A multi-stress accelerated test evaluation method based on mixed effects

Abstract

The application discloses a multi-stress accelerated test evaluation method based on a mixed effect, comprising the following steps: constructing a multi-stress accelerated model based on a mixed effect; estimating parameters of the multi-stress accelerated model by using a Monte Carlo expectation maximization algorithm; and calculating a correlation coefficient of an environmental parameter, determining a stress coupling condition and evaluating a product life according to the estimation result. The application considers the coupling effect between the multi-stresses by the mixed effect method, so that the accelerated model is more suitable for the actual situation, and the precision of the model evaluation is improved. The parameter estimation is performed by using the Monte Carlo expectation maximization method, so that the problem that the multi-stress accelerated model parameters are complex and cannot be directly calculated by multiple integrals is solved. By considering the coupling effect between the multi-stresses and adopting the expectation maximization algorithm, the calculation efficiency of the algorithm is improved while the accuracy of the parameter estimation is improved, and finally the purpose of improving the accuracy of the life evaluation is achieved.

Description

Technical Field

[0001] This invention relates to the field of lifetime prediction technology. More specifically, it relates to a multi-stress accelerated testing evaluation method based on mixed effects. Background Technology

[0002] Accelerated life testing is a technique that uses environmental or load stresses during actual product service to obtain product lifespan and reliability information within a shorter timeframe. Current accelerated life testing research primarily focuses on single-stress scenarios; however, with technological advancements, multi-stress accelerated life testing is gaining traction. The main reasons for conducting multi-stress accelerated life testing are to make the testing more realistic and to further shorten testing time and reduce costs. However, in multi-stress accelerated life testing, the complex coupling effects between combined stresses can impact the extrapolation results.

[0003] Multi-stress accelerated models are a crucial component influencing experimental extrapolation results. Whether the accelerated model accurately reflects the product's actual conditions directly impacts the accuracy of reliability assessments. Based on an accurate model, appropriate accelerated life testing methods can be used for life assessment, yielding relatively accurate results. Most existing multi-stress accelerated models are based on generalized log-linear models, largely neglecting the coupling between multiple stresses. A few models that do consider this only include linear relationships between stresses, which are insufficiently realistic. Furthermore, there are no corresponding parameter estimation methods to handle the complexities of these accelerated models.

[0004] Based on this, the present invention proposes a multi-stress accelerated test evaluation method based on the mixed effect. A multi-stress accelerated model based on the mixed effect is established to consider the coupling effect between stresses, and the Monte Carlo expectation maximization algorithm is used to solve the parameter estimation problem of the complex model. Then, the product life is more accurately evaluated based on the parameter estimation results. Summary of the Invention

[0005] One object of the present invention is to provide a multi-stress accelerated test evaluation method based on the hybrid effect.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The first aspect of this invention provides a multi-stress accelerated test evaluation method based on hybrid effects, which requires the following settings:

[0008] Setting 1: When conducting accelerated life tests on products, there are multiple stresses. The cumulative failure function form that the product follows under different stresses is the same, and the range of applied stress does not change the product's failure mechanism.

[0009] Setting 2: The product lifespan t follows either a Weibull distribution or a Gamma distribution, with the probability density functions of each distribution being:

[0010] ①Weibull distribution:

[0011]

[0012] ②Gamma distribution:

[0013]

[0014] Where η and β are the scale parameter and shape parameter of the Weibull distribution, respectively, and α and λ are the shape parameter and scale parameter of the gamma distribution, respectively.

[0015] This method is implemented through the following steps:

[0016] A multi-stress acceleration model is constructed based on the hybrid effect;

[0017] The parameters of the multi-stress acceleration model are estimated using the Monte Carlo expectation maximization algorithm.

[0018] Based on the estimation results, the correlation coefficients of environmental parameters are calculated, the stress coupling situation is determined, and the product lifespan is evaluated.

[0019] Optionally, the multi-stress acceleration model includes

[0020] The first part is to demonstrate the generalized linear relationship between the lifetime function and environmental stress under various comprehensive environments through a generalized log-linear model.

