Multi-stress acceleration model construction and selection method of product

Abstract

In order to describe the coupling effect of various stresses, two types of multi-stress acceleration models are respectively constructed, a selection method of the multi-stress acceleration models is provided, and the constructed multi-stress models comprise a multi-stress acceleration model based on stress synthesis and a multi-stress acceleration model based on a mixed effect; aiming at the two multi-stress acceleration models, an acceleration model selection method based on mechanism consistency is provided. The two established multi-stress acceleration models can quantitatively describe the positive correlation effect and the negative correlation effect among multiple stresses, the coupling effect among the multiple stresses is accurately described, and method support is provided for improving the product life prediction precision under the multi-stress condition.

Description

Technical Field

[0001] The present invention relates to the technical field of accelerated life test, and is applicable to an electromechanical product that is stored for a long time and used once. In order to characterize the coupling effect of multiple stresses, the present invention constructs two types of multi-stress acceleration models respectively, and further proposes an acceleration model selection method. Background Art

[0002] Some electromechanical products are technologically complex, have small reserves and high value. They widely adopt new principles, new processes and new materials, and are subjected to a variety of different stresses during storage. The storage failure mechanism under the influence of multiple stresses is unclear, and the traditional single stress accelerated life test evaluation method is difficult to apply. It is urgent to carry out research to understand the failure mechanism and failure law of the product under the influence of multiple stresses, and to carry out relevant multi-stress accelerated life test research to provide technical support for more accurate determination of product life.

[0003] Carrying out accelerated life tests provides a good way to evaluate the failure modes and failure laws of long-storage products. The accuracy of the acceleration model directly affects the accuracy of the accelerated test data. The acceleration model usually includes a single stress acceleration model and a multi-stress acceleration model. In engineering practice, it is often necessary to select the acceleration model according to actual conditions. Temperature, humidity, and electrical stresses such as voltage and current are the most common types of stress in accelerated life tests. Common single stress acceleration models, such as the Arrhenius model that describes the life-temperature relationship, the inverse power law model that describes the life-electrical stress relationship, and the Coffin-Manson model that describes the life-thermal cycle relationship, all reflect the law of change of product life under a single stress, which provides an important basis for judging product failure modes and failure laws. However, in engineering practice, products often experience the combined effects of multiple stresses during storage. How to accurately characterize the coupling effects between multiple environmental stresses and evaluate the storage life is a difficult problem in the current field of product reliability assessment. Summary of the invention

[0004] The purpose of the present invention is to accurately characterize the coupling effect between multiple stresses and improve the prediction accuracy of product life under multiple stress conditions. Two multi-stress acceleration models are established and an acceleration model selection method based on mechanism consistency is proposed.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] The multi-stress acceleration model based on stress synthesis includes a general log-linear model established when there are multiple environmental stresses, which regards the product life as a vector X=(X1, X2, ..., X n ), the mathematical model is as follows:

[0007]

[0008] Among them, θ is its characteristic life span; a k is an unknown parameter; x k is the kth environmental stress in the comprehensive environment; a0 is a constant. According to the definition of the acceleration factor, the acceleration factor of the model can be expressed as:

[0009]

[0010] Among them, x k,i and x k,j are the kth environmental stress in the ith comprehensive stress and the jth comprehensive stress respectively;

[0011] Furthermore, the generalized log-linear model adopts the Arrhenius model, which is expressed as follows:

[0012]

[0013] where S1, S2, …, S p is the p-dimensional stress, c0, c1, …, c l is the unknown coefficient, is a known function.

[0014] A multi-stress acceleration model based on mixed effects includes introducing mixed effects on the basis of existing multi-stress acceleration models to establish a failure time model that considers the multi-stress coupling relationship; the mixed effects include fixed effects and random effects, the fixed effects are mainly used to characterize general characteristics, and the random effects are used to reflect the correlation between random variables; the multi-stress failure time model integrating random effects can be divided into two layers, the first layer is used to describe the relationship between characteristic life and environmental stress under a certain composite environment, the second layer model uses the environmental coefficients in the first layer model as random variables, and represents the coupling effect between environmental stresses by establishing a joint distribution of coefficients; in the second layer model, a multivariate normal distribution is used as a joint distribution, wherein the mean of the multivariate normal distribution represents the fixed effect, and the covariance matrix represents the random effect.

