WO2023045024A1 - Step stress accelerated reliability testing method based on weibull distribution - Google Patents
Step stress accelerated reliability testing method based on weibull distribution Download PDFInfo
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- the invention relates to the technical field of accelerated reliability test, in particular to a method for accelerated reliability test of step-back stress based on Weibull distribution.
- the accelerated reliability test is divided into four types: constant stress test, step stress test, sequential stress test and step back stress test.
- step-back stress test has the highest test efficiency and the shortest test time among the four accelerated reliability test methods.
- the current accelerated reliability test research mainly focuses on constant stress test and step stress test, and there is no public literature report on the accelerated reliability test method of step-back stress based on Weibull distribution.
- the purpose of the present invention is to provide a step-back stress accelerated reliability test method based on Weibull distribution for the technical problem of reliability evaluation of high-reliability and long-life products.
- a step-back stress accelerated reliability test method based on Weibull distribution comprising the following steps:
- the first step is to select the accelerated life test physical model according to the failure mode of the product
- the physical model of the accelerated life test adopts the Arrhenius model or the inverse power law model
- the second step is to determine the relationship between the acceleration factor and the model parameters of the Weibull distribution accelerated reliability test
- the accelerated reliability test is the acceleration of the failure process.
- the failure characteristics of the tested product under the action of short-term high stress are consistent with the failure characteristics of the product under the action of long-term low stress; the relationship between the acceleration factor and the model parameters must satisfy the following relationship. In order to ensure the consistency of failure characteristics:
- Consistency of the failure process it means that there is the same definite function model between product life and stress; the function form of life distribution under different stress levels is the same, but the parameters of the function are different;
- Consistency of failure mechanism means that the failure mode remains unchanged.
- the shape parameter reflects the failure mechanism of the Weibull distribution. The same shape parameter is a necessary and sufficient condition for the consistency of the failure mechanism of the Weibull distribution accelerated life test;
- the third step is to determine the step-back stress acceleration reliability scheme based on Weibull distribution
- At least two stress gradients can be set in the step-back stress accelerated reliability test plan.
- the stress applied in the first stage is usually the ultimate stress of the product, and the stress in the second stage is lower than the stress in the first stage, but it should also be much greater than the normal working stress;
- the fifth step test data processing, reliability calculation
- the acceleration factor of the stress S 2 relative to the product life under the stress S 1 is obtained
- the product stress is mechanical stress or electrical stress
- the relationship between characteristic life and stress satisfies the inverse power law model, and the acceleration factor of stress S 2 relative to product life under stress S 1 according to and Solve to get the inverse power law model exponent n;
- the step-back stress accelerated reliability test method based on Weibull distribution proposed by the present invention provides the mathematical model of the accelerated reliability test when the product reliability obeys the Weibull distribution, the calculation formula of the acceleration factor of the constraint relationship of the model parameters, and the test method. Implementation steps and test data processing methods, and test cases are given to illustrate the solution process. Through the application of the present invention, it is beneficial to save test cost and test cycle, and has great practical significance for the reliability evaluation of high-reliability and long-life products.
- FIG. 1 is a flow chart of a step-back stress accelerated reliability test method based on Weibull distribution provided by an embodiment of the present invention.
- Fig. 2 is a histogram of stress S 2 failure data of an embodiment of the present invention.
- Fig. 3 is a Weibull probability distribution diagram of stress S 2 failure data according to an embodiment of the present invention.
- Fig. 4 is a fitting diagram of Weibull distribution of failure data under stress S 2 in an embodiment of the present invention.
- Fig. 5 is a Weibull probability distribution diagram of stress S 1 failure data according to an embodiment of the present invention.
- step-back stress accelerated reliability test method based on the Weibull distribution is implemented by the following steps:
- the first step is to select the appropriate accelerated life test physical model according to the failure mode of the product
- accelerated life testing uses the life characteristics under high stress to extrapolate the life characteristics under normal stress levels.
- the key is to establish the relationship between the life characteristics and the stress level, that is, the accelerated model.
- the most commonly used acceleration models are the Arrhenius model and the inverse power law model.
- the Arrhenius model is a life model based on temperature stress acceleration:
- L is a certain lifetime characteristic
- A is a constant
- E a represents the activation energy
- k represents the Boltzmann constant
- T is the absolute temperature.
- the Arrhenis model is widely used in accelerated life tests and accelerated storage life tests of electronic products.
- L is a certain life characteristic
- a and n are constants
- S represents the stress level.
- the second step is to determine the relationship between the acceleration factor and the model parameters of the Weibull distribution accelerated 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.
- the failure characteristics of the tested product under the action of high stress for a short time are consistent with the failure characteristics of the product under the action of low stress for a long time. Consistency of failure characteristics is manifested as:
- the regular consistency of the failure process refers to the existence of the same definite function model between the product life and stress.
- the function forms of the life distribution under different stress levels are the same, but the parameters of the functions are different.
- Consistency of failure mechanism means that the failure mode remains unchanged.
- the shape parameter reflects the failure mechanism of the Weibull distribution, and the same shape parameter is a necessary and sufficient condition for the consistency of the failure mechanism of the Weibull distribution accelerated life test.
- the acceleration factor of S2 with respect to stress S1 is:
- F(t) represents the cumulative unreliability
- ⁇ represents the scale parameter (characteristic life, constant under the same stress)
- m represents the shape parameter (constant under different stresses)
- t represents time.