[0021] The second part establishes the coupling effect of various environmental stresses through the covariance between environmental coefficients;

[0022] The steps for establishing the multi-stress acceleration model include:

[0023] Determine the single-stress acceleration model to which each stress follows. For the Arrhenius model, the acceleration stress X is... k The environmental stress function in the generalized log-linear model is expressed as g(X) k ) = 1 / X k For the inverse power-law model, its environmental stress function is expressed as xg(X) in the generalized log-linear model. k )=ln(X k );

[0024] Based on the known stress coupling situation, the multivariate normal distribution in the second part of the multi-stress acceleration model is determined, and the stresses without coupling are determined to have no correlation between their environmental coefficients, i.e., the corresponding covariance value is 0.

[0025] Optionally, the multi-stress acceleration model includes

[0026] The multi-stress acceleration model is as follows:

[0027]

[0028] in, Characteristic lifetime The function for the Weibull distribution For gamma distribution a k The environmental coefficients for the model are k = 0, 1, ..., p, l = 1, 2, ..., p, where p is the number of accelerating stresses; X k The function representing the k-th accelerating stress, μ = (μ k ,μ l )′ is (a k ,a l The mean of )′ For (a k ,a l The covariance matrix of )′, and the accelerating stress X k With X l The coupling effect is achieved through (a) k ,a l The covariance Cov(a)′ k ,a l )reflect.

[0029] Optionally, the parameters of the multi-stress acceleration model are estimated using the Monte Carlo expectation maximization algorithm, specifically through the following steps:

[0030] Establish the marginal maximum likelihood function L(θ), and assign environmental coefficients A = (a1, a2, ..., a...). n () as a hidden parameter;

[0031] When the lifetime distribution model is a Weibull distribution, the log-likelihood function lnL(θ) for the complete data is obtained:

[0032]

[0033] When the lifetime distribution model is a gamma distribution, the log-likelihood function lnL(θ) for the complete data is obtained as follows:

[0034]

[0035] Where L(θ) is the marginal likelihood function; θ is the parameter to be estimated, for the Weibull distribution θ=[A,β], for the gamma distribution θ=[A,α]; A=(a1,.a2,…,a…) n ) represents the environmental coefficient, which follows a multivariate normal distribution, μ A and Σ A G is the mean and variance of G.i ′ represents the stress function vector under environment i.

[0036] Optionally, the Monte Carlo expectation maximization algorithm can be used for parameter estimation. The specific steps are as follows:

[0037] Given the initial value of the parameter to be estimated θ, use the MCEM algorithm for iteration;

[0038] The MCEM algorithm iterates, including

[0039] E: Calculate the conditional distribution using the Monte Carlo simulation method;

[0040] S1: by p(A) i,j |t i,j Randomly select c groups of random numbers A1, ..., A c According to Bayes' theorem, given A ~ N(μ) A ,Σ A ), calculate A in data t i,j The conditional distribution p(A) under the following conditions i,j |t i,j ):

[0041] Weibull distribution:

[0042]

[0043] Gamma distribution:

[0044]

[0045] S2: Calculate the function Q(θ|θ) that needs to be maximized. (s) D)

[0046]

[0047] Where, θ (s) Represents the value of the parameter in the s-th loop; D is the accelerated life test data; c is the number of random numbers drawn in the E-step; lnL(θ|A k D) represents A k Given the conditional distribution of lnL(θ), find the value of D.

[0048] M: By maximizing Q(θ|θ) (s) ,D), to obtain θ (s+1) ; Repeat E-step and M-step, when |θ (s+1) -θ (s) When | < ε, the loop stops, and the parameter estimate is... ε is a preset value.

[0049] Optionally, based on the parameter estimation results, the correlation coefficients of the environmental parameters are calculated to determine the stress coupling situation. The specific steps are as follows:

[0050] Calculate the correlation coefficient of environmental parameters, where ρ is a k With a l The correlation coefficient is expressed as:

[0051]

[0052] Where, σ k With σ l These are the coefficients a k With a l Standard deviation, Cov(a) k ,a l ) is a k With a l The covariance.

[0053] The stress coupling situation is determined according to the magnitude of the correlation coefficient ρ. When the absolute value of the correlation coefficient is greater than 0.5, it is determined that there is a strong coupling relationship between the two stresses. At this time, a positive correlation coefficient indicates that the two stresses are positively correlated, and a negative correlation indicates that the two stresses on the surface are negatively correlated.