[0015] Furthermore, the first-level model is: assuming that the electronic device is mainly affected by p kinds of environmental stresses, these environmental stresses are represented as X1, X2, ..., X p .X i (i=1,…,p) can be temperature, humidity, electrical stress, mechanical stress, etc.; Assume that in the i-th comprehensive environment, the p environmental stresses are X 1,i ,X 2,i ,…,X p,i , then the life characteristic θ i It can be expressed as

[0016]

[0017] Among them, a k , k = 0, 1, ..., p is the environmental coefficient of the model, g(X k,i ) is the function of the kth environmental stress in the ith comprehensive environment. Through model transformation, we can get

[0018]

[0019] Among them, h(θ i ) is the characteristic life θ i function.

[0020] Furthermore, the second-level model is: considering the coupling effect between various environmental stresses, assuming that the coefficient a l with a m (l=0,1,…,p,m=0,1,…,p,l≠m) are correlated and obey the bivariate normal distribution. The joint density function can be expressed as

[0021]

[0022] Among them, μl l and μ m The coefficients a are l with a m The mean value, σ l and σ m The coefficients a are l with a m The standard deviation of l with a m The correlation coefficient can be expressed as

[0023]

[0024] Furthermore, based on the analysis of the above two-layer model, the multi-stress failure time model considering the coupling relationship can be specifically expressed as

[0025]

[0026] Among them, k=1,...,p, l=0,1,...,p, m=0,1,...,p, μ=(μ l ,μ m )′ is (a l ,a m )′, for (a l ,a m )′, the covariance matrix of environmental stress X l With X m The coupling effect is through (al ,a m )′ covariance Cov(a l ,a m ) to reflect.

[0027] A method for selecting a multi-stress acceleration model, characterized in that it comprises the following steps:

[0028] S1: Calculate the acceleration factor sample based on the estimated values ​​of the distribution model parameters under two stress levels;

[0029] S2: Calculate the mean value μ(K of the acceleration factor sample) i,i+1 ) and standard deviation σ(K i,i+1 );

[0030] S3: Calculate the coefficient of variation of the acceleration factor:

[0031]

[0032] Where k is the stress level number of the accelerated test, CV(K i,i+1 ) represents stress s i Relative to stress s i+1 The coefficient of variation of the acceleration factor;

[0033] S4: Compare the size of the coefficient of variation of the acceleration factor under different acceleration model assumptions, and select the acceleration model with the smallest coefficient of variation.

[0034] The beneficial effects of adopting the above technical solution are:

[0035] In order to characterize the comprehensive effects of multiple stresses, the present invention constructs two types of multi-stress acceleration models, namely: a multi-stress acceleration model based on stress synthesis and a multi-stress acceleration model based on mixed effect, both of which can quantitatively describe the positive correlation effect and negative correlation effect between multiple stresses. A method for selecting an acceleration model is further proposed, and the proposed method is verified in combination with a certain metering device. The present invention provides theoretical support for improving the accuracy of product life prediction under multi-stress conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Accelerated life test data for a certain type of metering device

[0037] Figure 2 The reliability and confidence limit curve of a certain type of metering device under the Weibull-mixed effect acceleration model DETAILED DESCRIPTION

[0038] The present invention provides a multi-stress acceleration model based on stress synthesis, which includes a general log-linear model established when there are multiple environmental stresses, and regards the product life as a vector X=(X1, X2, ..., X n ), the mathematical model is as follows:

[0039]

[0040] Among them, θ is its characteristic life span; a k is an unknown parameter; x k is the kth environmental stress in the comprehensive environment; a0 is a constant. According to the definition of the acceleration factor, the acceleration factor of the model can be expressed as:

[0041]

[0042] Among them, x k,i and x k,j are the kth environmental stress in the ith comprehensive stress and the jth comprehensive stress respectively;

[0043] Furthermore, the generalized log-linear model adopts the Arrhenius model, which is expressed as follows:

[0044]

[0045] where S1, S2, …, S p is the p-dimensional stress, c0, c1, …, c l is the unknown coefficient, is a known function. When using the generalized log-linear model, just replace X k By replacing the corresponding variables, the model can be used as a comprehensive stress acceleration model.

[0046] A multi-stress acceleration model based on mixed effects includes introducing mixed effects on the basis of existing multi-stress acceleration models to establish a failure time model that considers the multi-stress coupling relationship; the mixed effects include fixed effects and random effects, the fixed effects are mainly used to characterize general characteristics, and the random effects are used to reflect the correlation between random variables; the multi-stress failure time model integrating random effects can be divided into two layers, the first layer is used to describe the relationship between characteristic life and environmental stress under a certain composite environment, the second layer model uses the environmental coefficients in the first layer model as random variables, and represents the coupling effect between environmental stresses by establishing a joint distribution of coefficients; in the second layer model, a multivariate normal distribution is used as a joint distribution, wherein the mean of the multivariate normal distribution represents the fixed effect, and the covariance matrix represents the random effect.