- the third step is to determine the step-back stress acceleration reliability scheme based on Weibull distribution
- At least two stress gradients can be set in the step-back stress accelerated reliability test scheme.
- the stress applied in the first stage is usually the ultimate stress of the product.
- the stress in the second stage is lower than the stress in the first stage, but it should also be much greater than the normal working stress.
- the shape parameter m 2.2, the characteristic life accuracy is 10%, and the confidence level is 0.8, the number of test pieces is 12.
- a total of 24 samples are selected for the test, and 12 samples need to fail under the first set of stress S 2 , so that the shape parameters and characteristic life parameters of the Weibull distribution under the stress S 2 can be fitted.
- Six failures occurred under the second set of stress S 1 , which was used to fit the characteristic life parameters of the Weibull distribution under the stress S 1 .
- 18 samples failed and 6 samples remained.
- the test plan is shown in Table 1.
- the fifth step test data processing, reliability calculation.
- the distribution test is carried out on the failure data under the stress S 2 , and the hypothesis test results obey the Weibull distribution.
- the relationship between the life characteristics and the electrical stress satisfies the inverse power law model.
- the exponent n of the inverse power law model can be solved by using the acceleration factor ⁇ 2, 1 and the stresses S 2 and S 1 .
- the life of an electrical appliance obeys the Weibull distribution, the normal working voltage is 24V, and the maximum working voltage is 36V.
- the working life characteristics obey the inverse power law model at different voltages. Design an accelerated reliability test to find out how reliable an electrical appliance can be when the normal operating voltage is 24V and it works for 500 hours.
- the step-back stress acceleration reliability method based on Weibull distribution is adopted, and 24 test samples are selected.
- S 2 36V
- S 1 31V
- the test is selected as fixed number truncation.
- the simulation test data are shown in Table 4. A total of 12 products failed under stress S 2 , and the first stage of the test ended at 119.7h. The remaining samples were then tested under stress S 1 , a total of 6 products failed, and the test ended at 96.5h. See Table 2 for the failure data (time h) of the step-back stress test.
- the failure time under stress S 2 is drawn as a histogram, as shown in Figure 2.
- the stress S 2 test data is drawn with the Matlab function wblplot to draw the Weibull probability distribution diagram, as shown in Figure 3, it can be seen that the test data conforms to the logarithmic linear relationship in the Weibull probability diagram.
- Figure 2 and Figure 3 illustrate that product failure obeys the Weibull distribution.
- the test method of the present invention can obtain the life model of the highly reliable long-life product whose life obeys the Weibull distribution in a relatively short time, and provide the reliability index of its long-time work.
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Abstract
A step stress accelerated reliability testing method based on a Weibull distribution, comprising the steps: selecting an accelerated lifespan testing physical model according to a product failure mode; determining an acceleration factor and a model parameter relationship of a Weibull distribution accelerated reliability test; determining a step stress accelerated reliability solution based on the Weibull distribution; implementing the test; and performing test data processing and reliability calculation. When product reliability follows a Weibull distribution, the step stress accelerated reliability testing method provides a mathematical model for accelerated reliability testing, a formula for calculating a constraint relationship acceleration factor of the model parameter, test implementation steps and a test data processing method, and also provides a test case to illustrate the solution process, the application of which is beneficial to reducing testing costs and a testing period, and has great practical significance for reliability evaluation of a high-reliability, long-life product.
Description
本发明涉及加速可靠性试验技术领域，具体是涉及一种基于威布尔分布的步退应力加速可靠性试验方法。The invention relates to the technical field of accelerated reliability test, in particular to a method for accelerated reliability test of step-back stress based on Weibull distribution.
长期以来高可靠长寿命评估都是可靠性工程领域面临的一个技术难题。长寿命评估手段的不足对产品的研制和使用造成不利影响，其一，是新研产品的寿命指标无法在研制阶段进行充分验证，可能造成严重的寿命隐患；其二，使得某些产品提前报废，不能充分发挥产品的寿命潜力，造成巨大资源浪费。加速可靠性(寿命)试验技术的应用成为高可靠长寿命产品研制的必要手段。加速可靠性试验是在保持失效机理不变的条件下，通过加大试验应力水平来缩短试验周期的一种快速可靠性评估试验技术。加速可靠性试验技术满足了高可靠长寿命评估的工程需要，在可靠性工程领域得到广泛重视。目前已经在高端装备的机械、电子、机电、材料等诸多领域得到了广泛应用。For a long time, the evaluation of high reliability and long life has been a technical problem in the field of reliability engineering. Insufficient long-life evaluation methods have adverse effects on the development and use of products. First, the life indicators of newly developed products cannot be fully verified during the development stage, which may cause serious life hidden dangers; second, some products are scrapped in advance , can not give full play to the life potential of the product, resulting in a huge waste of resources. The application of accelerated reliability (life) test technology has become a necessary means for the development of high reliability and long life products. Accelerated reliability test is a rapid reliability evaluation test technology that shortens the test period by increasing the test stress level under the condition of keeping the failure mechanism unchanged. Accelerated reliability test technology meets the engineering needs of high reliability and long life evaluation, and has been widely valued in the field of reliability engineering. At present, it has been widely used in many fields such as machinery, electronics, electromechanical, and materials of high-end equipment.
