A method for designing accelerated reliability verification test scheme

Abstract

The present invention provides an accelerated reliability verification test scheme design method, that is, an accelerated reliability verification test scheme design method for a product life obeying a log-normal distribution, and the specific steps are as follows: one: estimating log-normal distribution parameters; two: establishing an inverse power law model, and extrapolating the distribution of acceleration factors based on model uncertainty; three: designing a log-normal distribution product reliability verification optimization scheme based on cost constraints; through the above steps, the problems of high reliability and long life of the product, model uncertainty, etc. in the process of designing the accelerated reliability verification optimization scheme for the log-normal distribution product are solved, and the effectiveness of the accelerated reliability verification optimization scheme design is guaranteed by introducing AF uncertainty, which conforms to the actual engineering situation, is simple to calculate, provides convenience for engineering and technical personnel, and has important application value.

Description

Technical Field

[0001] The present invention proposes an accelerated reliability verification test scheme design method, that is, an accelerated reliability verification test scheme design method for a product life that obeys a log-normal distribution; firstly, based on the life test data obtained under a constant accelerated stress test of a product, under the condition that the product life obeys a log-normal distribution, a maximum likelihood estimation method is used to estimate the product life distribution parameters; secondly, under the premise of ensuring the consistency of the failure mechanism, an inverse power law model of the distribution logarithmic mean parameter and the current stress is constructed; then, the model is logarithmically transformed to make it a univariate linear regression model, and the parameter estimation value of the univariate linear regression model is obtained by using the least squares estimation method, and then the distribution of the acceleration factor (Acelerate Factor, hereinafter abbreviated as AF) is extrapolated based on the uncertainty of the model; finally, considering the uncertainty of AF, an accelerated reliability verification test scheme is optimized under cost constraints, and an accelerated reliability verification test scheme is given;

[0002] The present invention is used for the design of accelerated reliability verification test scheme when the product life obeys the log-normal distribution, which can effectively reduce the impact of model uncertainty on the results in accelerated reliability verification; this patent is applicable to related technical fields such as reliability assessment and reliability verification. Background Art

[0003] Reliability verification test is a reliability test conducted to verify whether the reliability level of the product meets the predetermined design index requirements. The purpose is to verify the reliability level of batch products. There are many studies on traditional reliability verification methods (i.e., reliability verification methods based on normal stress tests) and they are becoming more mature. However, this method has a long test time and high test cost when the reliability level is high. The accelerated reliability verification method accelerates the product failure process by appropriately increasing the test stress level, significantly reducing the test time, and has attracted the attention of a large number of researchers and industrial personnel. Furthermore, in order to extrapolate the AF distribution information required for the design of accelerated reliability verification test schemes, it is necessary to carry out constant accelerated life under different test stresses. Life test, collect product life data under different accelerated stresses, obtain life distribution parameters under different accelerated stresses, and then establish an accelerated model of life distribution parameters and test stress, and extrapolate AF distribution type and its distribution parameters based on model uncertainty; At present, the existing accelerated reliability verification methods do not consider the uncertainty of the model, and the calculated test plan has deviations; Therefore, on the one hand, it is necessary to consider AF uncertainty, numerically integrate it and calculate the acceptance probability to find the result that meets the risk conditions of both parties; On the other hand, in order to meet the actual needs of the project and reduce the test cost, it is necessary to set the optimization goal with the minimum cost and complete the optimization design of the accelerated reliability verification test plan for log-normal distribution products;

[0004] In view of this, the present invention proposes an accelerated reliability verification test scheme design based on product constant accelerated life test data, which comprehensively applies maximum likelihood estimation method, inverse power law model, Bartlett test, univariate linear regression model and least squares estimation method. Summary of the invention

[0005] (1) Purpose of the present invention: The present invention aims at the problem of accelerated reliability verification caused by the influence of model uncertainty on products, and provides a method for designing an accelerated reliability verification test scheme, that is, a method for designing an accelerated reliability verification test scheme for products with life following a log-normal distribution. First, it is based on the constant accelerated life test data of the product, and in the case that the product life follows a log-normal distribution, the maximum likelihood estimation method is used to estimate the product life distribution parameters. Secondly, under the premise of ensuring the consistency of the failure mechanism, an inverse power law model of the distribution logarithmic mean parameter and the current stress is established. Then, the model is logarithmically transformed into a univariate linear regression model, and the least squares estimation method is used to obtain the estimated values ​​of the model parameters, and then the AF distribution is extrapolated based on the model uncertainty. Finally, considering the AF uncertainty, the accelerated reliability verification test scheme is optimized under cost constraints, and an accelerated reliability verification test scheme is given.