[0047] The first-level model is: Assume that the electronic equipment is mainly affected by p kinds of environmental stresses, and these environmental stresses are represented as X1, X2, ..., X p .X i (i=1,…,p) can be temperature, humidity, electrical stress, mechanical stress, etc.; Assume that in the i-th comprehensive environment, the p environmental stresses are X 1,i ,X 2,i ,…,X p,i , then the life characteristic θ i It can be expressed as

[0048]

[0049] Among them, a k , k = 0, 1, ..., p is the environmental coefficient of the model, g(X k,i ) is the function of the kth environmental stress in the ith comprehensive environment. Through model transformation, we can get

[0050]

[0051] Among them, h(θ i ) is the characteristic life θ i function.

[0052] The second-level model is: considering the coupling between various environmental stresses, assuming that the coefficient a l with a m (l=0,1,…,p,m=0,1,…,p,l≠m) are correlated and obey the bivariate normal distribution. The joint density function can be expressed as

[0053]

[0054] Among them, μ l and μ m The coefficients a are l with a m The mean value, σ l and σ m The coefficients a are l with a m The standard deviation of l with a m The correlation coefficient can be expressed as

[0055]

[0056] Based on the analysis of the above two-layer model, the multi-stress failure time model considering the coupling relationship can be specifically expressed as

[0057]

[0058] Among them, k=1,...,p, l=0,1,...,p, m=0,1,...,p, μ=(μ l ,μ m )′ is (a l ,a m )′, for (a l ,a m )′, the covariance matrix of environmental stress X l With X m The coupling effect is through (a l ,a m )′ covariance Cov(a l ,a m ) to reflect.

[0059] In the above multi-stress acceleration model considering mixed effects, the first-level model reflects the generalized linear relationship between the life function and environmental stress under various comprehensive environments, and the second-level model establishes the coupling effect between various environments through the covariance between environmental coefficients.

[0060] A selection method for multi-stress acceleration models based on stress comprehensive or mixed effects is proposed. The purpose is to compare the stability of the estimated results of product acceleration factors on the same scale. The coefficient of variation is used to measure the dispersion of the acceleration factor. According to the characteristics of the accelerated test data, a definition of the coefficient of variation of the acceleration factor is given for the optimization of the stress level of the constant stress accelerated test:

[0061] The sum of the coefficients of variation of the acceleration factors between adjacent stress levels, that is:

[0062]

[0063] Where k is the stress level number of the accelerated test, σ(K i,i' ) and μ(K i,i' ) is the standard deviation and mean of the estimated acceleration factor between the th and th stress levels, CV(K i,i' ) is the corresponding coefficient of variation.

[0064] The multi-stress acceleration model selection method includes the following steps:

[0065] S1: According to s i and i+1 Samples of acceleration factors calculated from estimated values ​​of distribution model parameters at two stress levels;

[0066] S2: Calculate the mean value μ(K of the acceleration factor sample) i,i+1 ) and standard deviation σ(K i,i+1 );

[0067] S3: Calculate the coefficient of variation of the acceleration factor:

[0068]

[0069] Where k is the stress level number of the accelerated test, CV(K i,i+1 ) represents stress s i Relative to stress s i+1 The coefficient of variation of the acceleration factor;

[0070] S4: Compare the size of the coefficient of variation of the acceleration factor under different acceleration model assumptions, and select the acceleration model with the smallest coefficient of variation.

[0071] The following are specific application examples of the present invention:

[0072] A metering device was subjected to a 7-year natural storage test in Daxing District, Beijing. During the test, 32 of the 586 metering devices failed after 7 years. The conditions of the natural storage test are: average temperature 288K, average humidity 40%RH, and working current 10A. According to the results of the natural storage test, it was calculated that the reliability of the metering device working for 7 years under this condition is approximately 0.95. In order to verify the reliability assessment results, three comprehensive accelerated tests of temperature, humidity, and electrical stress were further carried out on the same model of metering devices, and the performance parameter data of each sample were measured, based on which the pseudo-life data of the multi-stress accelerated test was obtained. The stress settings of the accelerated test are shown in Table 1, and the failure conditions of the metering device are shown in Table 1. Figure 1 shown.

