A method and device for identifying consistency of failure mechanism of nonlinear accelerated degradation test

Abstract

The application discloses a nonlinear accelerated degradation test failure mechanism consistency discrimination method, which comprises the following steps: obtaining a test piece of a to-be-tested degradation amount, and measuring the degradation amount of the test piece at equal time intervals; calculating parameter estimation values of the test piece at each time according to the measurement data; establishing a distribution model for the parameter estimation values at each time; calculating parameter values in the distribution model and calculating a degradation amount distribution density function according to a total probability formula; calculating the probability P that the test piece degrades to a target degradation level according to the distribution density function; calculating the time that the test piece degrades to the target level with the probability P, and obtaining a failure mechanism consistency discrimination condition according to the definition of an acceleration coefficient; and judging whether the failure mechanism is consistent or not through T test. The application provides a failure mechanism consistency discrimination method based on the principle of constant acceleration coefficient, and the method can also be applied to degradation data measured by destructive and non-destructive methods.

Description

Technical Field

[0001] This invention relates to a method and apparatus for determining the consistency of failure mechanisms in nonlinear accelerated degradation tests, belonging to the field of reliability test design technology. Background Technology

[0002] The increasing lifespan of products makes degradation testing a crucial source of information for product reliability assessment. Degradation is more likely to occur under high stress; therefore, accelerated degradation testing is commonly used to quickly obtain product degradation data. Effective accelerated degradation testing should ensure that the product exhibits the same failure mechanism under all accelerated stresses; otherwise, the degradation information under normal stress cannot be correctly extrapolated. In verifying the consistency of failure mechanisms in accelerated degradation testing, basic principles such as consistent degradation trajectories, constant acceleration coefficients, and constant activation energy are commonly used. Appropriate testing methods are often selected based on the degradation model, acceleration method, and acceleration model itself, such as parameter consistency testing methods based on the degradation model and data-based degradation trajectory consistency testing methods. However, for nonlinear accelerated degradation, the degradation trajectory is more complex, making degradation trajectory consistency testing methods unsuitable. Existing methods often assume that under the same stress, the degradation amount follows a fixed-effect degradation model, such as the Gamma process, Wiener process, or inverse Gaussian process, and use the principle of constant acceleration coefficients to verify the consistency of failure mechanisms. In engineering, data is often more random, and the degradation model of fixed effects cannot fully simulate the distribution of experimental data. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and device for judging the consistency of failure mechanism in nonlinear accelerated degradation test. It takes into account the nonlinearity of the degradation process and the random effect of degradation amount distribution parameters, establishes a degradation amount distribution model, and on this basis, based on the principle of constant acceleration coefficient, considers the parameters and statistics that affect the consistency of failure mechanism in the degradation amount distribution model under different stresses, and gives a method for judging the consistency of failure mechanism.

[0004] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0005] In a first aspect, the present invention provides a method for determining the consistency of failure mechanisms in nonlinear accelerated degradation tests, comprising:

[0006] Obtain a specimen with the amount of degradation to be measured, and measure the amount of degradation of the specimen at equal time intervals;

[0007] The estimated values ​​of the specimen parameters at each time point were calculated based on the measurement data;

[0008] Establish a distribution model for the parameter estimates at each time point;

[0009] Calculate the parameter values ​​in the distribution model and use the law of total probability to calculate the distribution density function of degradation.

[0010] Based on the distribution density function, calculate the probability P that the specimen degrades to the target degradation level;

[0011] Calculate the time it takes for the specimen to degrade to the target level with probability P, and obtain the consistency judgment condition of the failure mechanism based on the definition of the acceleration factor;

[0012] The T-test is used to determine whether the failure mechanisms are consistent.

[0013] Furthermore, the step of obtaining the specimen with the measured degradation amount and measuring the degradation amount of the specimen at equal time intervals includes:

[0014] Under stress S l , time t j The degradation amount was measured for n specimens, and the resulting sample data were recorded as follows:

[0015] x ijl ,i=1,2,…,n,j=1,2,…,m,l=1,2,…,s

[0016] Where n represents the number of specimens, m represents the number of measurements, s represents the total stress, and x ijl This represents the recorded degradation data; i represents the stress label; l represents the time label.

