Constant accelerated degradation test design method for inter-batch product difference and individual heterogeneity

Abstract

A constant accelerated degradation test design method for inter-batch product difference and individual heterogeneity belongs to the field of electrical digital data processing, and comprises the following steps: constructing a multi-stress factor constant accelerated degradation test model by using a multi-stress acceleration model and selecting a Wiener degradation process; product life time distribution is derived by using a multi-stress-factor constant accelerated degradation test model, unknown parameters of the multi-stress-factor constant accelerated degradation test model are solved, and the product life time distribution is calculated based on unknown parameter estimation values of the multi-stress-factor constant accelerated degradation test model and the average fault interval time of the product under the normal stress level. Solving a constant stress accelerated degradation test optimization design model in combination with the constraint condition and the optimization target; and searching an optimal test scheme through a particle swarm optimization algorithm. Tests prove that the method has good robustness and robustness, the product life prediction precision is high, and a theoretical basis can be provided for test cost control, degradation data collection, life prediction and reliability evaluation.

Description

Technical Field

[0001] The invention belongs to the technical field of electrical digital data processing, and in particular relates to a constant accelerated degradation test design method for batch product differences and individual heterogeneity. Background Art

[0002] Constant stress accelerated degradation test is an effective mechanical modeling method that collects more reliability-related information in a shorter time by conducting a more rigorous test environment than normal operating conditions. Constant stress accelerated degradation test is widely used to obtain quality characteristic information, and its degradation data is related to life, because degradation is the accumulation of product damage time. At present, the research on constant stress accelerated degradation test mainly focuses on performance degradation model, statistical analysis method of degradation data, and optimization design of constant stress accelerated degradation test.

[0003] The most widely used performance degradation models are Wiener degradation process, Gamma process and inverse Gaussian process. Since the Wiener degradation process is suitable for describing products with non-monotonic performance degradation trajectories and can well describe the dynamic characteristics of products, it is widely studied and applied in degradation data analysis. In engineering applications, products are usually subjected to a variety of stresses. The simultaneous action of multiple stress factors usually accelerates the degradation process, and due to the interaction between these stresses, the degradation process can be further propagated. Therefore, a single stress test cannot truly reflect the characteristics of the product. In order to obtain a larger acceleration factor while ensuring the invariance of the accelerated degradation mechanism, high-reliability and long-life products must use multiple stress factors as accelerating stresses. Fang (Fang G, Pan R, Stufken J. Optimal Setting of Test Conditions and Allocation of Test Units for Accelerated Degradation Tests With Two Stress Variables [J]. IEEE Transactions on Reliability, 2020, PP (99): 1-16.) et al. used the Eyring model to characterize the influence of two stress variables and provided a method for finding the optimal accelerated degradation test condition setting and test unit allocation for two environmental stresses: temperature and relative humidity. Shat (Shat H. Optimal design of stress levels in accelerated degradation testing for multivariate linear degradation models [J]. Journal of Applied Statistics, 2024, 51 (3): 534-554.) conducted a multi-stress factor accelerated degradation test optimization design study on the electric spindle based on the optimization criteria with multiple weights. In addition, for the degradation modeling of the Wiener degradation process, the existing accelerated degradation test design methods mainly focus on the correlation between the drift coefficient and stress, while ignoring the change of the diffusion coefficient. However, with the increase of stress level, the fluctuation range of most product performance parameters will also increase. Therefore, treating the diffusion coefficient as a constant may affect the accuracy of the test assessment.Qian et al. (Qian P, Hong L, Chen W, et al. Optimization of the Accelerated Degradation Test Plan for Electrical Connector Contact Pairs Based on a Nonlinear Wiener Process [J]. Mathematical Problems in Engineering, 2020, 2020) and Zheng et al. (Zheng B, Chen C, Lin Y, et al. Optimal design of step-stress accelerated degradation test oriented by nonlinear and distributed degradation process [J]. Reliability Engineering and System Safety, 2022, 217) used the same method as that of constructing the relationship between drift coefficient and stress when constructing the relationship between diffusion coefficient and stress. The above research work concluded that multiple stress factors and non-constant diffusion coefficient are the key to degradation modeling. However, they are treated separately. By consulting the literature, it can be seen that there is currently no relevant research in the optimization design of accelerated degradation tests that attempts to develop a generalized degradation model that simultaneously applies these two features.

[0004] In most studies of accelerated degradation testing, the observations obtained from each test unit are assumed to be independent. However, in practical applications, differences between test units may lead to misjudgment of the collected data. In order to improve the scope of application and fitting accuracy of the model, many studies have introduced individual differences in test units into Wiener-based degradation models. The heterogeneity of the unit is usually obtained by randomizing the drift coefficient part, such as normal distribution, Gamma distribution, and inverse Gaussian distribution. In addition, test units can be manufactured in different production batches or provided by different suppliers, so test units from the same production batch or the same supplier may have group effects and should be regarded as random effects from the test unit supplier. Seo et al. (Seo K, Lee W. Optimal experimental designs for clustered read-out data of reliability tests via particle swarm optimization[J]. Computers & Industrial Engineering, 2022, 171) represented the batch effect as a normal distribution with a mean of 0, and added the batch effect to the construction of the relationship between model parameters and stress.