加速可靠性试验按照应力加载的方式，分为恒定应力试验、步进应力试验、序进应力试验和步退应力试验四种类型。通过理论分析和数值仿真，已经证实步退应力试验在四种加速可靠性试验方式中试验效率最高，试验时间最短。但是，目前加速可靠性试验研究主要集中在恒定应力试验和步进应力试验，还没有公开文献报道基于威布尔分布的步退应力加速可靠性试验方法。According to the way of stress loading, the accelerated reliability test is divided into four types: constant stress test, step stress test, sequential stress test and step back stress test. Through theoretical analysis and numerical simulation, it has been confirmed that the step-back stress test has the highest test efficiency and the shortest test time among the four accelerated reliability test methods. However, the current accelerated reliability test research mainly focuses on constant stress test and step stress test, and there is no public literature report on the accelerated reliability test method of step-back stress based on Weibull distribution.
发明内容Contents of the invention
本发明的目的是针对高可靠长寿命产品可靠性评估的技术难题，提供一种基于威布尔分布的步退应力加速可靠性试验方法。The purpose of the present invention is to provide a step-back stress accelerated reliability test method based on Weibull distribution for the technical problem of reliability evaluation of high-reliability and long-life products.
本发明是这样实现的：The present invention is achieved like this:
一种基于威布尔分布的步退应力加速可靠性试验方法，包括以下步骤：A step-back stress accelerated reliability test method based on Weibull distribution, comprising the following steps:
第一步，根据产品失效模式，选择加速寿命试验物理模型；The first step is to select the accelerated life test physical model according to the failure mode of the product;
所述加速寿命试验物理模型采用阿伦尼斯模型或逆幂率模型；The physical model of the accelerated life test adopts the Arrhenius model or the inverse power law model;
第二步，确定威布尔分布加速可靠性试验的加速因子和模型参数关系；The second step is to determine the relationship between the acceleration factor and the model parameters of the Weibull distribution accelerated reliability test;
加速可靠性试验是失效过程的加速，受试产品在短时间高应力作用下，表现的失效特性与产品在长时间低应力作用下失效特性一致；加速因子和模型参数关系要满足下面的关系，才能保证失效特性的一致性：The accelerated reliability test is the acceleration of the failure process. The failure characteristics of the tested product under the action of short-term high stress are consistent with the failure characteristics of the product under the action of long-term low stress; the relationship between the acceleration factor and the model parameters must satisfy the following relationship. In order to ensure the consistency of failure characteristics:
(1)失效过程的规律一致性：指产品寿命与应力之间存在同一个确定的函数模型；不同应力水平下寿命分布的函数形式相同，只是函数的参数存在差异；(1) Consistency of the failure process: it means that there is the same definite function model between product life and stress; the function form of life distribution under different stress levels is the same, but the parameters of the function are different;
(2)失效机理的一致性：指失效模式不变，对于威布尔分布，形状参数反映威布尔分布的失效机理，形状参数相同是威布尔分布加速寿命试验失效机理一致性的充要条件；(2) Consistency of failure mechanism: means that the failure mode remains unchanged. For the Weibull distribution, the shape parameter reflects the failure mechanism of the Weibull distribution. The same shape parameter is a necessary and sufficient condition for the consistency of the failure mechanism of the Weibull distribution accelerated life test;
第三步，确定基于威布尔分布的步退应力加速可靠性方案；The third step is to determine the step-back stress acceleration reliability scheme based on Weibull distribution;
步退应力加速可靠性试验方案最少可以设置2个应力梯度，第1阶段施加的应力通常为产品的极限应力，第2阶段应力比第1阶段应力降低，但也应远大于正常工作应力；At least two stress gradients can be set in the step-back stress accelerated reliability test plan. The stress applied in the first stage is usually the ultimate stress of the product, and the stress in the second stage is lower than the stress in the first stage, but it should also be much greater than the normal working stress;
选取N件样品，设置引起样品失效的试验应力S
2，S
1，S
2>S
1，S
2为产品的极限应力，两组试验应力均大于产品正常工作应力S
0；
Select N samples, set the test stress S 2 that causes the failure of the sample, S 1 , S 2 > S 1 , S 2 is the ultimate stress of the product, and the two test stresses are greater than the normal working stress S 0 of the product;
针对N件样品在应力S
2下试验，直到N/2件样品失效时，第一阶段试验停止；
Test under stress S 2 for N samples, until N/2 samples fail, the first stage of the test stops;
针对剩余的N/2件样品，在应力S
1下试验，直到N/4件样品失效时，试验结束。
For the remaining N/2 samples, test under the stress S 1 until N/4 samples fail, and the test ends.
第四步，试验实施；The fourth step, test implementation;
根据第三步加速可靠性方案开展试验，并记录每一件样品失效应力和失效时间。Carry out the test according to the third-step accelerated reliability program, and record the failure stress and failure time of each sample.