[0006] (2) Technical Solution: Based on the above theory and ideas, the present invention provides an accelerated reliability verification test scheme design method, that is, an accelerated reliability verification test scheme design method for a product life that obeys a log-normal distribution. The specific implementation steps are as follows:

[0007] Step 1: Estimation of lognormal distribution parameters

[0008] First, the product life follows a log-normal distribution, so the probability density function f(t) of the product life t can be expressed as

[0009]

[0010] Where: μ is the logarithmic mean, σ is the logarithmic standard deviation;

[0011] Then, collect the constant stress accelerated life test data of the product; assume that there are r stress levels, denoted as {S l ; l=1,2,…,r}, there are n l samples, record different stress levels S l The failure time of each sample is calculated, and the failure time of the samples corresponding to each stress level is arranged in order. The obtained test data set is recorded as

[0012] {t (i，l) ; i = 1, 2, ..., n l ;l=1,2,…,r}, (2)

[0013] Where: i is the sample number, l is the stress number, n l is the number of samples at the lth stress level, r is the number of stress levels, t (i，l) is the failure time of the ith sample under the lth stress;

[0014] Finally, the maximum likelihood estimation method is used to calculate the parameter estimates of different stresses of the product Input the life data set and solve μ according to the likelihood function formula of the lognormal distribution. l and The maximum likelihood estimators of are

[0015]

[0016]

[0017] Where: i is the sample number, l is the stress number, n l is the number of samples at the lth stress level, t (i，l) is the failure time of the ith sample under the lth stress;

[0018] Step 2: Establish an inverse power law model and extrapolate the distribution of the acceleration factor based on model uncertainty

[0019] Through step 1, we can get the lognormal distribution double parameter μ under r stress levels: l and σ l , l = 1, 2, ..., r; In order to obtain the distribution of the acceleration factor AF, it is necessary to establish the relationship between the logarithmic life mean μ and the current stress I on the basis of keeping the failure mechanism unchanged (specifically expressed as σ remains unchanged), that is, the inverse power law model;

[0020] First, the rationality of the inverse power law model is tested. If the failure mechanism of the product under different stresses does not change, it means that σ is the same. Therefore, for the data set {σ l ; l = 1, 2, ..., r} for consistency test, i.e. variance homogeneity test; Among them, Bartlett test is a commonly used variance homogeneity test method, which can be used for variance test of multiple groups with unequal number of measurements. Its core idea is to obtain the chi-square statistic between different groups, and then judge whether the variance between groups is equal according to the value of the chi-square statistic; the steps of this method are as follows:

[0021] Establish the null hypothesis H0 and the alternative hypothesis H1

[0022] H0: σ1=σ2=…=σ r ; (5)

[0023] H1: σ1, σ2, …, σ r Different. (6)

[0024] Where: r is the stress level number, σ1, σ2, …, σ r is the logarithmic standard deviation at each stress level;

[0025] Calculate the statistic X 2

[0026]

[0027]

[0028]

[0029]

[0030] Where: is the sample variance of each group, s 2 is the overall sample variance, i is the sample number, l is the stress number, n l is the number of samples at the lth stress level, r is the number of stress levels, t (i，l) is the failure time of the ith sample under the lth stress;

[0031] Under the condition that the null hypothesis is true, the statistic X 2 Approximately obey the chi-square distribution with degrees of freedom v=r-1. This calculated value can be directly compared with the corresponding critical value in the chi-square distribution table. If the calculated value is greater than or equal to the critical value under a specific significance level (a), that is: Then the null hypothesis H0 of the test is rejected at this level; otherwise, the null hypothesis H0 is accepted and the failure mechanism remains unchanged;

[0032] Secondly, estimate the parameter σ of the product lognormal distribution; take the weighted average to calculate the overall estimate of the logarithmic standard deviation

