in Table 1.
Table 1 test sequence chart
Test sequence Stress Time to failure
1 S2 ti,(i=1-12)
2 S1 tj,(j=13-18)
Fourthly, carrying out a test;
stress S was applied to 24 samples in the test sequence of Table 12And the first stage test was completed until 12 sample failures occurred.
Stress S was applied to the remaining 12 samples1And the test is finished until 6 samples fail.
The stress to failure and time to failure of each sample was recorded during the test.
And fifthly, processing test data and calculating reliability.
To stress S2The failure data below were subjected to a distribution test, assuming that the test results obeyed a weibull distribution.
By means of stress S2Carrying out Weibull distribution parameter fitting on the failure data to obtain stress S2Characteristic life parameter eta of lower Weibull distribution2And a shape parameter m2
Under stress S1Lower m1=m2Then using the stress S1Characteristic life parameter eta of lower test data fitting Weibull distribution1
According to η2And η1The stress S can be determined2Lower relative stress S1The lower acceleration factor is a factor of the acceleration,
Figure 311866DEST_PATH_IMAGE018
if the electrical stress applied by the product, the relationship between the life characteristic and the electrical stress meets the inverse power rate model. Acceleration factor according to equation (4)
Figure 731346DEST_PATH_IMAGE019
And stress S2And S1Can solve the inverseThe power-law model index n.
Testing stress S according to an index n of an inverse power rate model2And the actual operating stress S0Life characteristic η2The actual working characteristic life eta can be solved0Weibull distribution shape parameter m under actual working stress0=m2
According to the Weibull distribution parameter η0And m0The reliability index R under the actual working stress can be solved0(t)。
The present invention will be further described in detail with reference to a test case of acceleration reliability of an electrical appliance.
Reliability parameter of certain electrical appliance
The service life of a certain electrical appliance follows Weibull distribution, the normal working voltage is 24V, and the maximum working voltage is 36V. The operating life characteristics at different voltages obey an inverse power rate model. An accelerated reliability test is designed, the normal working voltage is 24V, and the working reliability of a certain electric appliance can reach what level when the electric appliance works for 500 hours.
Accelerated life test scheme for certain electrical appliance
24 test samples are selected by adopting a Weibull distribution-based step-annealing stress acceleration reliability method. Selection of test stress S2=36V,S1=31V, test selection constant truncation. Under stress S2When the failure of the next 12 samples occurs, the first stage test is stopped, and the stress S is converted1The test was continued. Stress S1The test was terminated when the next 6 samples failed.
Test data
The simulation data are shown in Table 4. Stress S2The next 12 products failed and the 119.7h first stage test was complete. The remaining samples were then stressed at stress S1The test is carried out, 6 products fail, and the 96.5h test is finished. The step-back stress test failure data (time h) are shown in table 2.
Table 2 test failure data
S2Number of failures 1 2 3 4 5 6 7 8 9 10 11 12
S2Time to failure 14.2 50.1 67.6 72.8 79.9 88.2 93.0 99.9 108.1 109.4 117.1 119.7
S1Number of failures 1 2 3 4 5 6
S1Time to failure 10.0 33.8 38.5 56.5 78.1 96.5
Data analysis, reliability calculation
Stress S2The following failure times were histogram plotted as shown in fig. 2. Stress S2The test data is plotted by using a Matlab function wblplot to obtain a weibull probability distribution diagram, as shown in fig. 3, and it can be seen that the test data conforms to a logarithmic linear relationship in the weibull probability diagram. Fig. 2 and 3 illustrate that product failure follows a weibull distribution.
Applying stress S according to Weibull distribution cumulative probability failure equation (6)2Fitting the lower failure data to obtain a Weibull distribution characteristic parameter value:
m2=2.62,η2=140.3h, the parameter fit curve is shown in fig. 4.
Under stress S1The Weibull probability distribution of the lower failure data is shown in FIG. 5, and the failures follow the Weibull distribution.
Stress S1The lower failure data conforms to Weibull distribution, shape parameters and stress S2The same applies below, m1=m2= 2.62. According to stress S1Lower failure data fitting Weibull distribution characteristic lifetime eta1=288.4h。
From equation (7), the stress S can be calculated2And stress S1Acceleration factor of (2):
Figure 879430DEST_PATH_IMAGE020
from equation (4), the inverse power rate model index n =4.83 can be calculated.
From equation (4), the stress S can be calculated2And normal working stress S0Acceleration coefficient of (d):
Figure 28652DEST_PATH_IMAGE021
it can be known that under normal working stress, the product is lostIs subject to Weibull distribution, m0=m2=2.62, characteristic lifetime:
Figure 564675DEST_PATH_IMAGE022
according to the formula (6), the cumulative failure probability of a certain electric appliance working for 500h can be calculated: f (500) = 15.2%; reliability R (500) = 84.8%.