第五步，试验数据处理，可靠度计算；The fifth step, test data processing, reliability calculation;
对应力S
2下的失效数据进行分布检验，判断失效数据是否符合威布尔分布；利用应力S
2下的试验数据，进行威布尔分布参数拟合，得到应力S
2下的特征寿命η
2和形状参数m
2；
Carry out distribution inspection to the failure data under the stress S 2 , judge whether the failure data conforms to the Weibull distribution; use the test data under the stress S 2 , carry out Weibull distribution parameter fitting, obtain the characteristic life η 2 and the shape under the stress S 2 parameter m2 ;
在应力S
1下威布尔分布形状参数m
1＝m
2，利用应力S
1下试验数据拟合威布尔分布的特征寿命η
1；
Under the stress S 1, the Weibull distribution shape parameter m 1 =m 2 , using the test data under the stress S 1 to fit the characteristic life η 1 of the Weibull distribution;
根据特征寿命η
2和特征寿命η
1，求得应力S
2相对于应力S
1下产品寿命的加速因子
According to the characteristic life η 2 and the characteristic life η 1 , the acceleration factor of the stress S 2 relative to the product life under the stress S 1 is obtained
若产品应力为机械应力或电应力，特征寿命与应力之间的关系满足逆幂率模型，应力S
2相对于应力S
1下产品寿命的加速因子
根据
和
求解得到逆幂率模型指数n；
If the product stress is mechanical stress or electrical stress, the relationship between characteristic life and stress satisfies the inverse power law model, and the acceleration factor of stress S 2 relative to product life under stress S 1 according to and Solve to get the inverse power law model exponent n;
逆幂率模型下，应力S
1相对于应力S
0下产品寿命的加速因子
以及威布尔分布特征寿命表达的应力S
1相对于应力S
0下产品寿命加速因子
根据Q
和
计算得到正常工作应力S
0下特征寿命η
0，正常工作应力S
0下，威布尔分布的形状参数m
0＝m
1＝m
2；
Under the inverse power law model, the acceleration factor of product life under stress S 1 relative to stress S 0 And the stress S 1 expressed by the Weibull distribution characteristic life relative to the product life acceleration factor under the stress S 0 According to Q and The characteristic life η 0 under the normal working stress S 0 is calculated, and the shape parameter of the Weibull distribution under the normal working stress S 0 is m 0 =m 1 =m 2 ;
根据正常工作应力S
0下特征寿命η
0和形状参数m
0，依据威布尔分布累计失效概率分布函数计算得到产品在正常工作应力S
0下的累积失效概率
和可靠度R(t
0)＝F(t
0)。
According to the characteristic life η 0 and the shape parameter m 0 under the normal working stress S 0 , the cumulative failure probability of the product under the normal working stress S 0 is calculated according to the cumulative failure probability distribution function of the Weibull distribution Sum reliability R(t 0 )=F(t 0 ).
本发明提出的基于威布尔分布的步退应力加速可靠性试验方法，给出产品可靠性服从威布尔分布时，其加速可靠性试验的数学模型，模型参数的约束关系加速因子计算公式，以及试验实施步骤及试验数据处理方法，并给出试验案例，说明求解过程，通过本发明的应用，有利于节约试验成本和试验周期，对于高可靠长寿命产品的可靠性评估具有重大的实践意义。The step-back stress accelerated reliability test method based on Weibull distribution proposed by the present invention provides the mathematical model of the accelerated reliability test when the product reliability obeys the Weibull distribution, the calculation formula of the acceleration factor of the constraint relationship of the model parameters, and the test method. Implementation steps and test data processing methods, and test cases are given to illustrate the solution process. Through the application of the present invention, it is beneficial to save test cost and test cycle, and has great practical significance for the reliability evaluation of high-reliability and long-life products.
图1为本发明实施例提供的基于威布尔分布的步退应力加速可靠性试验方法的流程图。FIG. 1 is a flow chart of a step-back stress accelerated reliability test method based on Weibull distribution provided by an embodiment of the present invention.
图2为本发明实施例应力S
2失效数据直方图。
Fig. 2 is a histogram of stress S 2 failure data of an embodiment of the present invention.
图3为本发明实施例应力S
2失效数据威布尔概率分布图。
Fig. 3 is a Weibull probability distribution diagram of stress S 2 failure data according to an embodiment of the present invention.
图4为本发明实施例应力S
2下失效数据威布尔分布拟合图。
Fig. 4 is a fitting diagram of Weibull distribution of failure data under stress S 2 in an embodiment of the present invention.
图5为本发明实施例应力S
1失效数据威布尔概率分布图。
Fig. 5 is a Weibull probability distribution diagram of stress S 1 failure data according to an embodiment of the present invention.
为了使本技术领域的人员更好地理解本发明方案，以下对本发明进行详细说明。In order to enable those skilled in the art to better understand the solution of the present invention, the present invention is described in detail below.
参见图1所示，基于威布尔分布的步退应力加速可靠性试验方法，采用以下步骤实现：Referring to Figure 1, the step-back stress accelerated reliability test method based on the Weibull distribution is implemented by the following steps:
第一步，根据产品失效模式，选择合适的加速寿命试验物理模型；The first step is to select the appropriate accelerated life test physical model according to the failure mode of the product;
加速寿命试验的基本思想是利用高应力下的寿命特征去外推正常应力水平下的寿命特征。关键在于建立寿命特征与应力水平之间的关系，即加速模型。在加速模型中最常用的是阿伦尼斯模型和逆幂率模型。The basic idea of accelerated life testing is to use the life characteristics under high stress to extrapolate the life characteristics under normal stress levels. The key is to establish the relationship between the life characteristics and the stress level, that is, the accelerated model. The most commonly used acceleration models are the Arrhenius model and the inverse power law model.
(1)阿伦尼斯模型(1) Arronis model
阿伦尼斯模型是基于温度应力加速的寿命模型：The Arrhenius model is a life model based on temperature stress acceleration:
其中，L是某寿命特征，A为常数，E
a代表活化能，k表示玻尔兹曼常数，T为绝对温度。
Among them, L is a certain lifetime characteristic, A is a constant, E a represents the activation energy, k represents the Boltzmann constant, and T is the absolute temperature.