[0054] Optionally, assessing product lifespan includes

[0055] Point estimation, based on the selected optimal lifetime distribution model and acceleration model, substitutes the normal stress level to obtain its cumulative failure function F(t,Θ). Given the reliability R, the corresponding reliable lifetime t is calculated. R :

[0056]

[0057] Among them, F -1 (·) is the inverse function of the overall cumulative failure function;

[0058] Optionally, product lifetime assessment includes interval estimation, estimating the lower confidence limit of lifetime through the dispersion of the acceleration factor, where the acceleration factor follows a mean of . variance is The log-normal distribution;

[0059] in

[0060] in

[0061]

[0062]

[0063]

[0064] Based on this calculation, an interval estimate of the acceleration factor is obtained.

[0065]

[0066] Among them, AF ij,L ,AF ij,U These are the lower and upper confidence limits for the acceleration factor, respectively, Φ -1 (·) is the inverse function of the standard normal distribution. Confidence level;

[0067] Therefore, the interval estimate of the product lifespan is calculated.

[0068]

[0069] Among them, t iR For stress level combination s i With a reliable lifespan, AF ni,L ,AF ni,U These represent the normal stress level relative to the stress level combination s. i The lower and upper confidence limits of the acceleration factor, t R,L ,t R,U These represent the lower and upper confidence limits of the product's lifespan under normal stress conditions, respectively.

[0070] A second aspect of the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method provided in the first aspect of the present invention.

[0071] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method provided in the first aspect of the present invention.

[0072] The beneficial effects of this invention are as follows:

[0073] Compared with existing multi-stress acceleration models, this invention considers the potential coupling effects between multiple stresses through a mixed-effects method, making the acceleration model more realistic and improving its accuracy. Compared with existing maximum likelihood parameter estimation methods, this invention uses the Monte Carlo expectation maximization method for parameter estimation, solving the problems of complex parameters and the inability to directly calculate multiple integrals in multi-stress acceleration models. By considering the coupling effects between multiple stresses and employing the expectation maximization algorithm, this invention improves both the accuracy of parameter estimation and the computational efficiency of the algorithm, ultimately achieving the goal of improving the accuracy of lifetime assessment. Attached Figure Description

[0074] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0075] Figure 1 A flowchart of the method described in this invention is shown.

[0076] Figure 2 This diagram illustrates accelerated life test data for a smart meter in one embodiment of the present invention.

[0077] Figure 3 This diagram illustrates the normal stress reliability curve of a smart meter in one embodiment of the present invention. Detailed Implementation

[0078] To more clearly illustrate the present invention, the following description is in conjunction with preferred embodiments and accompanying drawings. Figure 1-3 The present invention will be further described below. Similar components in the accompanying drawings are indicated by the same reference numerals. Those skilled in the art should understand that the following detailed description is illustrative rather than restrictive and should not be construed as limiting the scope of protection of the present invention.

[0079] A multi-stress accelerated testing evaluation method based on mixed effects includes:

[0080] Establish the following basic settings

[0081] Setting 1: When conducting accelerated life tests on products, there are multiple stresses. The cumulative failure function form that the product follows under different stresses is the same, and the range of applied stress does not change the product's failure mechanism.

[0082] Setting 2: The product lifespan t follows either a Weibull distribution or a Gamma distribution, with the probability density functions of each distribution being:

[0083] ①Weibull distribution:

[0084]

[0085] ②Gamma distribution:

[0086]

[0087] Where η and β are the scale parameter and shape parameter of the Weibull distribution, respectively, and α and λ are the shape parameter and scale parameter of the gamma distribution, respectively.

[0088] It is characterized by being achieved through the following steps:

[0089] A multi-stress acceleration model is constructed based on the hybrid effect;

[0090] The parameters of the multi-stress acceleration model are estimated using the Monte Carlo expectation maximization algorithm.

[0091] Based on the estimation results, the correlation coefficients of environmental parameters are calculated, the stress coupling situation is determined, and the product lifespan is evaluated.

[0092] This method is implemented through the following steps:

[0093] Step 1: Construct a multi-stress acceleration model based on mixed effects.

[0094] Based on the hybrid effect, a multi-stress acceleration model is constructed as follows:

[0095]

[0096] in, Characteristic lifetime The function for the Weibull distribution For gamma distribution a k The environmental coefficients for the model are k = 0, 1, ..., p, l = 1, 2, ..., p, where p is the number of accelerating stresses; X k The function representing the k-th accelerating stress, μ = (μ k ,μ l )′ is (a k ,a l The mean of )′ For (a k ,a l The covariance matrix of )′, and the accelerating stress X k With X l The coupling effect is achieved through (a) k ,a l The covariance Cov(a)′ k ,a l )reflect.