[0033]

[0034] Where: l is the stress number, r is the stress level number, n l is the number of samples at the lth stress level, is the estimated logarithmic standard deviation of the lth stress level, is the overall estimate of the log standard deviation;

[0035] Then, an inverse power law model based on the influence of current stress is established; the relationship between the logarithmic life mean μ and the current stress I is expressed as

[0036] μ=AI -B , (12)

[0037] Where: A and B are constants; logarithmic linear processing is performed to obtain

[0038] lnμ=lnA-BlnI, (13)

[0039] In the formula: μ is the logarithmic mean, I is the current stress, A and B are constants; a univariate linear regression model is established:

[0040]

[0041] Where: l is the stress number, r is the stress level number, μ l is the logarithmic mean of the lth stress level, I l is the lth current stress level, ε l The error term for the lth stress level, is the error term variance, A and B are constants; import the data set {(I l , μ l ); l = 1, 2, ..., r}, and converted to {(lnI l , lnμ l ); l = 1, 2, ..., r}; Based on the least squares method, the parameters lnA, B and An estimated value of

[0042] Finally, the AF distribution is extrapolated based on the model uncertainty; since the error term follows a normal distribution, l=1,2,…,r, and lnμ1,…,lnμ r Independent of each other;

[0043] Assume that the electrical stress in the working environment is S W =I W , the electrical stress in the accelerated reliability verification test is S A =I A , the acceleration factor is AF, which reflects the speed of failure of the same product in stress environments of different magnitudes. The formula is

[0044]

[0045] Where: is the logarithmic mean value under the electrical stress of the working environment, is the logarithmic mean under electrical stress in the accelerated environment; logarithmic linear processing is obtained

[0046]

[0047] Where: is the logarithmic mean value under the electrical stress of the working environment, is the logarithmic mean under electrical stress in an accelerated environment; And the two are independent of each other, so

[0048]

[0049] Where: I W is the electrical stress of the working environment, I A is the magnitude of the electrical stress in the accelerated test, B is a constant, is the error term variance; so AF obeys the lognormal distribution, that is,

[0050]

[0051] Where: μ AF is the mean value of the acceleration factor, is the variance of the acceleration factor,

[0052] Step 3: Design of log-normal distribution product reliability verification optimization scheme based on cost constraints

[0053] Through step 2, the AF distribution parameter μ under accelerated stress level can be obtained: AF and And the product log-normal distribution parameter σ, on this basis, the accelerated reliability verification test plan for the product is designed;

[0054] First, an accelerated reliability verification scheme under lognormal distribution is established. Given the acceptable quality level μ0, limit quality μ1, production risk α, and user risk β under working stress, a timed truncation test scheme under constant accelerated life test is established to determine the accelerated test truncation time τ, the number of test samples n, and the number of judged failures c. The null hypothesis H0 and alternative hypothesis H1 under working stress are established, and a sampling test is performed on the product lognormal distribution parameter μ:

[0055]

[0056] Where: μ is the reliability verification index of working stress, μ0 is the acceptable quality level of working stress, and μ1 is the limit quality of working stress. Due to the accelerated reliability verification test, the inspection index is converted to the logarithmic normal distribution parameter μ′ of the product under accelerated stress, so the null hypothesis and alternative hypothesis under accelerated stress are converted to:

[0057]

[0058] Where: H′0 is the null hypothesis, H′1 is the alternative hypothesis, μ′ is the reliability verification index of the accelerated test, μ′0 is the acceptable quality level of the accelerated test, μ′0=μ0 / AF, μ′1 is the limit quality of the accelerated test, μ′1=μ1 / AF; the risk constraints of both parties are:

[0059]

[0060] Where: H′0 is the null hypothesis, μ′ is the reliability verification index of the accelerated test, μ′0 is the acceptable quality level of the accelerated test, μ′1 is the limit quality of the accelerated test, α is the risk of the manufacturer, and β is the risk of the user;

[0061] Formulate judgment criteria: when the cumulative number of failures in the test k≤c, the product is qualified and an acceptance judgment is made; when k>c, the product is unqualified and a rejection judgment is made; establish the equation group based on the risk constraints of both parties

[0062]