温度T
2相对于温度T
1下产品寿命的加速因子：
Acceleration factor for product life at temperature T2 relative to temperature T1 :
阿伦尼斯模型广泛应用电子产品加速寿命试验和加速贮存寿命试验中。The Arrhenis model is widely used in accelerated life tests and accelerated storage life tests of electronic products.
(2)逆幂率模型(2) Inverse power law model
除了温度应力以外，经常遇到的还有机械应力和电应力，大量试验数据证实，产品在机械应力与电应力作用下的寿命特征与应力的关系满足逆幂率模型：In addition to temperature stress, mechanical stress and electrical stress are often encountered. A large number of test data confirm that the relationship between product life characteristics and stress under the action of mechanical stress and electrical stress satisfies the inverse power law model:
L＝AS
-n (3)
L＝AS -n (3)
其中，L是某寿命特征，A和n为常数，S表示应力水平。Among them, L is a certain life characteristic, A and n are constants, and S represents the stress level.
应力S
2相对于应力S
1下产品寿命的加速因子：
Acceleration factor for product life under stress S 2 relative to stress S 1 :
第二步，确定威布尔分布加速可靠性试验的加速因子和模型参数关系；The second step is to determine the relationship between the acceleration factor and the model parameters of the Weibull distribution accelerated reliability test;
加速可靠性试验是在加速寿命试验的基础上，进一步考虑寿命的可靠性分布特征。加速可靠性试验是失效过程的加速，受试产品在短时间高应力作用下，表现的失效特性与产品在长时间低应力作用下失效特性一致。失效特性一致性具体表现为：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. The failure characteristics of the tested product under the action of high stress for a short time are consistent with the failure characteristics of the product under the action of low stress for a long time. Consistency of failure characteristics is manifested as:
(1)失效过程的规律一致性：指产品寿命与应力之间存在同一个确定的函数模型。不同应力水平下寿命分布的函数形式相同，只是函数的参数存在差异。(1) The regular consistency of the failure process: refers to the existence of the same definite function model between the product life and stress. The function forms of the life distribution under different stress levels are the same, but the parameters of the functions are different.
(2)失效机理的一致性：指失效模式不变。对于威布尔分布，形状参数反映威布尔分布的失效机理，形状参数相同是威布尔分布加速寿命试验失效机理一致性的充要条件。(2) Consistency of failure mechanism: means that the failure mode remains unchanged. For the Weibull distribution, the shape parameter reflects the failure mechanism of the Weibull distribution, and the same shape parameter is a necessary and sufficient condition for the consistency of the failure mechanism of the Weibull distribution accelerated life test.
加速可靠性试验的加速因子定义为：若产品在应力S
1和S
2分别作用时间t
1与t
2的累积失效概率相同，即F
1(t
1)＝F
2(t
2)，则应力S
2相对于应力S
1的加速因子为：
The acceleration factor of the accelerated reliability test is defined as: If the cumulative failure probability of the product is the same when the stress S 1 and S 2 act on time t 1 and t 2 respectively, that is, F 1 (t 1 )=F 2 ( t 2 ) , then the stress The acceleration factor of S2 with respect to stress S1 is:
威布尔分布的累积失效概率表达式为：The cumulative failure probability expression for the Weibull distribution is:
式中，F(t)表示累积不可靠度，η表示尺度参数(特征寿命，同一应力下为常数)，m表示形状参数(不同应力下均为常数)，t表示时间。In the formula, F(t) represents the cumulative unreliability, η represents the scale parameter (characteristic life, constant under the same stress), m represents the shape parameter (constant under different stresses), and t represents time.
两种应力条件下，威布尔分布的加速因子：Acceleration factors for the Weibull distribution for two stress conditions:
第三步，确定基于威布尔分布的步退应力加速可靠性方案；The third step is to determine the step-back stress acceleration reliability scheme based on Weibull distribution;
步退应力加速可靠性试验方案最少可以设置2个应力梯度，第1阶段施加的应力通常为产品的极限应力，第2阶段应力比第1阶段应力降低，但也应远大于正常工作应力。At least two stress gradients can be set in the step-back stress accelerated reliability test scheme. The stress applied in the first stage is usually the ultimate stress of the product. The stress in the second stage is lower than the stress in the first stage, but it should also be much greater than the normal working stress.
威布尔分布形状参数m越小需要试验件数量越多，当形状参数m＝2.2，特征寿命精度10％，置信水平0.8时，需要试件数12。The smaller the shape parameter m of the Weibull distribution, the more test pieces are required. When the shape parameter m=2.2, the characteristic life accuracy is 10%, and the confidence level is 0.8, the number of test pieces is 12.
试验总样本选24件，在第一组应力S
2下需要12件样品发生失效，即可拟合出应力S
2下威布尔分布的形状参数和特征寿命参数。在第二组应力S
1下发生6件失效，用来拟合应力S
1下威布尔分布的特征寿命参数。试验结束时18件样本发生失效，剩余6个样本。试验方案见表1。
A total of 24 samples are selected for the test, and 12 samples need to fail under the first set of stress S 2 , so that the shape parameters and characteristic life parameters of the Weibull distribution under the stress S 2 can be fitted. Six failures occurred under the second set of stress S 1 , which was used to fit the characteristic life parameters of the Weibull distribution under the stress S 1 . At the end of the test, 18 samples failed and 6 samples remained. The test plan is shown in Table 1.