[0017] Furthermore, the step of calculating the parameter estimates of the specimen at each moment based on the measurement data includes:

[0018] Based on the measurement data, the parameter estimates for each time step of the sample are calculated using maximum likelihood estimation:

[0019]

[0020] Furthermore, establishing a distribution model for the parameter estimates at each time point includes:

[0021] Establish a distribution model for the parameter estimates at each time point. Assume that under the same stress, given time t, μ tl It follows a normal distribution, and the mean of the distribution exhibits a non-linear property over time. The variance of the distribution is related to the degradation factor X. tl The variances are the same, but At a given time, it follows a Gamma distribution, i.e. ν tl ~Gamma(α) l t -1 ,β l ),in

[0022] Further, the parameter values ​​in the distribution model are calculated, and the degradation distribution density function is calculated using the law of total probability, including:

[0023] Obtain the parameter values ​​in the distribution model, and obtain the maximum likelihood estimate of the parameters using numerical methods, denoted as . Calculate the degradation amount X at time t using the law of total probability. tl Distribution density function:

[0024]

[0025] Where d represents the differential symbol; Γ represents the Gamma function;

[0026] For x tl Perform variable substitution

[0027]

[0028] Get y tl Distribution density function:

[0029]

[0030] From this density function, we can know that y tl ~T(γ) l ), which follows a T-distribution.

[0031] Furthermore, based on the distribution density function, the probability P of the specimen degrading to the target degradation level is calculated, including:

[0032] If the target degradation level is set to D, then the probability that the product degradation at time t will not exceed this target degradation level is:

[0033]

[0034] Furthermore, the time it takes for the specimen to degrade to the target level with probability P is calculated, and the consistency criteria for the failure mechanism are obtained based on the definition of the acceleration factor, including:

[0035] Calculate the stress S respectively l The time it takes for the product with the same probability P under S0 to degenerate to this target level is denoted as t. l,P With t 0,P The formula is as follows:

[0036]

[0037] According to the acceleration coefficient K l0 The definition, and its principle that it does not change with probability P, are calculated as follows:

[0038]

[0039] in, The conditions for eventual consistency can be obtained as follows:

[0040]

[0041] Right now It should be a constant value to ensure that the failure mechanism is consistent.

[0042] Furthermore, the step of determining whether the failure mechanisms are consistent through the T-test includes:

[0043] To each Perform a T-test, where... When performing the T-test, the question is whether the failure mechanism remains consistent under the new stress l1, i.e., to determine... l1≥3 and To determine whether there is a significant difference in the mean, the following steps are taken:

[0044] a) Calculate the judgment statistic T l for:

[0045]

[0046] in They are respectively The sample mean and sample standard deviation,

[0047]

[0048] b) Given a confidence level α, find T from the T-distribution quantile table. α / 2 (l1-1);

[0049] c) Comparison T α / 2 (l1-1), if If the failure mechanism is not consistent under stress l1, then it is considered that the failure mechanism is consistent; otherwise, it is considered that the failure mechanism is consistent.

[0050] In a second aspect, the present invention provides a device for determining the consistency of failure mechanisms in nonlinear accelerated degradation tests, including a processor and a storage medium;

[0051] The storage medium is used to store instructions;

[0052] The processor is configured to operate according to the instructions to perform the steps of the method according to any of the preceding claims.

[0053] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the preceding methods.

[0054] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0055] This invention considers the nonlinearity of the degradation process under the same stress and the random effect of the degradation amount distribution parameters, and establishes a degradation amount distribution model. Without determining the failure threshold, it can derive the parameters and statistics affecting the consistency of failure mechanism in the degradation amount distribution model under different stresses based on the principle of constant acceleration coefficient. With reasonable assumptions, the discrimination conditions are simplified, and the failure mechanism consistency discrimination method is shown to be applicable to degradation data obtained by destructive measurement through T test. Moreover, this method is applicable to degradation data obtained by both destructive and non-destructive measurement. Attached Figure Description

[0056] Figure 1 This is a flowchart of a nonlinear accelerated degradation test failure mechanism consistency judgment method provided by an embodiment of the present invention. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0058] Example 1

[0059] This embodiment introduces a method for consistent determination of failure mechanisms in nonlinear accelerated degradation tests, including:

[0060] Obtain a specimen with the amount of degradation to be measured, and measure the amount of degradation of the specimen at equal time intervals;

[0061] The estimated values ​​of the specimen parameters at each time point were calculated based on the measurement data;

[0062] Establish a distribution model for the parameter estimates at each time point;

[0063] Calculate the parameter values ​​in the distribution model and use the law of total probability to calculate the distribution density function of degradation.