[0063] Where: μ′ is the reliability verification index of the accelerated test, μ′0 is the acceptable quality level of the accelerated test, μ′1 is the limit quality of the accelerated test, α is the risk of the manufacturer, β is the risk of the user, k is the cumulative number of failures, and c is the number of judged failures. Expand the acceptance probability formula to get

[0064]

[0065] Where: μ is the reliability verification index of working stress, μ′ is the reliability verification index of accelerated test, σ is the logarithmic standard deviation, τ is the test time, n is the number of test samples, k is the cumulative number of failures, and c is the number of judged failures. When AF considers uncertainty, the acceptance probability is

[0066]

[0067] Where: μ′ is the reliability verification index of the accelerated test, f(AF) is the probability distribution function of the acceleration factor; Combining equation (23) and equation (24), the risk constraint conditions of both parties are expanded as follows:

[0068]

[0069] Where: μ0 is the acceptable quality level of working stress, μ1 is the limit quality of working stress, σ is the logarithmic standard deviation, τ is the test time, n is the number of test samples, k is the cumulative number of failures, c is the number of judged failures, μ AF is the mean value of the acceleration factor, is the variance of the acceleration factor, α is the producer risk, and β is the user risk;

[0070] Then, the optimization goal of the reliability verification scheme is established; on the basis of satisfying the risk constraints of both parties, the cost index is set to find the most cost-saving optimization scheme; according to the actual situation of the test, the cost includes three parts: the test cost related to the test truncation time τ value, the sample cost related to the sample number n value, and the accelerated stress I AThe risk cost associated with the value; TC is used to represent the total cost of the experiment, and the cost function is as follows:

[0071] TC=c1*τ+c2*n+c3*(I A / I W -1), (26)

[0072] In the formula: c1 is the test cost per unit time, c2 is the cost of a single sample, c3 is the unit risk cost, τ is the test time, n is the number of test samples, I W is the electrical stress of the working environment, I A is the magnitude of the electrical stress in the accelerated test;

[0073] Finally, the reliability verification optimization scheme is designed; Substituting into equation (25), the optimal reliability verification scheme can be obtained by solving the following optimization problem:

[0074] min TC=c1*τ+c2*n+c3*(I A / I W -1),

[0075]

[0076] In the formula: c1 is the test cost per unit time, c2 is the cost of a single sample, c3 is the unit risk cost, τ is the test time, n is the number of test samples, I W is the electrical stress of the working environment, I A is the magnitude of the electrical stress of the accelerated test, μ0 is the acceptable quality level of the working stress, μ1 is the limit quality of the working stress, σ is the logarithmic standard deviation, k is the cumulative number of failures, c is the number of judged failures, is the variance of the error term, α is the producer risk, β is the user risk, B is a constant, I Amin is the minimum electrical stress, I Amax is the maximum electrical stress, n max is the maximum number of test samples; calculate the optimal accelerated reliability verification scheme (n, τ, c, I A );

[0077] Through the above steps, the problems of high reliability and long life of products, model uncertainty, etc. in the design process of accelerated reliability verification optimization scheme for log-normal distribution products are solved. The effectiveness of the design of accelerated reliability verification optimization scheme is guaranteed by introducing AF uncertainty. It conforms to the actual engineering situation, is simple to calculate, provides convenience for engineering and technical personnel, and has important application value.

[0078] (3) Advantages:

[0079] The invention discloses an accelerated reliability verification test scheme design method, i.e., an accelerated reliability verification test scheme design method for a product whose lifespan obeys a log-normal distribution, which has the following advantages:

[0080] ① The present invention aims at the problem of accelerated reliability verification caused by the uncertainty of the model for products whose lifespan follows the log-normal distribution. It establishes an optimization scheme for accelerated reliability verification under cost constraints by considering the uncertainty of AF, effectively manages the risks of both parties and significantly saves the test costs.