[0097] The first part of the model uses a generalized log-linear model to represent the generalized linear relationship between the lifetime function and environmental stress under various integrated environments. The second part uses the covariance between environmental coefficients to establish the coupling effect of various environmental stresses.

[0098] The specific steps for building the model are as follows:

[0099] I. Determine the single-stress acceleration model to which each stress follows. For stresses such as temperature and humidity, the Arrhenius model is typically used, with its environmental stress function g(X)... k ) = 1 / X k For stresses such as electrical stress, the model usually follows an inverse power law, and its environmental stress function is g(X). k )=ln(X k ).

[0100] II. Based on the known stress coupling situation, determine the multivariate normal distribution in the second part of the model, and determine the stress in the uncoupled case, where the environmental coefficients are uncorrelated, i.e., the corresponding covariance value is 0; other cases are reflected in the second part of the model.

[0101] III. Combine the first two parts to construct the multi-stress acceleration model as shown in equation (3).

[0102] Step 2: Use the Monte Carlo expectation maximization algorithm to estimate the model parameters.

[0103] The Monte Carlo Expectation Maximization (MCEM) algorithm is used to address the problem that multivariate integrals in the marginal likelihood function cannot be directly calculated, and parameter estimation is performed on the model. The specific steps are as follows:

[0104] I. Establish the marginal maximum likelihood function L(θ):

[0105] ①Weibull distribution:

[0106]

[0107] ②Gamma distribution:

[0108]

[0109] Where L(θ) is the marginal likelihood function; θ is the parameter to be estimated, for the Weibull distribution θ=[A,β], for the gamma distribution θ=[A,α]; A=(a1,.a2,…,a…) n ) represents the environmental coefficient, which follows a multivariate normal distribution, μ A and Σ A For its mean and variance, G′ i Let be the stress function vector under environment i.

[0110] II. The environmental coefficient A = (a1, a2, ..., a...) n Using θ as a hidden parameter, we obtain the log-likelihood function lnL(θ) under the complete data:

[0111] ①Weibull distribution:

[0112]

[0113] ②Gamma distribution:

[0114]

[0115] III. Parameter estimation using the MCEM algorithm: The specific steps are as follows:

[0116] (1) Give the initial value of the parameter to be estimated, θ.

[0117] (2) Iteration using the MCEM algorithm:

[0118] E-step: Since the mean and variance of the distribution cannot be obtained directly, Monte Carlo simulation is used to complete the E-step.

[0119] MCE1 step: From p(A) i,j |t i,j Randomly select c groups of random numbers A1, ..., A c According to Bayes' theorem, given A ~ N(μ) A ,Σ A ), calculate A in data t i,j The conditional distribution p(A) under the following conditions i,j |t i,j ):

[0120] ①Weibull distribution:

[0121]

[0122] ②Gamma distribution:

[0123]

[0124] MCE2 step: S2: Calculate the function Q(θ|θ) that needs to be maximized. (s) D)

[0125]

[0126] Where, θ (s) Represents the parameter value in the s-th loop; D is the accelerated life test data; m is the number of test stress groups; n is the number of failure samples in each test group; c is the number of random numbers drawn in the E-step; lnL(θ|A k D) represents A k Given the conditional distribution of lnL(θ), find the value of D.

[0127] M-step: By maximizing Q(θ|θ) (s) ,D), to obtain θ (s+1) Repeat the E-step and M-step cycles until |θ (s+1) -θ (s) When | < ε, the algorithm stops, and the parameter estimate is... ε is a preset value (ε is a set small value).

[0128] Step 3: Determine the stress coupling situation based on the parameter estimation results.

[0129] Based on the parameter estimation results, the correlation coefficients of the environmental parameters are calculated to determine the stress coupling situation. The specific steps are as follows:

[0130] I. Calculate the correlation coefficients of environmental parameters. ρ is ak With a l The correlation coefficient is expressed as:

[0131]

[0132] Among them, a k With a l These are the coefficients a k With a l Standard deviation, Cov(a) k ,a l ) is a k With a l The covariance.