[0005] In summary, individual differences, batch-to-batch product difference modes, and supplier heterogeneity need to be incorporated into the design of accelerated degradation tests, and when the impact of test stress conditions is the main concern of accelerated degradation tests, the estimation bias caused by these factors needs to be considered in the test design stage. Summary of the invention

[0006] The purpose of the present invention is to provide a method for designing a constant accelerated degradation test considering batch product differences and individual heterogeneity, specifically a Wiener multi-stress factor constant accelerated degradation test optimization design method considering batch product difference modalities and individual differences.

[0007] To achieve the above purpose, the specific technical scheme of a constant accelerated degradation test design method for batch product differences and individual heterogeneity provided by the present invention is as follows:

[0008] The present invention provides a method for designing a constant accelerated degradation test for batch product differences and individual heterogeneity, comprising the following steps:

[0009] Step S1: using a multi-stress acceleration model and selecting a Wiener degradation process to construct a multi-stress factor constant acceleration degradation test model;

[0010] Step S2: constructing a constant stress accelerated degradation test optimization design model;

[0011] Step S201: deriving the product life time distribution using a multi-stress factor constant accelerated degradation test model;

[0012] Step S202: solving unknown parameters of the multi-stress factor constant acceleration degradation test model;

[0013] Step S203: solving the constant stress accelerated degradation test optimization design model based on the unknown parameter estimation values ​​of the multi-stress factor constant accelerated degradation test model and the mean time between failures of the product under normal stress level, combined with the constraint conditions and the optimization goal;

[0014] Step S3: Using the constant stress accelerated degradation test optimization design model to search for the optimal test plan through the particle swarm optimization algorithm.

[0015] Furthermore, the mathematical expression of the multi-stress acceleration model is shown in formula (1):

[0016] exp (1)

[0017] in, represents characteristic lifetime; A, B, C and D are all unknown constants; F is activation energy; K is the Boltzmann constant; T is absolute temperature; RH is relative humidity.

[0018] Furthermore, the mathematical expression of the multi-stress factor constant accelerated degradation test model is:

[0019] (3)

[0020] in, represents the drift coefficient; represents the diffusion coefficient; α and β are both random variables that obey the normal distribution, representing individual differences in the degradation process; , , , , All are unknown coefficients, obtained through parameter estimation; represents the standardized stress value of the e-th stress factor at the k-th stress level; represents the standardized stress value of the uth stress factor at the kth stress level; represents the standardized stress value of the vth stress factor at the kth stress level; z represents a random variable describing the mode of product difference between batches; Represents a random variable The mean of Represents a random variable The mean of represents variance; represents the standard deviation; E represents the number of stress factors.

[0021] Further, in step S201, the product life G is defined as the time when the performance degradation of the product under the normal stress level reaches the failure threshold for the first time. Time:

[0022] (4)

[0023] Where t represents the total test time, It represents the standardized stress value of E different stress factors under normal stress level, It indicates the degradation amount of the product under the influence of the standardized stress value of E different stress factors at the normal stress level;

[0024] The product life G obeys the inverse Gaussian distribution, and its probability density function is:

[0025] (5)

[0026] in, and represent the variance and mean of the product degradation amount of the standardized stress value under normal stress level respectively;

[0027] The average failure interval time of the product under normal stress level is obtained from formula (4):

[0028] (6)

[0029] in, Represents a random variable The mean of , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor under normal stress level, represents the standardized stress value of the uth stress factor under normal stress level, represents the standardized stress value of the vth stress factor under normal stress level, E represents the number of stress factors, Represents the variance that describes the differences in products between batches.

[0030] Furthermore, the variance The mathematical expression is:

[0031]

[0032] in, Represents a random variable The variance of represents the variance describing the differences between batches of products, Represents a random variable The variance of Represents a random variable The mean of Represents a random variable The mean of represents the error coefficient, , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor under normal stress level, represents the standardized stress value of the uth stress factor under normal stress level, represents the standardized stress value of the vth stress factor under normal stress level, and E represents the number of stress factors.

[0033] Furthermore, the mean The mathematical expression is:

[0034]

[0035] in, Represents a random variable The mean of , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor under normal stress level, represents the standardized stress value of the uth stress factor under normal stress level, represents the standardized stress value of the vth stress factor under normal stress level, and E represents the number of stress factors.

[0036] Furthermore, in step S202, the following assumptions are first established:

[0037] 1) Assume that there are l stress levels in the multi-stress factor constant accelerated degradation test, and the stress values ​​of each stress level satisfy ;

[0038] 2) The test units are provided in Q batches, and the number of units provided in each batch is , ; The test unit allocation ratio of different batches at the kth stress level is , ;

[0039] 3) The test time allocation ratio under the kth stress level is , the measurement interval at each stress level remains unchanged, and the number of measurements is the same for all test units; therefore, the measurement interval at each stress level is The total number of measurements is ; represents the number of measurements at the kth stress level, represents the test time under the kth stress level;

[0040] 4) For , , , Indicated in is the jth observation value of the ith test unit under the kth stress level;

[0041] Assuming that N test units are subjected to multi-stress factor constant accelerated degradation tests under the above assumptions, the performance degradation increment is The probability density function of is:

[0042] (7)

[0043] The performance degradation increment The log-likelihood function of is:

[0044] (8)