[0064] Based on the distribution density function, calculate the probability P that the specimen degrades to the target degradation level;

[0065] Calculate the time it takes for the specimen to degrade to the target level with probability P, and obtain the consistency judgment condition of the failure mechanism based on the definition of the acceleration factor;

[0066] The T-test is used to determine whether the failure mechanisms are consistent.

[0067] like Figure 1 As shown in this embodiment, the method for consistent determination of failure mechanisms in nonlinear accelerated degradation tests involves the following steps in its application:

[0068] Step 1: Under stress S l , time t jThe degradation amount of n products was measured separately, and the resulting sample data was recorded as follows:

[0069] x ijl ,i=1,2,…,n,j=1,2,…,m,l=1,2,…,s;

[0070] Where n represents the number of specimens, m represents the number of measurements, s represents the total stress, and x ijl This represents the recorded degradation data; i represents the stress label; l represents the time label.

[0071] Step 2: Based on the above data, the estimated values ​​of the parameters of the sample at each time step can be obtained by maximum likelihood estimation:

[0072]

[0073] Step 3: Establish a distribution model for the parameter estimates at each time point. Assume that under the same stress, given time t, μ tl It follows a normal distribution, and the mean of the distribution exhibits a non-linear property over time. The variance of the distribution is related to the degradation factor X. tl The variances are the same, but At a given time, it follows a Gamma distribution, that is... ν tl ~Gamma(α) l t -1 ,β l ),in

[0074] Step 4: Combining steps 2 and 3, obtain the maximum likelihood estimate of the parameters using numerical methods, denoted as... Calculate the degradation amount X at time t using the law of total probability. tl Distribution density function:

[0075]

[0076] Where d represents the differential symbol; Γ represents the Gamma function;

[0077] Step 5: For x tl Perform variable substitution

[0078]

[0079] Get y tl Distribution density function:

[0080]

[0081] From this density function, we can know that y tl ~T(γ) l ), which is a T-distribution

[0082] Step 6: If the target degradation level is limited to D, then the probability that the product degradation at time t does not exceed the target degradation level is:

[0083]

[0084] Step 7: Calculate the stress S respectively. l The time it takes for the product with the same probability P under S0 to degenerate to this target level is denoted as t. l,P With t 0,P

[0085]

[0086] Step 8: Based on the acceleration coefficient K l0 The definition, and its principle that it does not change with probability P, are calculated as follows:

[0087]

[0088] Step 9: Since accelerated degradation tests are usually conducted on new products, the variance of degradation, which represents the degree of fluctuation in degradation, usually decreases gradually until it tends to stabilize. Therefore, the Gamma distribution should exhibit a right-skewed state with a small kurtosis, i.e., the shape parameter α... l t -1 It should be relatively large, at which point 2α l t -1 The T-distribution of degrees of freedom shows small differences among quantiles, therefore The conditions for eventual consistency can be obtained.

[0089]

[0090] Right now It should be a constant value to ensure that the failure mechanism is consistent.

[0091] Step 10: Considering the randomness of the data, the results obtained under different stresses They should not be completely equal; considering their purely random fluctuations with normality, a T-test is performed on each separately to... For example, whether the failure mechanism remains consistent under the new stress l1, i.e., judging... l1≥3 and To determine whether there is a significant difference in the mean, the following steps are taken.

[0092] a) Calculate the judgment statistic T l for

[0093]

[0094] in They are respectively The sample mean and sample standard deviation,

[0095]

[0096] b) Given a confidence level α, find T from the T-distribution quantile table. α / 2 (l1-1)

[0097] c) Comparison T α / 2 (l1-1), if If the failure mechanism is not consistent under stress l1, then it is considered that the failure mechanism is consistent; otherwise, it is considered that the failure mechanism is consistent.