表1试验顺序表Table 1 Test sequence list
| 试验顺序Test sequence | 应力stress | 失效时间Expiration time |
| 11 | S 2 S 2 | t i,(i＝1-12) t i ,(i=1-12) |
| 22 | S 1 S 1 | t j,(j＝13-18) t j ,(j＝13-18) |
第四步，试验实施；The fourth step, test implementation;
按照表1的试验顺序，针对24件样品施加应力S
2，直到出现12件样品失效，第一阶段试验结束。
According to the test sequence in Table 1, the stress S 2 was applied to 24 samples until 12 samples failed, and the first stage of the test ended.
针对剩余12件样品施加应力S
1，直到出现6件样品失效，试验结束。
Apply stress S 1 to the remaining 12 samples until 6 samples fail, and the test ends.
试验过程中记录每一件样品失效应力和失效时间。Record the failure stress and failure time of each sample during the test.
第五步，试验数据处理，可靠度计算。The fifth step, test data processing, reliability calculation.
对应力S
2下的失效数据进行分布检验，假设检验结果服从威布尔分布。
The distribution test is carried out on the failure data under the stress S 2 , and the hypothesis test results obey the Weibull distribution.
利用应力S
2下的失效数据，进行威布尔分布参数拟合，得到应力S
2下威布尔分布的特征寿命参数η
2和形状参数m
2。
Using the failure data under stress S 2 , the parameters of Weibull distribution are fitted, and the characteristic life parameter η 2 and shape parameter m 2 of Weibull distribution under stress S 2 are obtained.
在应力S
1下m
1＝m
2，接着利用应力S
1下试验数据拟合威布尔分布的特征寿命参数η
1。
Under the stress S 1 m 1 =m 2 , then use the experimental data under the stress S 1 to fit the characteristic life parameter η 1 of the Weibull distribution.
根据η
2和η
1可以求得应力S
2下相对于应力S
1下加速因子，
According to η 2 and η 1 , the acceleration factor under the stress S 2 relative to the stress S 1 can be obtained,
若产品施加的电应力，寿命特征与电应力的关系满足逆幂率模型。根据式(4)用加速因子α
2，1和应力S
2和S
1可以求解逆幂率模型指数n。
If the electrical stress is applied to the product, the relationship between the life characteristics and the electrical stress satisfies the inverse power law model. According to formula (4), the exponent n of the inverse power law model can be solved by using the acceleration factor α 2, 1 and the stresses S 2 and S 1 .
根据逆幂率模型的指数n，试验应力S
2和实际工作应力S
0，寿命特征η
2，可以求解实际工作特征寿命η
0，实际工作应力下威布尔分布形状参数m
0＝m
2。
According to the exponent n of the inverse power law model, the test stress S 2 and the actual working stress S 0 , and the life characteristic η 2 , the actual working characteristic life η 0 and the Weibull distribution shape parameter m 0 =m 2 under the actual working stress can be solved.
根据威布尔分布参数η
0和m
0，可以求解实际工作应力下可靠度指标R
0(t)。
According to Weibull distribution parameters η 0 and m 0 , the reliability index R 0 (t) under actual working stress can be solved.
下面结合某电器加速可靠性试验案例对本发明作进一步的详细说明。The present invention will be further described in detail below in conjunction with an electrical appliance accelerated reliability test case.
某电器可靠性参数Reliability parameters of an electrical appliance
某电器寿命服从威布尔分布，正常工作电压24V，最高工作电压36V。在不同电压下工作寿命特征服从逆幂率模型。设计加速可靠性试验，求解正常工作电压24V，工作500h时，某电器工作可靠度能达到多少。The life of an electrical appliance obeys the Weibull distribution, the normal working voltage is 24V, and the maximum working voltage is 36V. The working life characteristics obey the inverse power law model at different voltages. Design an accelerated reliability test to find out how reliable an electrical appliance can be when the normal operating voltage is 24V and it works for 500 hours.
某电器加速寿命试验方案Accelerated life test plan for an electrical appliance
采用基于威布尔分布的步退应力加速可靠性方法，试验样本选24件。试验应力选择S
2＝36V，S
1＝31V，试验选择定数截尾。在应力S
2下发生12件样品失效时，第一阶段试验停止，转为应力S
1继续试验。应力S
1下出现6件样品失效时，试验结束。
The step-back stress acceleration reliability method based on Weibull distribution is adopted, and 24 test samples are selected. The test stress is selected as S 2 =36V, S 1 =31V, and the test is selected as fixed number truncation. When 12 samples failed under the stress S 2 , the first stage of the test was stopped, and the test was transferred to the stress S 1 to continue the test. The test ends when 6 samples fail under stress S1 .
试验数据Test Data
仿真试验数据见表4。应力S
2下共12件产品失效，第119.7h第一阶段试验结束。剩余样品接着在应力S
1下进行试验，共6件产品失效，第96.5h试验结束。步退应力试验失效数据(时间h)见表2。
The simulation test data are shown in Table 4. A total of 12 products failed under stress S 2 , and the first stage of the test ended at 119.7h. The remaining samples were then tested under stress S 1 , a total of 6 products failed, and the test ended at 96.5h. See Table 2 for the failure data (time h) of the step-back stress test.