[0045] in, and They represent the variance and mean of the product degradation of the standardized stress value at the kth stress level, respectively, and θ represents the unknown parameters of the model;

[0046] Take the log-likelihood function for the random variable The mean The first partial derivative of :

[0047] (9)

[0048] in, represents the product of the total sample size and the total test time, Indicates that there are no random variables Drift coefficient , represents the increment of product degradation under the kth stress level, It represents the variance describing the differences between batches of products;

[0049]

[0050] in, , ,…, represents the sample size provided by each Q batch, , ,…, represents the sample allocation ratio of Q batches at the kth stress level, represents the test time allocation ratio under the kth stress level, , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor at the k-th stress level, represents the standardized stress value of the uth stress factor at the kth stress level, represents the standardized stress value of the vth stress factor at the kth stress level, and E represents the number of stress factors;

[0051] Let (9) be 0 to get the unknown parameters The maximum likelihood estimate of is substituted into formula (9) to obtain the profile likelihood function of other unknown parameters; the maximum likelihood estimate of the remaining unknown parameters is obtained by maximizing the profile likelihood function through multidimensional search, and the maximum likelihood estimate of the mean time between failures of the product under normal stress level is obtained as follows:

[0052] (10)

[0053] in, Represents a random variable The estimated value of the mean.

[0054] Furthermore, in step S203, the constraint condition is:

[0055] 1) The total test time t should not exceed the specified test time ;

[0056] 2) The number of test units provided in different batches should not exceed the number of available test units ;

[0057] 3) The total cost of the experiment TC should not exceed the pre-set budget ;

[0058] Among them, the mathematical expression of the total test cost TC is:

[0059] (12)

[0060] in, , ,…, represents the sample size provided by each Q batch, represents the unit cost of each test unit, represents the unit operating cost of the test equipment, represents the cost of making a single observation of the experiment, represents the test time allocation ratio under the kth stress level, Indicates the measurement interval time at each stress level;

[0061] Then the mathematical expression of the constant stress accelerated degradation test optimization design model is:

[0062] (13)

[0063] in, represents the asymptotic variance of the maximum likelihood estimate of the mean time between failures of the product under normal stress level, represents the asymptotic variance of the maximum likelihood estimate of the mean time between failures of the product under normal stress level, represents the decision variable, , ,…, Respectively represent the 1st, 2nd, ..., The test time allocation ratio under each stress level.

[0064] Furthermore, the asymptotic variance of the maximum likelihood estimate of the mean time between failures of the product under normal stress level is The mathematical expression is:

[0065] (11)

[0066] Where Avar represents the asymptotic variance; represents the decision variable, ; represents the Fisher information matrix; It represents the maximum likelihood estimate of the mean time between failures of the product under normal stress level. A column vector consisting of the first-order partial derivatives of the unknown parameters of the model; Represents unknown parameters of the model An estimated value of express The transpose of : .

[0067] The beneficial effects of the present invention are:

[0068] The invention discloses a method for designing a constant accelerated degradation test for batch product differences and individual heterogeneity. The method describes the degradation trajectory of the product through the Wiener degradation process. The system considers the influence of batch factors and individual factors, takes minimizing the asymptotic variance of the estimated value of the mean time between failures of the product under normal working stress as the optimization goal, and ensures the accuracy of product life prediction.

[0069] The present invention designs an optimal test scheme through an automotive LED lamp engineering case, and conducts model comparison analysis, constraint condition analysis and parameter sensitivity analysis to verify the feasibility and effectiveness of the model. The test results show that the method of the present invention has good robustness and stability.

[0070] The present invention fully considers factors such as product nonlinearity, measurement error and diffusion coefficient randomness, and comprehensively designs the optimal test plan, providing a theoretical basis for test cost control, degradation data collection, life prediction and reliability evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 The present invention provides a flow chart of a method for designing a constant accelerated degradation test for batch product differences and individual heterogeneity.

[0072] Figure 2 This is a comparison chart of the asymptotic variance and total cost of the maximum likelihood estimate of the mean time between failures of the product under normal stress level in different degradation model test optimization schemes.

[0073] Figure 3 Comparison of results for different constraint condition optimization schemes (experiment time limit , test unit restrictions ).

[0074] Figure 4 Compare the results of the optimization schemes for different constraints (experimental budget constraints , test unit restrictions ).

[0075] Figure 5 Comparison of optimization results for different constraint conditions (experimental budget constraints , test unit restrictions ). DETAILED DESCRIPTION

[0076] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a constant accelerated degradation test design method for batch product differences and individual heterogeneity provided by the present invention in conjunction with the accompanying drawings.

[0077] The invention provides a method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity, which can more comprehensively design the optimal test plan for factors affecting product degradation data, such as Figure 1 As shown, the specific implementation process is as follows:

[0078] Step S1: Using the multi-stress acceleration model and selecting the Wiener degradation process to construct a multi-stress factor constant acceleration degradation test model.

[0079] The mathematical expression of the multi-stress acceleration model used in the present invention is shown in formula (1):

[0080] exp (1)

[0081] in, represents characteristic life, such as median life, etc.; A, B, C and D all represent undetermined constants; F represents activation energy, which is mainly related to the material of the product; K represents the Boltzmann constant, ; T represents absolute temperature; RH represents relative humidity.