[0073] Table 1 Multi-stress accelerated test conditions for a certain type of metering device

[0074]

[0075]

[0076] In the case of Weibull distribution, the multi-stress acceleration model based on stress synthesis and the multi-stress acceleration model considering mixed effects will be used to evaluate and predict its life, and the two evaluation results will be compared and analyzed.

[0077] (2) Construction and evaluation of multi-stress acceleration model

[0078] The normal working stress of the metering device is temperature 293K, humidity 45%RH, and current 10A. This stress level combination is recorded as S1. The highest stress conditions applied in the five groups of tests are temperature 353K, humidity 90%RH, and current 60A. This stress level combination is recorded as S2.

[0079] 1) Construction and evaluation of multi-stress acceleration model based on stress synthesis

[0080] According to the stress type, temperature stress and humidity stress obey the Arrhenius model, and current stress obeys the inverse power law model. The logarithmic forms of the two types of acceleration models are combined according to the generalized log-linear model to construct the acceleration model as shown in Table 2. i RH i and I i are respectively the temperature stress, humidity stress and current stress under the i-th group of stress level combination, η i is the characteristic life of the Weibull distribution.

[0081] Table 2 Construction of stress comprehensive acceleration model for a certain type of metering device

[0082]

[0083]

[0084] Based on the nonlinear optimization genetic algorithm, the parameter estimation results are shown in Table 2.

[0085] Table 3 Estimation results of metering device parameters under Weibull-stress comprehensive acceleration model

[0086] <![CDATA[α1]]> <![CDATA[α2]]> <![CDATA[α3]]> <![CDATA[α4]]> <![CDATA[α5]]> <![CDATA[α6]]> <![CDATA[α0]]> β Model 1 3.50 3.11 <![CDATA[-2.69×10 -8 ×10 -8 ]]> 0 0 0 -5.87 2.67 Model 2 <![CDATA[1.47×10 -5 ]]> -12.27 0.73 4.95 0 0 -13.82 3.07 Model 3 <![CDATA[8.77×10 -6 ]]> 2.18 -3.83 0 1.55 0 -5.69 2.86 Model 4 0.32 54.25 14.09 0 0 -13.26 -59.30 2.76 Model 5 <![CDATA[8.77×10 -7 ]]> 0 -3.13 0.73 1.31 0 -5.69 2.86 Model 6 <![CDATA[2.54×10 -6 ]]> -15.30 <![CDATA[-1.35×10 -6 ]]> 4.99 0 0.71 -2.85 2.83 Model 7 -9.18 26.53 -2.61 0 3.16 -6.14 -2.39 2.94 Model 8 -7.52 3.27 0.33 5.00 1.43 -3.95 1.08 3.09

[0087] According to the selection method considering the coefficient of variation of the logarithmic acceleration factor, the mean, variance and coefficient of variation of the logarithmic acceleration factor of stress level S2 relative to stress level S1 in each model are calculated. The calculation results are shown in Table 3.

[0088] Table 3 Calculation results of coefficient of variation of logarithmic acceleration factor of Weibull-stress comprehensive acceleration model for a certain type of metering device

[0089] Logarithmic acceleration factor mean Logarithmic acceleration factor variance Coefficient of variation of logarithmic acceleration factor Model 1 5.5497 0.5977 0.1393 Model 2 6.7265 2.6094 0.2402 Model 3 3.4995 0.0912 0.0863 Model 4 89.01 247.56 0.1768 Model 5 3.9344 2.4836 0.4005 Model 6 5.2393 11.3608 0.6433 Model 7 13.6902 7.5559 0.2008 Model Eight 13.1287 14.2698 0.2877

[0090] According to the calculation results in Table 3, the coefficient of variation of the logarithmic acceleration factor corresponding to model 3 reaches the minimum value of 0.0863. At this time, there is a coupling effect between temperature and current. Therefore, model 3 is selected as the acceleration model. When the reliability R = 0.95, the reliable life of the product under normal stress can be obtained as t R =4.3840 years.

[0091] 2) Construction and evaluation of multi-stress acceleration model based on mixed effects

[0092] The life of this type of metering device obeys the Weibull-mixed effect model

[0093]

[0094] Among them, η iis the characteristic life under stress level combination i, β is the shape parameter of Weibull distribution, a1, a2, a3 are model coefficients, and they obey multivariate normal distribution.

[0095] The parameter estimation results calculated using the Monte Carlo expectation maximization algorithm are shown in Table 4.