[0081] ② The method proposed in the present invention is simple to calculate, easy to implement, and more in line with engineering practice, convenient for engineering and technical personnel to master and use, and the method is scientific and easy to apply and promote. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0083] The present invention provides an accelerated reliability verification test scheme design method, that is, an accelerated reliability verification test scheme design method for a product life that obeys a log-normal distribution, and its flow chart is as follows: Figure 1 As shown;

[0084] The present invention is further described in detail below by taking a certain type of white organic light-emitting diode (White Organic Light-Emitting Diode, hereinafter referred to as WOLED) product as an example;

[0085] In the WOLED accelerated life test, the accelerated stress is current, and the stress levels of the test are set to I1=9.64mA, I2=17.09mA and I3=22.58mA respectively. Under each current stress, a certain number of samples are arranged to carry out constant accelerated life test; during the test, their failure time is recorded and then sorted by time size;

[0086] In the WOLED accelerated reliability verification test, the working stress I W =3.2mA, accelerated stress given range I A ∈[9mA, 23mA]; the reliability verification index is the reliable life t R (Reliability R = 0.9), the indicators of both parties are t R0 =600h, t R1 = 400h, risk of both parties α = β = 0.2;

[0087] The present invention proposes an accelerated reliability verification test scheme design method, that is, an accelerated reliability verification test scheme design for a log-normal life distribution product, and its specific implementation steps are as follows:

[0088] Step 1: Estimation of lognormal distribution parameters

[0089] The current stress levels of I1=9.64mA, I2=17.09mA and I3=22.58mA were set respectively, and the failure time data after sorting under different stresses were obtained through constant accelerated life test, as shown in Table 1;

[0090] Table 1 Accelerated life test data of WOLED

[0091]

[0092] The maximum likelihood estimation method is used to calculate the parameter estimates μ of different stresses of the product. l , Input the life span data set sorted from small to large, and solve μ according to the likelihood function formula of the lognormal distribution l and The maximum likelihood estimators are The results of lognormal distribution parameter estimation are shown in Table 2;

[0093] Table 2 Estimation results of lognormal distribution parameters under different accelerated stresses

[0094]

[0095] Step 2: Establish an inverse power law model and extrapolate the distribution of the acceleration factor based on model uncertainty

[0096] From step 1, we can see that the estimated values ​​of the log-normal distribution parameters under three current stress levels are calculated based on the accelerated life test data in Table 1. and Next, it is necessary to establish the relationship between the logarithmic life mean μ and the current stress I while keeping the failure mechanism unchanged;

[0097] First, the consistency test of failure mechanism is performed; if the failure mechanism of the product does not change under different current stresses, it means that the logarithmic standard deviation σ is the same; for the data set {σ l ; l = 1, 2, 3}, use the Bartlett method to test whether the hypothesis H0 is true:

[0098] Different.(28)

[0099] Where: r is the stress level number, σ1, σ2, …, σ r is the logarithmic standard deviation at each stress level; as the statistic for testing H0, according to formula (7), we can get:

[0100] X 2 =1.2973. (29)

[0101] When r = 3, a = 0.05, satisfy Therefore, the original hypothesis holds, and the parameter σ of the lognormal distribution has no significant change;

[0102] Second, take a weighted average to find an estimate of the common lognormal distribution parameter σ

[0103]

[0104] Where: l is the stress number, r is the stress level number, n l is the number of samples at the lth stress level, is the estimated logarithmic standard deviation of the lth stress level, is the overall estimate of the log standard deviation;

[0105] Then, an inverse power law model of WOLED under the influence of current stress is established; the inverse power law equation of the logarithmic life mean μ and the current stress I in equation (12) and the linear equation in equation (13) are established; at the same time, according to the parameter estimation values ​​of each current stress in Table 2 Use least squares estimation to obtain the parameter estimates of the univariate linear regression model of formula (14): Among them, R 2 =0.9994, which proves that the regression model has a good fitting effect;

[0106] Finally, the AF distribution is extrapolated based on the model uncertainty; the electrical stress under the known working environment is I W =3.2mA, electrical stress I in accelerated reliability verification test A Uncertain; According to formula (15) and formula (16), in,

[0107] Step 3: Design of log-normal distribution product reliability verification optimization scheme based on cost constraints

[0108] Through step 2, the AF distribution parameter μ under accelerated stress level can be obtained: AF and and the common log-normal distribution parameter σ, on this basis, the accelerated reliability verification test plan for the product is designed;

[0109] First, the reliability index is changed from t R Converted to μ; Since the reliability formula of the lognormal distribution is