[0082] The present invention optimizes the design of the multi-stress factor constant accelerated degradation test scheme for high-reliability products, taking into account the test units provided by Q batches. , total test time t, measurement interval time , the sample distribution ratio of Q different batches under different stress levels , , test time allocation ratio under different stress levels And the standardized stress values ​​of E different stress factors at different stress levels The optimization problem Under normal use conditions and budget constraints, the product is designed to minimize the mean time between failures under normal stress levels. Optimal experimental plan for asymptotic variance design.

[0083] The Wiener degradation process used in the present invention is a common random process model, which can not only accurately reflect the change of product life over time, but also effectively deal with the problems caused by measurement errors. Represents the degradation process at time t. Considering nonlinearity and measurement error, the Wiener degradation process can be:

[0084] (2)

[0085] Where s represents the standardized stress level; represents the drift coefficient, which increases with the increase of stress level; represents the diffusion coefficient, which varies with stress level; ( ) represents the standard Brownian motion process; It represents the time scale function, which is used to describe the nonlinear characteristics of product performance degradation; represents the error coefficient; represents the measurement error, .

[0086] set up represents the random effect of the batch, which conforms to the normal distribution, where N represents the sign of the normal distribution, represents the variance describing the differences between batches of products. Assume first that the batch effect is , z represents the random variable describing the mode of product difference between batches, and the degradation model considering random effects is used to describe the degradation differences between individuals. The multi-stress acceleration model is used to characterize the influence of multiple stress factor variables, and multiple stress factors are standardized. In the Wiener degradation process, the diffusion coefficient is usually a constant, and the drift coefficient is used to describe the acceleration relationship of stress. However, since the fluctuation range of most product performance parameters increases with the increase of stress level, if the diffusion coefficient is regarded as a constant, it will affect the evaluation accuracy of the test. Establish the drift coefficient of the Wiener degradation process and diffusion coefficient The multi-stress factor constant accelerated degradation test model of the Wiener degradation process coefficient and stress relationship is constructed, and its mathematical expression is as follows:

[0087] (3)

[0088] in, represents the drift coefficient; represents the diffusion coefficient; α and β are both random variables that obey the normal distribution, representing individual differences in the degradation process; , , , , All are unknown coefficients, which can be obtained through parameter estimation; represents the standardized stress value of the e-th stress factor at the k-th stress level; represents the standardized stress value of the uth stress factor at the kth stress level; represents the standardized stress value of the vth stress factor at the kth stress level; z represents a random variable describing the mode of product difference between batches; Represents a random variable The mean of Represents a random variable The mean of represents variance; represents the standard deviation; E represents the number of stress factors.

[0089] Step S2: Constructing a constant stress accelerated degradation test optimization design model.

[0090] The construction process of the constant stress accelerated degradation test optimization design model is mainly completed by three parts. First, the product life time distribution is derived using the multi-stress factor constant accelerated degradation test model; second, the unknown parameters of the multi-stress factor constant accelerated degradation test model are solved; finally, based on the estimated values ​​of the unknown parameters of the multi-stress factor constant accelerated degradation test model and the average failure interval time of the product under normal stress level, combined with the constraints and optimization objectives, the constant stress accelerated degradation test optimization design model is solved.

[0091] The specific operation process is as follows:

[0092] Step S201: deriving the product life time distribution using a multi-stress factor constant accelerated degradation test model.

[0093] The life of a product reflects the use of the product under normal working stress. Using the multi-stress factor constant accelerated degradation test model, the life of the product under normal working stress level can be deduced based on the degradation path of the product under accelerated stress level. Therefore, the life of the product G is defined as the time when the performance degradation of the product under normal stress level reaches the failure threshold for the first time. The time is as shown in formula (3):

[0094] (4)

[0095] Where t represents the total test time, It represents the standardized stress value of E different stress factors under normal stress level, It indicates the degradation amount of the product under the influence of the standardized stress value of E different stress factors at the normal stress level;

[0096] According to the properties of the Wiener degradation process, it can be deduced that the product life G obeys the inverse Gaussian distribution, and according to equations (2) and (3), the mean and variance of the product degradation value of the standardized stress value under the normal stress level can be obtained respectively:

[0097] variance :

[0098]

[0099] Mean :

[0100]

[0101] in, represents variance; It represents the variance describing the differences between batches of products; represents standard deviation; Represents a random variable The mean of Represents a random variable The mean of represents the error coefficient; , , All are undetermined coefficients; represents the standardized stress value of the e-th stress factor under normal stress level; represents the standardized stress value of the uth stress factor under normal stress level; represents the standardized stress value of the vth stress factor under normal stress level;

[0102] Then the probability density function of product life G is shown in formula (5):

[0103] (5)

[0104] From formula (4), the average failure interval of the product under normal stress level is:

[0105] (6)

[0106] Step S202: solving the unknown parameters of the multi-stress factor constant acceleration degradation test model.

[0107] Assume that there are N test units that can be subjected to multi-stress factor constant accelerated degradation tests under the following assumptions:

[0108] 1) Assume that there are l stress levels in the multi-stress factor constant accelerated degradation test, and the stress values ​​of each stress level satisfy ;

[0109] 2) The test units are provided in Q batches, and the number of units provided in each batch is , ; The test unit allocation ratio of different batches at the kth stress level is , ;

[0110] 3) The test time allocation ratio under the kth stress level is , the measurement interval at each stress level remains unchanged, and the number of measurements is the same for all test units; therefore, the measurement interval at each stress level is The total number of measurements is ; represents the number of measurements at the kth stress level, represents the test time under the kth stress level;

[0111] 4) For , , , Indicated in is the jth observation value of the ith test unit under the kth stress level.