Through test case inspection, the test method disclosed by the invention can be used for a short time, so that a service life model of a high-reliability long-service-life product with the service life complying with Weibull distribution can be obtained, and a reliability index of long-time work of the product is given.
The above is only one embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and adjustments can be made without departing from the principle of the present invention, and these modifications and adjustments should also be regarded as the protection scope of the present invention.

Claims (4)

1. The step-annealing stress acceleration reliability test method based on Weibull distribution is characterized by comprising the following steps of:
firstly, selecting an accelerated life test physical model according to a product failure mode;
the accelerated life test physical model adopts an Allen-nier model and an inverse power rate model;
secondly, determining the relation between an acceleration factor and a model parameter of a Weibull distribution acceleration reliability test;
thirdly, determining a step-annealing stress acceleration reliability scheme based on Weibull distribution;
the step-annealing stress acceleration reliability test scheme can set at least 2 stress gradients, the stress applied in the 1 st stage is usually the ultimate stress of the product, and the stress in the 2 nd stage is lower than that in the 1 st stage, but is far greater than the normal working stress;
selecting N samples, and setting test stress S causing sample failure2,S1,S2 >S1,S2To produceThe ultimate stress of the product and the two groups of test stresses are both larger than the normal working stress S of the product0
Stress S for N samples2The test is carried out, and the first stage test is stopped until the N/2 samples fail;
for the remaining N/2 samples, at stress S1The test is carried out until the N/4 samples fail, and the test is finished;
fourthly, carrying out a test;
carrying out a test according to the third accelerated reliability scheme, and recording the failure stress and the failure time of each sample;
and fifthly, processing test data and calculating reliability.
2. The Weibull distribution-based step-back stress acceleration reliability test method according to claim 1, wherein the reliability calculation is performed by the steps of:
to stress S2Carrying out distribution inspection on the failure data, and judging whether the failure data accords with Weibull distribution; by means of stress S2The test data is subjected to Weibull distribution parameter fitting to obtain stress S2Characteristic life η of2And a shape parameter m2
Under stress S1Lower weibull distribution shape parameter m1=m2By means of stress S1Characteristic lifetime η of fitting Weibull distribution to lower test data1
According to characteristic lifetime η2And characteristic lifetime η1And finding the stress S2With respect to stress S1Acceleration factor for lower product life
Figure 744523DEST_PATH_IMAGE001
If the product stress is mechanical stress or electrical stress, the relationship between the characteristic life and the stress satisfies the inverse power-law model, stress S2With respect to stress S1Acceleration factor for lower product life
Figure 758615DEST_PATH_IMAGE002
According to
Figure 700026DEST_PATH_IMAGE001
And
Figure 79055DEST_PATH_IMAGE002
solving to obtain an inverse power rate model index n;
stress S under inverse power rate model1With respect to stress S0Acceleration factor for lower product life
Figure 597761DEST_PATH_IMAGE003
And stress S expressed by Weibull distribution characteristic lifetime1With respect to stress S0Lower product life acceleration factor
Figure 290911DEST_PATH_IMAGE004
According to
Figure 834631DEST_PATH_IMAGE003
And
Figure 745081DEST_PATH_IMAGE004
calculating to obtain normal working stress S0Lower characteristic life
Figure 219924DEST_PATH_IMAGE005
(ii) a Normal working stress S0Shape parameter m of Weibull distribution0=m1=m2
According to normal working stress S0Lower characteristic life
Figure 106978DEST_PATH_IMAGE005
And a shape parameter m0Calculating according to the cumulative failure probability distribution function of Weibull distribution to obtain the normal working stress S of the product0Cumulative probability of failure
Figure 491823DEST_PATH_IMAGE006
And degree of reliability
Figure 44945DEST_PATH_IMAGE007
3. The accelerated reliability test method of step annealing stress based on Weibull distribution as claimed in claim 1, wherein the accelerated reliability test is the acceleration of failure process, and the tested product has failure characteristics under short-time high stress action consistent with the failure characteristics of the product under long-time low stress action.
4. The Weibull distribution-based step annealing stress acceleration reliability test method according to claim 1, wherein the relationship between the acceleration factor and the model parameter is such that the consistency of the failure characteristics can be ensured only if the following relationship is satisfied:
(1) regular consistency of failure process: the method is characterized in that the same determined function model exists between the service life of a product and stress; the function forms of the service life distribution under different stress levels are the same, and only the parameters of the functions are different;
(2) consistency of failure mechanism: the failure mode is unchanged, for Weibull distribution, the shape parameters reflect the failure mechanism of the Weibull distribution, and the same shape parameters are the essential conditions for the consistency of the failure mechanism of the Weibull distribution accelerated life test.
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