[0110]

[0111] μ can be written as R The formula is

[0112] μ=lnt R -σφ -1 (1-R). (32)

[0113] Where: μ is the logarithmic mean, σ is the logarithmic standard deviation, R is the reliability, t R is the reliable life; so according to formula (32), the reliability index of both parties is obtained

[0114] μ0=lnt R0 -σφ -1 (1-R)=6.525, (33)

[0115] μ1=lnt R1 -σφ -1 (1-R)=6.358. (34)

[0116] Then, the WOLED reliability verification optimization scheme is designed; the existing information such as the reliability indexes and risks of both parties are substituted into the optimization model of formula (27), and c1 = 300 yuan / h, c2 = 3000 yuan / piece, c3 = 1000 yuan, n max =10, we get

[0117] min TC=300*τ+3000*n+1000*(I A / 3.2-1),

[0118] Where: τ is the test time, n is the number of test samples, I A is the magnitude of the electrical stress of the accelerated test, k is the cumulative number of faults, and c is the number of judged faults;

[0119] Finally, the WOLED reliability verification optimization solution results are calculated; I A The range is scaled with 1 mA, and the solution with the lowest cost is found among the solutions that satisfy the risk constraints of both parties. The results are shown in Table 3.

[0120] Table 3 Minimum cost of reliability verification scheme under different accelerated stress

[0121]

[0122] By comparison, the optimal accelerated reliability verification scheme (n, τ, c, I A)=(6, 59h, 0, 16mA), the actual risks of both parties are 0.1973 and 0.1866 respectively, and the minimum test cost is 39700 yuan; by applying the present invention to the case of WOLED products, an accelerated reliability verification optimization scheme of log-normal distribution is established; the results show that the scheme effectively controls the risks of both parties, and at the same time finds the optimal result according to the optimization model, which significantly saves the test cost;

[0123] In summary, the present invention takes a certain type of WOLED product as a case, and aims at the problem of accelerated reliability verification caused by the influence of model uncertainty on products whose lifespan obeys lognormal distribution. Firstly, based on the constant accelerated life test data of the product, the maximum likelihood estimation method is used to estimate the lognormal distribution parameters; secondly, under the premise of ensuring the consistency of the failure mechanism, an inverse power law model of the logarithmic mean parameter of the distribution and the current stress is constructed; then, the model is logarithmically transformed into a univariate linear regression model, and the least squares estimation method is used to obtain the estimated value of the model parameter, and then the distribution of the acceleration factor is extrapolated based on the model uncertainty; finally, combined with the AF uncertainty, the cost-constrained accelerated reliability verification test scheme is optimized and designed, and the accelerated reliability verification test scheme is given, which effectively completes the design of the accelerated reliability verification test scheme for products whose lifespan obeys lognormal distribution.