[0112] The performance degradation increment The probability density function of is shown in formula (7):

[0113] (7)

[0114] Performance degradation increment The log-likelihood function of is shown in formula (8):

[0115] (8)

[0116] in, and represent the variance and mean of the product degradation of the standardized stress value under the kth stress level, and θ represents the unknown parameters of the model.

[0117] Take the log-likelihood function for the random variable The mean The first-order partial derivative of (unknown parameter) is calculated as shown in formula (9):

[0118] (9)

[0119] in, represents the product of the total sample size and the total test time, Indicates that there are no random variables Drift coefficient , represents the increment of product degradation under the kth stress level, It represents the variance describing the differences between batches of products;

[0120]

[0121] in, , ,…, represents the sample size provided by each Q batch, , ,…, represents the sample allocation ratio of Q batches at the kth stress level, Represents the test time allocation ratio under the kth stress level.

[0122] Let (9) be 0 to get the unknown parameters The maximum likelihood estimate of is substituted into formula (9) to obtain the profile likelihood function of other unknown parameters. By maximizing the profile likelihood function through multidimensional search, the maximum likelihood estimate of the remaining unknown parameters is obtained, and the maximum likelihood estimate of the mean time between failures of the product under normal stress level is obtained, as shown in formula (10):

[0123] (10)

[0124] in, Represents a random variable The estimated value of the mean.

[0125] Step S203: Based on the unknown parameter estimates of the multi-stress factor constant accelerated degradation test model and the mean time between failures of the product under normal stress levels, combined with constraint conditions and optimization objectives, the constant stress accelerated degradation test optimization design model is solved.

[0126] The asymptotic variance can reflect the degree of deviation in the estimation of the time before product failure. By minimizing the asymptotic variance of the maximum likelihood estimate of the mean time between failures of the product under normal stress level, a higher prediction accuracy of the time before failure can be obtained. Therefore, the objective function is to minimize the asymptotic variance of the maximum likelihood estimate of the mean time between failures of the product under normal stress level:

[0127] (11)

[0128] Where Avar represents the asymptotic variance; represents the decision variable, ; represents the Fisher information matrix; It represents the maximum likelihood estimate of the mean time between failures of the product under normal stress level. A column vector consisting of the first-order partial derivatives of the unknown parameters of the model; Represents unknown parameters of the model An estimated value of express The transpose of : .

[0129] The constraints in the design of constant stress accelerated degradation test scheme usually include the following aspects:

[0130] 1) The total test time t should not exceed the specified test time ;

[0131] 2) The number of test units provided in different batches should not exceed the number of available test units ;

[0132] 3) The total cost of the experiment TC should not exceed the pre-set budget ;

[0133] Among them, the total cost of the test TC can be expressed as:

[0134] (12)

[0135] in, , ,…, represents the sample size provided by each Q batch, represents the unit cost of each test unit, represents the unit operating cost of the test equipment, represents the cost of making a single observation of the experiment.

[0136] In summary, the mathematical expression of the constructed constant stress accelerated degradation test optimization design model is shown in formula (13):

[0137] (13)

[0138] in, , ,…, Respectively represent the 1st, 2nd, ..., The test time allocation ratio under each stress level.

[0139] Step S3: Using the constant stress accelerated degradation test optimization design model, the optimal test plan is searched through PSO (Particle Swarm Optimization, particle swarm optimization algorithm).

[0140] In the design of constant stress accelerated degradation test scheme, the data from the reliability test of the test unit may have many heterogeneities, such as different batches, equipment and operators, which will lead to the problem of low test evaluation accuracy. The present invention proposes a multi-stress factor constant accelerated degradation test scheme optimization design method based on the Wiener degradation process, which comprehensively considers the modal differences and individual differences of batch product differences. The present invention establishes an optimization model with the test cost, the specified test time and the number of available test units as constraints, and the asymptotic variance minimization of the mean failure interval time as the goal, and adopts the corresponding PSO (Particle Swarm Optimization, particle swarm optimization algorithm) to efficiently solve the optimal value of the constant stress accelerated degradation test optimization design model to obtain the optimal test scheme.

[0141] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0142] The following is a case analysis of the degradation data of automotive LED lights under the combined influence of two stress factors, temperature and humidity. A comparative analysis and parameter sensitivity analysis of the dual stress factor constant accelerated degradation test schemes under different models and different constraints, whether considering the modal differences of batch product differences and individual differences, are carried out to verify the effectiveness and robustness of the present invention.

[0143] The specific test process of the present invention is as follows:

[0144] 1. Numerical example analysis

[0145] Assume that there are 2 batches of test units, and the number of test units provided in each batch is , There are degradation differences between individuals in the same batch, and the observed values ​​of test units provided by the same batch are correlated.

[0146] The multi-stress factor constant accelerated degradation test model constructed by the present invention was adopted, the influence of the dual stress factors of temperature and relative humidity and the interaction between stresses were considered, and the optimization design research of the constant stress accelerated degradation test (CSADT) scheme for automotive LED lamps was carried out in combination with specific test conditions.