[0096] Table 4 Parameter estimation results of Weibull-mixed effect acceleration model for a certain type of metering device

[0097]

[0098] According to the correlation coefficient formula, the correlation coefficients between the three stress corresponding parameters are calculated, as shown in Table 5.

[0099] Table 5 Correlation coefficient results of parameters of Weibull-mixed effect acceleration model for a certain type of metering device

[0100] Correlation coefficient Correlation coefficient value <![CDATA[r(a1,a2)]]> -0.086 <![CDATA[r(a1,a3)]]> 0.40 <![CDATA[r(a2,a3)]]> 0.89

[0101] Through the calculation results in Table 5, it is found that the correlation coefficient between parameters a2 and a3 is 0.89, which is greater than 0.5, indicating that there is a large positive correlation between humidity stress and current stress, and the correlation coefficient between parameters a1 and a3 is 0.40, indicating that there is also a certain correlation between temperature stress and current stress.

[0102] Combined with the multi-stress acceleration model selection method based on mixed effects, the mean, variance and coefficient of variation of the logarithmic acceleration factor of stress level S2 relative to stress level S1 are calculated, and the calculation results are shown in Table 6.

[0103] Table 6 Calculation results of logarithmic acceleration factor of Weibull-mixed effect acceleration model for a certain type of metering device

[0104] Logarithmic acceleration factor mean Logarithmic acceleration factor variance Coefficient of variation of logarithmic acceleration factor Calculation results 4.0643 0.0159 0.0310

[0105] When the reliability R = 0.95, the reliable life of the product can be obtained as t R =3.6994 years.

[0106] (3) Model selection

[0107] Comparison of the coefficient of variation of the logarithmic acceleration factor of the above two types of models is shown in Table 7. It is found that the coefficient of variation of the logarithmic acceleration factor corresponding to the multi-stress acceleration model based on mixed effects is the smallest. According to the model selection method considering the coefficient of variation of the logarithmic acceleration factor, the multi-stress acceleration model based on mixed effects is selected as the optimal model.

[0108] Table 7 Comparison of coefficient of variation of logarithmic acceleration factor of three models of a certain type of metering device

[0109] Model Category Coefficient of variation of logarithmic acceleration factor Multi-stress acceleration model based on stress synthesis 0.0863 Multi-stress acceleration model based on mixed effect 0.0310

[0110] Finally, according to the selected Weibull-mixed effect acceleration model, the reliable life of the measuring device under normal stress conditions when the reliability is 0.95, 0.9, and 0.8, as well as the lower confidence limit of the reliable life when the reliability is 0.95, 0.9, and 0.8 under a given confidence level are calculated. The calculation results are shown in Table 8. The reliability curve under this model and the lower confidence limit curve of the reliability when the confidence level is 0.95, 0.9, and 0.8 are shown in Table 8. Figure 2 shown.

[0111] Table 8 Life prediction results of a certain type of metering device based on Weibull-mixed effect multi-stress acceleration model

[0112] Reliability 0.95 Reliability 0.9 Reliability 0.8 Reliable life 3.70 4.82 6.36 Confidence level 0.95 lower limit of lifespan 3.34 4.36 5.74 Confidence level 0.9 lower limit of lifespan 3.41 4.45 5.88 Confidence level 0.8 lower limit of lifespan 3.51 4.58 6.04

[0113] (3) Results analysis

[0114] The multi-stress acceleration model based on stress synthesis and the multi-stress acceleration model based on mixed effect are used to predict the average life of the metering device under five stress combinations, and the results are compared with the actual average life under each stress combination. In addition, the reliable life of the metering device under the natural storage test stress when the reliability is 0.95 is predicted based on parameter estimation, and the results are compared with the actual natural storage test results. The comparison results are shown in Table 9.

[0115] Table 9 Comparison of relative errors of two models of a certain type of metering device

[0116]

[0117] After comparison, it was found that the multi-stress acceleration model based on mixed effects was superior to the multi-stress acceleration model based on stress synthesis in the relative error comparison of the average life of the five groups of accelerated tests and the relative error comparison of the natural storage test, indicating that the model has the highest prediction accuracy. Therefore, for this product, in order to improve the effectiveness of the evaluation results of the natural storage test and the accelerated storage test, the multi-stress acceleration model based on mixed effects should be selected, and the negative interaction between temperature stress and humidity stress (the coefficients of the two in the covariance matrix are negative), the positive interaction between temperature stress and electrical stress (the coefficients of the two in the covariance matrix are positive), and the positive interaction between humidity stress and electrical stress (the coefficients of the two in the covariance matrix are positive) should be considered. In this case, the evaluation results of the accelerated storage test are closest to the evaluation results of the natural storage test.