Claims

1. A method for designing an accelerated reliability verification test plan. Features: The specific steps are as follows: Step 1: Estimation of lognormal distribution parameters First, the product life follows a log-normal distribution, so the probability density function f(t) of the product life t is expressed as Where: μ is the logarithmic mean, σ is the logarithmic standard deviation; Then, collect the constant stress accelerated life test data of the product; suppose there are r stress levels in total, denoted as {S l ; l=1,2,…,r}, there are n l samples, record different stress levels S l The failure time of each sample is calculated, and the failure time of the samples corresponding to each stress level is arranged in order. The obtained test data set is recorded as {t (i，l) ;i=1,2,…,n l ;l=1,2,…,r}, (2) Where: i is the sample number, l is the stress number, n l is the number of samples at the lth stress level, r is the number of stress levels, t (i，l) is the failure time of the ith sample under the lth stress; Finally, the maximum likelihood estimation method is used to calculate the parameter estimates of different stresses of the product μ l , Input the life data set and solve μ according to the likelihood function formula of the lognormal distribution. l and The maximum likelihood estimators are Where: i is the sample number, l is the stress number, n l is the number of samples at the lth stress level, t (i，l) is the failure time of the ith sample under the lth stress; Step 2: Establish an inverse power law model and extrapolate the distribution of the acceleration factor based on model uncertainty Through step 1, we can obtain the lognormal distribution double parameter μ under r stress levels: l and σ l , l = 1, 2, ..., r; In order to obtain the distribution of the acceleration factor AF, it is necessary to establish the relationship between the logarithmic life mean μ and the current stress I on the basis of keeping the failure mechanism unchanged, that is, the inverse power law model; First, the rationality of the inverse power law model is tested; if the failure mechanism of the product under different stresses does not change, it means that σ is the same; therefore, for the data set {σ l ; l = 1, 2, ..., r} for consistency test, i.e. variance homogeneity test; Among them, Bartlett test is a commonly used variance homogeneity test method, which is used for variance test of multiple groups with unequal number of measurements, and then the value of chi-square statistic is used to judge whether the variances between groups are equal; the steps of this method are as follows: Establish the null hypothesis H 0 With the alternative hypothesis H 1 H 0 :s 1 =s 2 =…=s r (5) H 1 :s 1 ,s 2 ,…,s r different; (6) Where: r is the stress level number, σ 1 , σ 2 , …, σ r is the logarithmic standard deviation at each stress level; Calculate the statistic X 2 Where: is the sample variance of each group, s 2 is the overall sample variance, i is the sample number, l is the stress number, n l is the number of samples at the lth stress level, r is the number of stress levels, t (i，l) is the failure time of the ith sample under the lth stress; Under the condition that the null hypothesis is true, the statistic X 2 Approximately obey the chi-square distribution with degrees of freedom v=r-1. Directly compare this calculated value with the corresponding critical value in the chi-square distribution table. If the calculated value is greater than or equal to the critical value under a specific significance level (a), that is: At this level, the null hypothesis H is rejected. 0 Otherwise, accept the null hypothesis H 0 , the failure mechanism remains unchanged; Secondly, estimate the parameter σ of the product lognormal distribution; take the weighted average to calculate the overall estimate of the logarithmic standard deviation Where: l is the stress number, r is the stress level number, n l is the number of samples at the lth stress level, is the estimated logarithmic standard deviation of the lth stress level, is the overall estimate of the log standard deviation; Then, an inverse power law model based on the influence of current stress is established; the relationship between the logarithmic life mean μ and the current stress I is expressed as μ=AI -B , (12) Where: A and B are constants; logarithmic linear processing is performed to obtain lnμ=InA-BlnI, (13) In the formula: μ is the logarithmic mean, I is the current stress, A and B are constants; a univariate linear regression model is established: Where: l is the stress number, r is the stress level number, μ l is the logarithmic mean of the lth stress level, I l is the lth current stress level, ε l The error term for the lth stress level, is the error term variance, A and B are constants; import the data set {(I l , μ l ); l = 1, 2, ..., r}, and converted to {(lnI l , lnμ l ); l = 1, 2, ..., r}; Based on the least squares method, the parameters lnA, B and An estimated value of Finally, the AF distribution is extrapolated based on the model uncertainty; since the error term follows a normal distribution, l=1,2,…,r,and lnμ 1 ,…,lnμ r Independent of each other; Assume the electrical stress in the working environment is S W =I W , the electrical stress in the accelerated reliability verification test is S A =I A , the acceleration factor is AF, which reflects the speed of failure of the same product in stress environments of different magnitudes. The formula is Where: is the logarithmic mean value under the electrical stress of the working environment, is the logarithmic mean under electrical stress in the accelerated environment; logarithmic linear processing is obtained Where: is the logarithmic mean value under the electrical stress of the working environment, is the logarithmic mean under electrical stress in an accelerated environment; And the two are independent of each other, so Where: I W is the electrical