[0147] The objective function is to minimize the asymptotic variance of the product MTTF (mean time to failure) estimate under normal working stress. Suppose the variance of the batch effect is ,Based on the test data of automotive LED lights, the maximum likelihood estimation of the unknown parameters of the multi-stress factor constant acceleration degradation test model is carried out, and the results are shown in Table 1.

[0148] Table 1. Table of unknown parameter estimates .

[0149] in, Represents a random variable The estimated mean of represents the variance estimate, , , , All represent the estimated values ​​of the unknown coefficients. Represents a random variable The estimated mean of represents the estimated standard deviation, , , , All represent the estimated values ​​of the unknown coefficients. Represents the error coefficient estimate.

[0150] According to the actual situation of the project, the normal temperature stress level is 25℃, the extreme temperature stress level is 140℃, the normal relative humidity stress level is 50%, and the extreme relative humidity stress level is 85%. The cost coefficient in the experiment is assumed to be Without losing generality, assume and Between 0 and 0.8, , , , , and Represent the standardized stress values ​​of the 1st, 2nd, and 3rd stress levels of the 1st stress factor, respectively. , and Represent the standardized stress values ​​of the 1st, 2nd, and 3rd stress levels of the 2nd stress factor, respectively. Based on the above assumptions, the optimization design model of the constant stress accelerated degradation test can be expressed as:

[0151]

[0152] Then, using the PSO method, when When , the optimal test scheme of the above-mentioned constant stress accelerated degradation test optimization design model can be obtained as shown in Table 2.

[0153] Table 2 Optimal CSADT solution for automotive LED lights .

[0154] 2. Comparative analysis of different models

[0155] In order to further illustrate the rationality and applicability of the constant stress accelerated degradation test optimization design model constructed by the present invention, a comparative analysis was conducted on various models that consider whether the batch product difference mode and individual difference are taken into account. The model construction, parameter estimation and optimization analysis methods of the present invention can obtain the stress level of different degradation models. The optimization scheme of the constant stress accelerated degradation test under the condition of Figure 2 As shown. Among them, The constant stress accelerated degradation test optimization design model constructed by the present invention comprehensively considers the difference modes between batches of products and individual differences:

[0156] ;

[0157] A degradation model that takes individual differences into account without considering the modal differences between batches of products:

[0158] ;

[0159] The degradation model that takes into account the difference mode between batch products without considering individual differences is:

[0160] ;

[0161] is a degradation model that does not consider the difference modes between batches and individual differences:

[0162] .

[0163] Table 3 Comparison results of optimization schemes for different degradation model tests .

[0164] Through Table 3 and Figure 2 Analysis shows that , , and Asymptotic variance of the maximum likelihood estimate of the mean time between failures for products of four models under normal stress levels They are , , , , explaining the model The experimental scheme is optimal. At the same time, the total experimental costs of the four models after optimization account for 99.9%, 97.2%, 94.9% and 89.8% of the constraint cost (budget) respectively. The cost utilization rate is the highest, indicating that the model Maximizes the use of limited resources. Compared with the model ,Model With model The difference in sample allocation is greater, indicating that the difference between batches mainly affects the sample allocation at each stress level. The stress level value is selected to be closer to the model , indicating that individual differences mainly affect the selection of each stress level value. The above analysis can verify that the constant stress accelerated degradation test optimization design model constructed by the present invention is more effective than the traditional degradation model.

[0165] 3. Comparative analysis of different constraints

[0166] In order to study the influence of different constraints on the CSADT scheme, for the three constraints set by the present invention, an experimental optimization scheme is obtained by fixing two of the three constraints and changing the last constraint.

[0167] Table 4 Comparison results of optimization schemes under different constraint conditions (test time limit , test unit restrictions ) .

[0168] Table 5 Comparison results of optimization schemes under different constraints (experimental budget constraints , test unit restrictions ) .

[0169] Table 6 Comparison results of optimization schemes under different constraints (experimental budget constraints , test unit restrictions ) .

[0170] Through Tables 4-6 and Figure 3-Figure 5 From the analysis, we can see that all three constraints have a significant impact on the results. As the value of one of the constraints increases, the other two remain unchanged, and the change in the test optimization plan becomes smaller and smaller. This result is correct because when the constraint becomes large enough, it will fail. In this case, the test optimization plan is completely determined by the other two constraints. Therefore, the constraints should be reasonably formulated in practical applications. In addition, from Table 4 and Figure 3 It can be seen from Table 5 that when the budget increases, the number of test units allocated to stress level 1, that is, the low stress level, will increase, while the number of test units allocated to stress level 2 will decrease. Among them, when the cost increases from 35,000 to 40,000, the number of test units at stress level 1 decreases, while the number of test units at stress level 2 increases, but the number of test units at stress level 3 does not change significantly. From Table 5 and Figure 4 It can be seen that when the specified test time increases, the number of test units under stress level 1 increases, the number of test units under stress level 2 decreases, and the number of test units under stress level 3 increases when the specified test time is 3000h. The number of test units in the other cases remains almost unchanged. Figure 3 and Figure 4 Analysis shows that when the budget and test time limit increase, the test time will be extended, and a longer test time will lead to a reduction in the number of test units required under high stress levels. Figure 5It can be seen that when the number of available test units increases, the number of test units allocated to each stress level will increase, but when the number of available test units increases to 70, the number of test units under stress level 1 will decrease instead.