[0118] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-stress acceleration model based on stress synthesis, characterized in that: It includes a general log-linear model established when there are multiple environmental stresses, which treats the product life as a vector X=(X1, X2, ..., X n ), the mathematical model is as follows: Among them, θ is its characteristic life span; a k is an unknown parameter; x k is the kth environmental stress in the comprehensive environment; a0 is a constant. According to the definition of the acceleration factor, the acceleration factor of the model can be expressed as: Among them, x k,i and x k,j are the kth environmental stress in the ith comprehensive stress and the jth comprehensive stress respectively.

2. The multi-stress acceleration model based on stress synthesis according to claim 1 is characterized in that: The generalized log-linear model adopts the Arrhenius model, which is expressed as follows: where S1, S2, …, S p is the p-dimensional stress, c0, c1, …, c l is the unknown coefficient, is a known function.

3. Multi-stress acceleration model based on mixed effect, characterized in that: It includes introducing mixed effects on the basis of existing multi-stress acceleration models to establish a failure time model that considers the multi-stress coupling relationship; the mixed effects include fixed effects and random effects, the fixed effects are mainly used to characterize general characteristics, and the random effects are used to reflect the correlation between random variables; the multi-stress failure time model integrating random effects can be divided into two layers, the first layer is used to describe the relationship between characteristic life and environmental stress under a certain composite environment, the second layer model uses the environmental coefficients in the first layer model as random variables, and represents the coupling effect between environmental stresses by establishing a joint distribution of coefficients; in the second layer model, the multivariate normal distribution is used as the joint distribution, in which the mean of the multivariate normal distribution represents the fixed effect, and the covariance matrix represents the random effect.

4. The multi-stress acceleration model based on mixed effect according to claim 3 is characterized in that: The first-level model is: Assume that the electronic equipment is mainly affected by p kinds of environmental stresses, and these environmental stresses are represented as X1, X2, ..., X p .X i (i=1,…,p) can be temperature, humidity, electrical stress, mechanical stress, etc.; Assume that in the i-th comprehensive environment, the p environmental stresses are X 1,i ,X 2,i ,…,X p,i , then the life characteristic θ i It can be expressed as Among them, a k , k = 0, 1, ..., p is the environmental coefficient of the model, g(X k,i ) is the function of the kth environmental stress in the ith comprehensive environment. Through model transformation, we can get Among them, h(θ i ) is the characteristic life θ i function.

5. The multi-stress acceleration model based on mixed effect according to claim 4 is characterized in that: The second-level model is: considering the coupling between various environmental stresses, assuming that the coefficient a l with a m (l=0,1,…,p,m=0,1,…,p,l=m) are correlated and obey the bivariate normal distribution. The joint density function can be expressed as Among them, μ l and μ m The coefficients a are l with a m The mean value, σ l and σ m The coefficients a are l with a m The standard deviation of l with a m The correlation coefficient can be expressed as 6. The multi-stress acceleration model based on mixed effect according to claim 5, characterized in that: Based on the analysis of the above two-layer model, the multi-stress failure time model considering the coupling relationship can be specifically expressed as Among them, k=1,...,p, l=0,1,...,p, m=0,1,...,p, μ=(μ l ,μ m )′ is (a l ,a m )′, for (a l ,a m )′, the covariance matrix of environmental stress X l With X m The coupling effect is achieved through (a l ,a m )′ covariance Cov(a l ,a m ) to reflect.

7. A method for selecting a multi-stress acceleration model based on stress comprehensive or mixed effect as claimed in claims 1 to 6, characterized in that: The following steps are involved: S1: According to s i and i+1 Samples of acceleration factors calculated from estimated values ​​of distribution model parameters at two stress levels; S2: Calculate the mean value μ(K of the acceleration factor sample) i,i+1 ) and standard deviation σ(K i,i+1 ); S3: Calculate the coefficient of variation of the acceleration factor: Where k is the stress level number of the accelerated test, CV(K i,i+1 ) represents stress s i Relative to stress s i+1 The coefficient of variation of the acceleration factor; S4: Compare the size of the coefficient of variation of the acceleration factor under different acceleration model assumptions, and select the acceleration model with the smallest coefficient of variation.

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