stress of the working environment, I A is the magnitude of the electrical stress in the accelerated test, B is a constant, is the error term variance; so AF obeys the lognormal distribution, that is, Where: μ AF is the mean value of the acceleration factor, is the variance of the acceleration factor, Step 3: Design of log-normal distribution product reliability verification optimization scheme based on cost constraints Through step 2, we can obtain the AF distribution parameter μ under the accelerated stress level. AF and And the product log-normal distribution parameter σ, on this basis, the accelerated reliability verification test plan for the product is designed; First, an accelerated reliability verification scheme under lognormal distribution is established; the acceptable quality level μ under known working stress is 0 , limiting mass μ 1 , production risk α, user risk β, establish a timed truncation test plan under constant accelerated life test, determine the accelerated test truncation time τ, the number of test samples n and the number of judged failures c; establish the original hypothesis H under working stress 0 With the alternative hypothesis H 1 , perform sampling test on the product log-normal distribution parameter μ: Where: μ is the reliability verification index of working stress, μ 0 is the acceptable quality level of working stress, μ 1 is the limit quality of working stress; due to the accelerated reliability verification test, the inspection index is converted to the logarithmic normal distribution parameter μ′ under the accelerated stress of the product, so the null hypothesis and the alternative hypothesis under accelerated stress are converted to: Where: H′ 0 is the null hypothesis, H′ 1 is the alternative hypothesis, μ′ is the reliability verification index of the accelerated test, and μ′ 0 is the acceptable quality level of the accelerated test, μ′ 0 =μ 0 / AF, μ′ 1 is the limit mass of the accelerated test, μ′ 1 =μ 1 / AF; the risk constraints of both parties are: Where: H′ 0 is the null hypothesis, μ′ is the reliability verification index of the accelerated test, and μ′ 0 is the acceptable quality level of the accelerated test, μ′ 1 is the limit quality of the accelerated test, α is the risk of the manufacturer, and β is the risk of the user; Formulate judgment criteria: when the cumulative number of failures in the test k≤c, the product is qualified and an acceptance judgment is made; when k>c, the product is unqualified and a rejection judgment is made; establish the equation group based on the risk constraints of both parties Where: μ′ is the reliability verification index of the accelerated test, μ′ 0 is the acceptable quality level of the accelerated test, μ′ 1 is the limit quality of the accelerated test, α is the risk of the manufacturer, β is the risk of the user, k is the cumulative number of failures, and c is the number of judged failures; expand the acceptance probability formula to get Where: μ is the reliability verification index of working stress, μ′ is the reliability verification index of accelerated test, σ is the logarithmic standard deviation, τ is the test time, n is the number of test samples, k is the cumulative number of failures, and c is the number of judged failures. When AF considers uncertainty, the acceptance probability is Where: μ′ is the reliability verification index of the accelerated test, f(AF) is the probability distribution function of the acceleration factor; Combining equation (23) and equation (24), the risk constraint conditions of both parties are expanded as follows: Where: μ 0 is the acceptable quality level of working stress, μ1 is the limit quality of working stress, σ is the logarithmic standard deviation, τ is the test time, n is the number of test samples, k is the cumulative number of failures, c is the number of judged failures, μ AF is the mean value of the acceleration factor, is the variance of the acceleration factor, α is the producer risk, and β is the user risk; Then, the optimization goal of the reliability verification scheme is established; on the basis of satisfying the risk constraints of both parties, the cost index is set to find the most cost-saving optimization scheme; the cost includes three parts: the test cost related to the test truncation time τ value, the sample cost related to the sample number n value, and the accelerated stress I A The risk cost associated with the value; TC is used to represent the total cost of the experiment, and the cost function is as follows: TC=c 1 *τ+c 2 *n+c 3 *(I A / I W -1), (26) Where: c 1 is the testing cost per unit time, c 2 is the cost of a single sample, c 3 is the unit risk cost, τ is the test time, n is the number of test samples, I W is the electrical stress of the working environment, I A is the magnitude of the electrical stress in the accelerated test; Finally, the reliability verification optimization scheme is designed; Substituting into equation (25), the optimal reliability verification scheme is obtained by solving the following optimization problem: Where: c 1 is the testing cost per unit time, c 2 is the cost of a single sample, c 3 is the unit risk cost, τ is the test time, n is the number of test samples, I W is the electrical stress of the working environment, I A is the magnitude of the electrical stress in the accelerated test, μ 0 is the acceptable quality level of working stress, μ 1 is the limit quality of working stress, σ is the logarithmic standard deviation, k is the cumulative number of failures, c is the number of judged failures, is the variance of the error term, α is the producer risk, β is the user risk, B is a constant, I Amin is the minimum electrical stress, I Amax is the maximum electrical stress, n max is the maximum number of test samples; calculate the optimal accelerated reliability verification scheme (n, τ, c, I A ).

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