[0171] 4. Model parameter sensitivity analysis

[0172] The present invention uses historical test data to obtain model parameter estimates through maximum likelihood estimation, but there may be deviations between the model parameter estimates and the true values, which may affect the accuracy of the test optimization design. Therefore, in order to determine the robustness of the test optimization scheme when the model parameters have deviations, and then verify the effectiveness of the test optimization scheme, parameter sensitivity analysis needs to be carried out. , respectively for the random variables The mean With variance ,random variable The mean With standard deviation , drift coefficient parameters , diffusion coefficient and error coefficient The fluctuation within the deviation range was carried out, and ±10% deviation was added respectively. The results of the sensitivity analysis of the model parameters are shown in Table 6.

[0173] Table 6 Results of model parameter sensitivity analysis .

[0174] It can be seen from Table 6 that the estimated deviation of model parameters will lead to fluctuations in decision variables in the test optimization scheme. The estimated value of has a great influence on the number of test samples; the diffusion coefficient The estimated value of has the most serious impact on the total test time; the fluctuation of the test time interval is mainly affected by the random variable Standard Deviation The estimated value of . Among all parameters, the random variable Mean The asymptotic variance of the estimated mean time between failures of a product under normal working stress is affected by the increase of The biggest impact is on the sample allocation ratio and test time allocation ratio under each stress level, but the changes in the sample allocation ratio and test time allocation ratio under each stress level are not significant. From the perspective of cost constraints, the total cost of each test optimization scheme is The sensitivity analysis of the above model parameters shows that the change of each parameter has little effect on the test optimization scheme, which further verifies that the method of the present invention has good robustness.

[0175] The present invention considers the difference modes and individual differences between batches of products to conduct a multi-stress factor constant accelerated degradation test optimization design study based on the Wiener degradation process, and obtains the following conclusions:

[0176] (1) The present invention establishes a constant accelerated degradation test model under the combination of multiple stress factors. The model performance degradation obeys the Wiener degradation process. At the same time, the influence of the modal difference and individual difference of batch products is considered. Based on the Wiener degradation process, the constant stress accelerated degradation test scheme is optimized and designed; a method based on maximum likelihood estimation of the parameters of the accelerated degradation model and the mean time between failures of the product under normal stress level is constructed to minimize the asymptotic variance of the estimated value of the mean time between failures of the product under normal working stress. As the objective function, multiple decision variables are optimized simultaneously, and the particle swarm optimization algorithm is used to give the optimal test plan.

[0177] (2) Based on the accelerated degradation data of automotive LED lamps under constant stress of temperature and humidity, the present invention uses the constructed constant stress accelerated degradation test optimization design model to optimize the design of the constant stress accelerated degradation test scheme, calculates the optimal test scheme under different constraints, and conducts a comparative analysis of four degradation models that consider whether the modal differences between batches of products and individual differences are considered, verifying the effectiveness of the model.

[0178] (3) In order to examine the stability of the model's influence on the degradation parameters, the experimental optimization scheme with a deviation of ±10% of the model parameters was analyzed. It was found that the decision variables mainly affected by the fluctuations of different model parameters were also different. At the same time, the asymptotic variance of the estimated value of the mean time between failures of the product under normal working stress was It will also change, and in most cases increase. From the analysis results, it can be seen that the moderate deviation of the model parameters has little effect on the model results. Although there is a slight fluctuation, it can be ignored within a certain fluctuation range, indicating that the method of the present invention has good robustness and robustness.

[0179] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity, characterized in that: The following steps are involved: Step S1: using a multi-stress acceleration model and selecting a Wiener degradation process to construct a multi-stress factor constant acceleration degradation test model; Step S2: constructing a constant stress accelerated degradation test optimization design model; Step S201: deriving the product life time distribution using a multi-stress factor constant accelerated degradation test model; Step S202: solving unknown parameters of the multi-stress factor constant acceleration degradation test model; Step S203: based on the unknown parameter estimation values ​​of the multi-stress factor constant accelerated degradation test model and the mean time between failures of the product under normal stress level, combined with the constraint conditions and the optimization goal, solving the constant stress accelerated degradation test optimization design model; Step S3: Using the constant stress accelerated degradation test optimization design model to search for the optimal test plan through the particle swarm optimization algorithm.

2. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 1, characterized in that: The mathematical expression of the multi-stress acceleration model is shown in formula (1): exp (1) in, represents characteristic lifetime; A, B, C and D are all unknown constants; F is activation energy; K is the Boltzmann constant; T is absolute temperature; RH is relative humidity.

3. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 1, characterized in that: The mathematical expression of the multi-stress factor constant accelerated degradation test model is: (3) in, represents the drift coefficient; represents the diffusion coefficient; α and β are both random variables that obey the normal distribution, representing individual differences in the degradation process; , , , , All are unknown coefficients, obtained through parameter estimation; represents the standardized stress value of the e-th stress factor at the k-th stress level; represents the standardized stress value of the uth stress factor at the kth stress level; represents the standardized stress value of the vth stress factor at the kth stress level; z represents a random variable describing the mode of product difference between batches; Represents a random variable The mean of Represents a random variable The mean of represents variance; represents the standard deviation; E represents the number of stress factors.

4. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 1, characterized in that: In step S201, the product life G is defined as the time when the performance degradation of the product under normal stress level reaches the failure threshold for the first time. Time: (4) Where t represents the total test time, It represents the standardized stress value of E different stress factors under normal stress level, It indicates the degradation amount of the product under the influence of the standardized stress value of E different stress factors at the normal stress level; The product life G obeys the inverse Gaussian distribution, and its probability density function is: (5) in, and represent the variance and mean of the product degradation amount of the standardized stress value under normal stress level respectively; The average failure interval time of the product under normal stress level is obtained from formula (4): (6) in, Represents a random variable The mean of , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor under normal stress level, represents the standardized stress value of the uth stress factor under normal stress level, represents the standardized stress value of the vth stress factor under normal stress level, E represents the number of stress factors, Represents the variance that describes the differences in products between batches.

5. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 4, characterized in that: The variance The mathematical expression is: ； in, Represents a random variable The variance of represents the variance describing the differences between batches of products, Represents a random variable The variance of Represents a random variable The mean of Represents a random variable The mean of represents the error coefficient, , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor under normal stress level, represents the standardized stress value of the uth stress factor under normal stress level, represents the standardized stress value of the vth stress factor under normal stress level, and E represents the number of stress factors.

6. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 4, characterized in that: The mean The mathematical expression is: ； in, Represents a random variable The mean of , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor under normal stress level, represents the standardized stress value of the uth stress factor under normal stress level, represents the standardized stress value of the vth stress factor under normal stress level, and E represents the number of stress factors.

7. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 1, characterized in that: In step S202, the following assumptions are first established: 1) Assume that there are l stress levels in the multi-stress factor constant accelerated degradation test, and the stress values ​​of each stress level satisfy ; 2) The test units are provided in Q batches, and the number of units provided in each batch is , ; The test unit allocation ratio of different batches at the kth stress level is , ; 3) The test time allocation ratio under the kth stress level is , the measurement interval at each stress level remains unchanged, and the number of measurements is the same for all test units; therefore, the measurement interval at each stress level is The total number of measurements is ; represents the number of measurements at the kth stress level, represents the test time under the kth stress level; 4) For , , , Indicated in is the jth observation value of the ith test unit under the kth stress level; Assuming that N test units are subjected to multi-stress factor constant accelerated degradation tests under the above assumptions, the performance degradation increment is The probability density function of is: (7) The performance degradation increment The log-likelihood function of is: (8) in, and They represent the variance and mean of the product degradation of the standardized stress value at the kth stress level, respectively, and θ represents the unknown parameters of the model; Take the log-likelihood function for the random variable The mean The first partial derivative of : (9) in, represents the product of the total sample size and the total test time, Indicates that there are no random variables Drift coefficient , represents the increment of product degradation under the kth stress level, It represents the variance describing the differences between batches of products; ； in, , ,…, represents the sample size provided by each Q batch, , ,…, represents the sample allocation ratio of Q batches at the kth stress level, represents the test time allocation ratio under the kth stress level, , , are all undetermined coefficients, represents the standardized stress value of the e-th stress factor at the k-th stress level, represents the standardized stress value of the uth stress factor at the kth stress level, represents the standardized stress value of the vth stress factor at the kth stress level, and E represents the number of stress factors; Let (9) be 0 to get the unknown parameters The maximum likelihood estimate of is substituted into formula (9) to obtain the profile likelihood function of other unknown parameters; the maximum likelihood estimate of the remaining unknown parameters is obtained by maximizing the profile likelihood function through multidimensional search, and the maximum likelihood estimate of the mean time between failures of the product under normal stress level is obtained as follows: (10) in, Represents a random variable The estimated value of the mean.

8. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 1, characterized in that: In step S203, the constraint condition is: 1) The total test time t should not exceed the specified test time ; 2) The number of test units provided in different batches should not exceed the number of available test units ; 3) The total cost of the experiment TC should not exceed the pre-set budget ; Among them, the mathematical expression of the total test cost TC is: (12) in, , ,…, represents the sample size provided by each Q batch, represents the unit cost of each test unit, represents the unit operating cost of the test equipment, represents the cost of making a single observation of the experiment, represents the test time allocation ratio under the kth stress level, Indicates the measurement interval time at each stress level; Then the mathematical expression of the constant stress accelerated degradation test optimization design model is: (13) in, represents the asymptotic variance of the maximum likelihood estimate of the mean time between failures of the product under normal stress level, represents the asymptotic variance of the maximum likelihood estimate of the mean time between failures of the product under normal stress level, represents the decision variable, , ,…, Respectively represent the 1st, 2nd, ..., The test time allocation ratio under each stress level.

9. The method for designing a constant accelerated degradation test for batch-to-batch product differences and individual heterogeneity according to claim 8, characterized in that: The asymptotic variance of the maximum likelihood estimate of the mean time between failures for the product under normal stress level The mathematical expression is: (11) Where Avar represents the asymptotic variance; represents the decision variable, ; represents the Fisher information matrix; It represents the maximum likelihood estimate of the mean time between failures of the product under normal stress level. A column vector consisting of the first-order partial derivatives of the unknown parameters of the model; Represents unknown parameters of the model An estimated value of express The transpose of : .

Images