表2 试验失效数据Table 2 Test failure data
数据分析，可靠度计算Data analysis, reliability calculation
应力S
2下的失效时间进行直方图绘制，如图2所示。应力S
2试验数据用Matlab函数wblplot绘制威布尔概率分布图，如图3所示，可以看出试验数据在威布尔概率图中符合对数线性关系。图2、图3说明产品失效服从威布尔分布。
The failure time under stress S 2 is drawn as a histogram, as shown in Figure 2. The stress S 2 test data is drawn with the Matlab function wblplot to draw the Weibull probability distribution diagram, as shown in Figure 3, it can be seen that the test data conforms to the logarithmic linear relationship in the Weibull probability diagram. Figure 2 and Figure 3 illustrate that product failure obeys the Weibull distribution.
根据威布尔分布累积概率失效公式(6)，应用应力S
2下失效数据，拟合得到威布尔分布特征参数值：
According to the cumulative probability failure formula (6) of the Weibull distribution, the failure data under the stress S 2 is applied, and the characteristic parameter values of the Weibull distribution are obtained by fitting:
m
2＝2.62，η
2＝140.3h，参数拟合曲线见图4。
m 2 =2.62, η 2 =140.3h, the parameter fitting curve is shown in Figure 4.
在应力S
1下失效数据威布尔概率分布图见图5，失效服从威布尔分布。
The Weibull probability distribution diagram of the failure data under the stress S 1 is shown in Fig. 5, and the failure obeys the Weibull distribution.
应力S
1下失效数据符合威布尔分布，形状参数与应力S
2下相同，m
1＝m
2＝2.62。依据应力S
1下失效数据拟合威布尔分布特征寿命η
1＝288.4h。
The failure data under stress S 1 conforms to Weibull distribution, and the shape parameters are the same as those under stress S 2 , m 1 =m 2 =2.62. According to the failure data under stress S 1 , the characteristic life of Weibull distribution is fitted to η 1 =288.4h.
根据式(7)，可以计算得到应力S
2与应力S
1的加速因子：
According to formula (7), the acceleration factors of stress S 2 and stress S 1 can be calculated:
根据式(4)，可以计算得到逆幂率模型指数n＝4.83。According to formula (4), the inverse power law model exponent n=4.83 can be calculated.
根据式(4)，可以计算得到应力S
2与正常工作应力S
0的加速系数：
According to formula (4), the acceleration coefficient of stress S 2 and normal working stress S 0 can be calculated:
可知正常工作应力下，产品失效服从威布尔分布，m
0＝m
2＝2.62，特征寿命：
It can be seen that under normal working stress, the failure of the product obeys the Weibull distribution, m 0 =m 2 =2.62, and the characteristic life is:
η
0＝α
2，0·η
2＝997.7h
η 0 =α 2,0 ·η 2 =997.7h
根据式(6)，可以计算得到某电器工作500h时的累积失效概率：F(500)＝15.2％；可靠度R(500)＝84.8％。According to formula (6), the cumulative failure probability of an electrical appliance can be calculated when it works for 500 hours: F(500)=15.2%; reliability R(500)=84.8%.
经过试验案例检验，本发明的试验方法，使用较短时间，能够得到寿命服从威布尔分布的高可靠长寿命产品的寿命模型，并给出其长时间工作的可靠度指标。Through test case inspection, the test method of the present invention can obtain the life model of the highly reliable long-life product whose life obeys the Weibull distribution in a relatively short time, and provide the reliability index of its long-time work.
以上所述仅是本发明的一种实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和调整，这些改进和调整也应视为本发明的保护范围。The above is only one embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and adjustments can also be made. These improvements and adjustments It should also be regarded as the protection scope of the present invention.
Claims (4)
- 基于威布尔分布的步退应力加速可靠性试验方法，其特征在于，包括以下步骤：The step-back stress accelerated reliability test method based on Weibull distribution is characterized in that it comprises the following steps:第一步，根据产品失效模式，选择加速寿命试验物理模型；The first step is to select the accelerated life test physical model according to the failure mode of the product;所述加速寿命试验物理模型采用阿伦尼斯模型和逆幂率模型；The physical model of the accelerated life test adopts the Arrhenis model and the inverse power law model;第二步，确定威布尔分布加速可靠性试验的加速因子和模型参数关系；The second step is to determine the relationship between the acceleration factor and the model parameters of the Weibull distribution accelerated reliability test;第三步，确定基于威布尔分布的步退应力加速可靠性方案；The third step is to determine the step-back stress acceleration reliability scheme based on Weibull distribution;步退应力加速可靠性试验方案最少可以设置2个应力梯度，第1阶段施加的应力通常为产品的极限应力，第2阶段应力比第1阶段应力降低，但也应远大于正常工作应力；At least two stress gradients can be set in the step-back stress accelerated reliability test plan. The stress applied in the first stage is usually the ultimate stress of the product, and the stress in the second stage is lower than the stress in the first stage, but it should also be much greater than the normal working stress;选取N件样品，设置引起样品失效的试验应力S 2，S 1，S 2>S 1，S 2为产品的极限应力，两组试验应力均大于产品正常工作应力S 0； Select N samples, set the test stress S 2 that causes the failure of the sample, S 1 , S 2 > S 1 , S 2 is the ultimate stress of the product, and the two test stresses are greater than the normal working stress S 0 of the product;针对N件样品在应力S 2下试验，直到N/2件样品失效时，第一阶段试验停止； Test under stress S 2 for N samples, until N/2 samples fail, the first stage of the test stops;针对剩余的N/2件样品，在应力S 1下试验，直到N/4件样品失效时，试验结束； For the remaining N/2 samples, test under the stress S 1 until N/4 samples fail, and the test ends;第四步，试验实施；The fourth step, test implementation;根据第三步加速可靠性方案开展试验，并记录每一件样品失效应力和失效时间；Carry out the test according to the third-step accelerated reliability plan, and record the failure stress and failure time of each sample;第五步，试验数据处理，可靠度计算。The fifth step, test data processing, reliability calculation.