[0133] II. Determine the stress coupling situation according to the magnitude of the correlation coefficient ρ.

[0134] When the absolute value of the correlation coefficient is greater than 0.5, it is determined that there is a strong coupling relationship between the two stresses. At this time, a positive correlation coefficient indicates that the two stresses are positively correlated, while a negative correlation coefficient indicates that the two stresses on the surface are negatively correlated.

[0135] Step 4: Assess product lifespan.

[0136] (1) Point estimation

[0137] Based on the selected optimal lifetime distribution model and acceleration model, and substituting the normal stress level, the cumulative failure function F(t,Θ) is obtained. Given the reliability R, the corresponding reliable lifetime t is calculated. R :

[0138]

[0139] Among them, F -1 (·) is the inverse function of the overall cumulative failure function.

[0140] (2) Interval estimation

[0141] The confidence lower bound of lifetime is estimated by considering the dispersion of the acceleration factor. First, as discussed in the previous section, the logarithmic acceleration factor follows a normal distribution. Therefore, the acceleration factor has a mean of [missing value]. variance is The log-normal distribution; where

[0142] in

[0143]

[0144]

[0145]

[0146] Based on this calculation, an interval estimate of the acceleration factor is obtained.

[0147]

[0148] Among them, AF ij,L ,AF ij,U These are the lower and upper confidence limits for the acceleration factor, respectively, Φ -1 (·) is the inverse function of the standard normal distribution. , where is the confidence level.

[0149] Next, the interval estimate of the product lifespan is calculated.

[0150]

[0151] Among them, t iR For stress level combination s i With a reliable lifespan, AF ni,L ,AF ni,U These represent the normal stress level relative to the stress level combination s. i The lower and upper confidence limits of the acceleration factor, t R,L ,t R,U These represent the lower and upper confidence limits of the product's lifespan under normal stress conditions, respectively.

[0152] One specific embodiment,

[0153] Taking a multi-stress accelerated life test of a smart meter as an example, the technical solution of the present invention will be further described in detail.

[0154] As high-precision and high-reliability products, smart meters require rapid and accurate assessment of their lifespan and reliability. During use, they are primarily affected by temperature, humidity, and electrical stress. Increased temperature increases the resistivity of the high-manganese copper resistor, leading to a higher sampled current value. This reduces the accuracy and stability of the manganese copper shunt and current transformer, resulting in increased metering errors. Furthermore, prolonged temperature stress can cause deformation of the liquid crystal cell material, changes in refractive index, and increased resistance, leading to liquid crystal leakage, reduced brightness, and display abnormalities. Humidity affects smart meters primarily by allowing moisture to penetrate the chip's plastic encapsulation through gaps in the pins, causing the chip to absorb moisture.

[0155] Water vapor forms in high-temperature environments, and the resulting pressure causes the chip resin encapsulation to crack and the internal metal of the chip device to oxidize, leading to product failure.

[0156] In this case, the combined effects of temperature and humidity stress on the lifespan of smart meters need to be considered. The impact of electrical stress is mainly reflected in the fact that the current sampling circuit generates significant heat in the smart meter. Excessive electrical stress can cause thermal instability within the metering device, leading to temperature increases. Since various components inside the smart meter are particularly sensitive to temperature rise, this can cause drift in the electrical parameters of these components, resulting in increased errors in the smart meter.

[0157] Failure mechanism analysis revealed that there may be coupling effects between the sensitive stresses of smart meters. Therefore, a multi-stress acceleration model based on hybrid effects was used to consider the possible coupling between stresses and to conduct statistical analysis and life assessment.

[0158] In the multi-stress accelerated test of smart meters, the accelerated stress settings are shown in Table 1, and the failure conditions are as follows: Figure 2 As shown. The normal stress conditions for this smart meter are temperature 293K, humidity 45%RH, and current 10A. Its lifespan follows a Weibull distribution.

[0159] Table 1. Multi-stress accelerated test conditions for a smart meter

[0160] Experiment 1 353 80 60 Experiment 2 328 80 40 Experiment 3 328 95 20 Experiment 4 343 95 60 Experiment 5 343 95 40

[0161] Step 1: Construct a multi-stress acceleration model based on mixed effects.

[0162] A multi-stress acceleration model based on hybrid effects is established. Temperature and humidity stresses both follow the Arrhenius model, current stress follows an inverse power-law model, and there may be pairwise coupling effects between the three stresses. The smart meter's lifespan follows a Weibull distribution. Therefore, the multi-stress acceleration model based on hybrid effects is established as follows:

[0163]

[0164] Where, η i Let be the characteristic lifetime under stress level combination i, β be the shape parameter of the Weibull distribution, and a1, a2, a3 be the model coefficients, which follow a multivariate normal distribution.

[0165] Step 2: Use the Monte Carlo expectation maximization algorithm to estimate the model parameters.

[0166] Using the parameter estimation method based on the Monte Carlo expectation maximization algorithm described above, the parameter estimation results are shown in Table 2.

[0167] Table 2. Parameter estimation results of a hybrid effect acceleration model for a smart meter.

[0168]

[0169] Step 3: Determine the stress coupling situation based on the parameter estimation results.

[0170] Based on the correlation coefficient formula, the correlation coefficients between the three stress-corresponding parameters were calculated, as shown in Table 3.

[0171] Table 3. Correlation coefficients of parameters in a hybrid effect acceleration model for a smart meter.

[0172] <![CDATA[r(a1,a2)]]> -0.086 <![CDATA[r(a1,a3)]]> 0.40 <![CDATA[r(a2,a3)]]> 0.89

[0173] The calculation results in Table 3 show that the correlation coefficient between parameters a2 and a3 is 0.89, which is greater than 0.5, indicating a strong positive correlation between humidity stress and current stress. The correlation coefficient between parameters a1 and a3 is 0.40, indicating a certain correlation between temperature stress and current stress.

[0174] Step 4: Assess product lifespan.

[0175] (1) Point estimation

[0176] When the reliability R = 0.95, the reliable life of the product can be obtained as t. R =3.6994 years, its reliability curve under normal stress is as follows Figure 3 As shown.

[0177] (2) Interval estimation

[0178] The reliable lifespan of the smart meter under normal stress conditions with reliability levels of 0.95, 0.9, and 0.8 was calculated; the lower confidence limits of the reliable lifespan at confidence levels of 0.95, 0.9, and 0.8 were also calculated. The calculation results are shown in Table 4.

[0179] Table 4. Lifetime Assessment Results of the Hybrid Effect Acceleration Model for Smart Meters

[0180] Reliable life (years) 3.70 4.82 6.36 Confidence level 0.95, lower limit of lifetime (years) 3.34 4.36 5.74 Confidence level 0.9, lower limit of lifetime (years) 3.41 4.45 5.88 Confidence level 0.8, lower limit of lifetime (years) 3.51 4.58 6.04

[0181] This invention's multi-stress accelerated life test is widely used due to its ability to reduce test time and better reflect actual conditions. Existing multi-stress accelerated life models typically only consider the effect of stress itself on lifespan. However, in reality, the combined effect of stresses is often not a simple linear superposition. Therefore, it is necessary to consider the coupling effects between stresses. Thus, a mixed-effects model is used to reflect the relationship between stress and lifespan through both fixed effects and random effects. Specifically, in establishing a multi-stress accelerated life model considering coupling effects, the model is divided into two layers. The first layer is a generalized log-linear model, and the second layer assumes that the environmental coefficients follow a multivariate normal distribution. The mean of the multivariate normal distribution reflects the fixed effects, and the covariance reflects the random effects. The multivariate normal distribution in this model makes parameter estimation difficult. This invention proposes a parameter estimation method based on the Monte Carlo maximization method to solve this problem. This method obtains the stress coupling situation and more accurately extrapolates product lifespan.