- 根据权利要求1所述的基于威布尔分布的步退应力加速可靠性试验方法，其特征在于，所述可靠度计算的步骤如下：The step-back stress accelerated reliability test method based on Weibull distribution according to claim 1, wherein the steps of calculating the reliability are as follows:对应力S 2下的失效数据进行分布检验，判断失效数据是否符合威布尔分布；利用应力S 2下的试验数据，进行威布尔分布参数拟合，得到应力S 2下的特征寿命η 2和形状参数m 2； Carry out distribution inspection to the failure data under the stress S 2 , judge whether the failure data conforms to the Weibull distribution; use the test data under the stress S 2 , carry out Weibull distribution parameter fitting, obtain the characteristic life η 2 and the shape under the stress S 2 parameter m2 ;在应力S 1下威布尔分布形状参数m 1＝m 2，利用应力S 1下试验数据拟合威布尔分布的特征寿命η 1； Under the stress S 1, the Weibull distribution shape parameter m 1 =m 2 , using the test data under the stress S 1 to fit the characteristic life η 1 of the Weibull distribution;根据特征寿命η 2和特征寿命η 1和求得应力S 2相对于应力S 1下产品寿命的加速因子According to characteristic life η 2 and characteristic life η 1 sum, obtain the acceleration factor of stress S 2 relative to product life under stress S 1
若产品应力为机械应力或电应力，特征寿命与应力之间的关系满足逆幂率模型，应力S 2相对于应力S 1下产品寿命的加速因子根据
和
求解得到逆幂率模型指数n； If the product stress is mechanical stress or electrical stress, the relationship between characteristic life and stress satisfies the inverse power law model, and the acceleration factor of stress S 2 relative to product life under stress S 1
according toandSolve to get the inverse power law model exponent n;逆幂率模型下，应力S 1相对于应力S 0下产品寿命的加速因子以及威布尔分 布特征寿命表达的应力S 1相对于应力S 0下产品寿命加速因子
根据
和
计算得到正常工作应力S 0下特征寿命η 0；正常工作应力S 0下，威布尔分布的形状参数m 0＝m 1＝m 2； Under the inverse power law model, the acceleration factor of product life under stress S 1 relative to stress S 0
And the stress S 1 expressed by the Weibull distribution characteristic life relative to the product life acceleration factor under the stress S 0according toandCalculate the characteristic life η 0 under the normal working stress S 0 ; under the normal working stress S 0 , the shape parameter of the Weibull distribution m 0 =m 1 =m 2 ;根据正常工作应力S 0下特征寿命η 0和形状参数m 0，依据威布尔分布累计失效概率分布函数计算得到产品在正常工作应力S 0下的累积失效概率和可靠度R(t 0)＝1-F(t 0)。 According to the characteristic life η 0 and the shape parameter m 0 under the normal working stress S 0 , the cumulative failure probability of the product under the normal working stress S 0 is calculated according to the cumulative failure probability distribution function of the Weibull distribution
and reliability R(t 0 )=1-F(t 0 ). - 根据权利要求1所述的基于威布尔分布的步退应力加速可靠性试验方法，其特征在于，加速可靠性试验是失效过程的加速，受试产品在短时间高应力作用下，表现的失效特性与产品在长时间低应力作用下失效特性一致。The step-back stress accelerated reliability test method based on Weibull distribution according to claim 1, characterized in that the accelerated reliability test is the acceleration of the failure process, and the tested product exhibits failure characteristics under the action of short-term high stress It is consistent with the failure characteristics of the product under long-term low stress.
- 根据权利要求1所述的基于威布尔分布的步退应力加速可靠性试验方法，其特征在于，加速因子和模型参数关系要满足下面的关系，才能保证失效特性的一致性：The step-back stress accelerated reliability test method based on Weibull distribution according to claim 1 is characterized in that the relationship between the acceleration factor and the model parameters must satisfy the following relationship to ensure the consistency of failure characteristics:(1)失效过程的规律一致性：指产品寿命与应力之间存在同一个确定的函数模型；不同应力水平下寿命分布的函数形式相同，只是函数的参数存在差异；(1) Consistency of the failure process: it means that there is the same definite function model between product life and stress; the function form of life distribution under different stress levels is the same, but the parameters of the function are different;(2)失效机理的一致性：指失效模式不变，对于威布尔分布，形状参数反映威布尔分布的失效机理，形状参数相同是威布尔分布加速寿命试验失效机理一致性的充要条件。(2) Consistency of failure mechanism: It means that the failure mode remains unchanged. For the Weibull distribution, the shape parameter reflects the failure mechanism of the Weibull distribution. The same shape parameter is a necessary and sufficient condition for the consistency of the failure mechanism of the Weibull distribution accelerated life test.
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