[0182] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A multi-stress accelerated test evaluation method based on mixed effects, which requires the following settings: Setting 1: When conducting accelerated life tests on products, there are multiple stresses. The cumulative failure function form that the product follows under different stresses is the same, and the range of applied stress does not change the product's failure mechanism. Setting 2: The product lifespan t follows either a Weibull distribution or a Gamma distribution, with the probability density functions of each distribution being: ①Weibull distribution: ②Gamma distribution: in, and These are the scale parameter and shape parameter of the Weibull distribution, respectively. and These are the shape and scale parameters of the gamma distribution, respectively. in, and m are the scale parameter and shape parameter of the Weibull distribution, respectively. and These are the shape and scale parameters of the gamma distribution, respectively. The method is characterized by the following steps: A multi-stress acceleration model is constructed based on the hybrid effect; The parameters of the multi-stress acceleration model are estimated using the Monte Carlo expectation maximization algorithm. Based on the estimation results, the correlation coefficients of environmental parameters are calculated to determine the stress coupling situation and to assess the product lifespan. The multi-stress acceleration model includes The first part is to demonstrate the generalized linear relationship between the lifetime function and environmental stress under various comprehensive environments through a generalized log-linear model. The second part establishes the coupling effect of various environmental stresses through the covariance between environmental coefficients; The steps for establishing the multi-stress acceleration model include: Determine the single-stress acceleration model to which each stress follows. For the Arrhenius model, the acceleration stress X is... k The environmental stress function is expressed in the generalized log-linear model as: For the inverse power-law model, its environmental stress function is expressed as x in the generalized log-linear model. ; Based on the known stress coupling situation, the multivariate normal distribution in the second part of the multi-stress acceleration model is determined. For stresses without coupling, there is no correlation between their environmental coefficients, that is, the corresponding covariance value is 0. The multi-stress acceleration model is as follows: in, Characteristic lifetime The function for the Weibull distribution For gamma distribution ; The environmental coefficients of the model. , , To increase the number of stresses; A function representing the k-th accelerating stress. for The mean, for The covariance matrix of the accelerated stress and The coupling effect is achieved through covariance reflect; Parameter estimation using the Monte Carlo expectation maximization algorithm includes providing the parameters to be estimated. The initial value is obtained by iterating using the MCEM algorithm; The MCEM algorithm iterates, including E: Calculate the conditional distribution using the Monte Carlo simulation method; S1: By Randomly selected Group of random numbers According to Bayes' theorem, given ,calculate In data Conditional distribution under the following conditions : Weibull distribution: Gamma distribution: S2: Calculate the function that needs to be maximized. in, Representing the The values ​​of the parameters in each loop, For accelerated life test data, c is the number of random numbers drawn from E. express Under known circumstances Conditional distribution, The number of test stress groups, The number of failure samples in each test group; M: By maximization ,get ; Cycle E and M, when When the loop stops, the parameter estimate is... , This is the default value.

2. The method according to claim 1, characterized in that, The parameters of the multi-stress acceleration model are estimated using the Monte Carlo expectation maximization algorithm. The specific steps are as follows: Establish the marginal maximum likelihood function and environmental factor As a hidden parameter; When the lifetime distribution model is a Weibull distribution, the log-likelihood function under complete data is obtained. ； When the lifetime distribution model is a gamma distribution, the log-likelihood function under complete data is obtained. in, Let's consider the marginal likelihood function. For the parameters to be estimated, given the Weibull distribution... For gamma distribution ; The environmental coefficient follows a multivariate normal distribution. and Let its mean and variance be... For the environment The stress function vector, The number of test stress groups, This represents the number of failed samples in each test group.

3. The method according to claim 1, characterized in that, The steps for calculating the correlation coefficients of environmental parameters and determining stress coupling based on the estimation results are as follows: Calculate the correlation coefficients of environmental parameters. yes and The correlation coefficient is expressed as: in, and They are coefficients and standard deviation for and The covariance, according to the correlation coefficient The magnitude of the stress coupling determines the stress coupling situation.

4. The method according to claim 1, characterized in that, The assessment of product lifespan includes... Point estimation, based on the selected lifetime distribution model and acceleration model, substitutes the normal stress level to obtain its cumulative failure function. Given reliability Calculate the corresponding reliable life. in, It is the inverse function of the overall cumulative failure function.

5. The method according to claim 1, characterized in that, The product life assessment includes Interval estimation estimates the lower confidence limit of lifetime based on the dispersion of the acceleration factor, which follows a mean of [value missing]. variance is The log-normal distribution; in ； , ； The interval estimate of the acceleration factor was calculated. in, These are the lower and upper confidence limits for the acceleration factor, respectively. It is the inverse function of the standard normal distribution. Confidence level; Therefore, the interval estimate of the product lifespan is calculated. in, Stress level combination Lower reliable lifespan These represent the normal stress level relative to the stress level combination. The lower and upper confidence limits of the acceleration factor are as follows: These represent the lower and upper confidence limits of the product's lifespan under normal stress conditions, respectively.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-5.

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