[0098] Compared with the prior art, the present invention has the following advantages:

[0099] (1) It can be applied to degraded data obtained by destructive measurements.

[0100] (2) No failure threshold needs to be determined; only the target degradation level needs to be given, making the application conditions relatively lenient.

[0101] (3) Applicable to nonlinear degradation processes.

[0102] (4) Through theoretical derivation, it is possible to objectively provide the criteria for evaluating the consistency of failure mechanisms.

[0103] (5) The complex model has been simplified and simple discrimination conditions have been given.

[0104] Example 2

[0105] This embodiment provides a device for determining the consistency of failure mechanisms in nonlinear accelerated degradation tests, including a processor and a storage medium;

[0106] The storage medium is used to store instructions;

[0107] The processor is configured to operate according to the instructions to perform the steps of the method according to any one of Embodiment 1.

[0108] Example 3

[0109] This embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the methods described in Embodiment 1.

[0110] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for consistent determination of failure mechanisms in nonlinear accelerated degradation tests, characterized in that, include: Obtain a specimen to be tested for degradation, and measure the degradation of the specimen at equal time intervals, including: Under stress ,time Below The degradation amount of each specimen was measured, and the obtained degradation amount sample data were recorded as follows: in, Indicates the number of test specimens. Indicates the number of measurements. Indicates the total stress. This represents the amount of degradation data recorded. Indicates stress label; Indicates a time label; The estimated parameter values ​​of the specimen at each time point are calculated based on the measurement data, including: Based on the measurement data, the parameter estimates for each time step of the sample are calculated using maximum likelihood estimation: in, This is an estimate of the parameter of the sample distribution mean. This is an estimate of the variance parameter of the sample distribution; Establish distribution models for the parameter estimates at each time point, including: Establish a distribution model for the parameter estimates at each time point, assuming the same stress, at a given time... , It follows a normal distribution, but the mean of the distribution exhibits a non-linear property over time. The variance of the distribution is related to the degradation. The variances are the same, but At a given time, it follows a Gamma distribution, that is... , ,in , The mean parameter of the sample distribution. It is the reciprocal of the sample distribution variance parameter. for The mean parameter of the distribution, It is a constant. for The distribution parameters; Calculating the parameter values ​​in the distribution model and calculating the degradation probability density function using the law of total probability includes: Obtain the parameter values ​​in the distribution model, and obtain the maximum likelihood estimate of the parameters using numerical methods, denoted as . , , , The degradation at time t is calculated using the law of total probability. Distribution density function: in, Represents the differential symbol; Represents the Gamma function; right Perform variable substitution get Distribution density function: From this density function, we can know It follows a T-distribution; Based on the distribution density function, the probability P of the specimen degrading to the target degradation level is calculated, including: Limit the target degradation level to Then the product time The probability that the degradation does not exceed the target degradation level is ； Calculate the time it takes for the specimen to degrade to the target level with probability P, and obtain the consistency criteria for the failure mechanism based on the definition of the acceleration factor; including: Calculate the stress respectively. , The time it takes for the same probability P of the product to degenerate to this target level is denoted as . and The formula is as follows: According to the acceleration coefficient The definition, and its principle that it does not change with probability P, are calculated as follows: in, Thus, the conditions for eventual consistency can be obtained: Right now , It should be a constant value to ensure that the failure mechanism is consistent; The T-test is used to determine whether the failure mechanisms are consistent, including: To each , Perform a T-test, where... When performing the T-test, the new stress Whether the failure mechanism still has a consistent failure mechanism, i.e., to determine , and To determine whether there is a significant difference in the mean, the following steps are taken: a) Calculate the judgment statistic for: in , They are respectively The sample mean and sample standard deviation, ， ； b) Given a confidence level From the T-distribution quantile table, we can obtain... ; c) Comparison , ,like Then the stress is considered to be The failure mechanism is not consistent; otherwise, the failure mechanism is considered to be consistent.

2. A device for determining the consistency of failure mechanisms in nonlinear accelerated degradation tests, characterized in that: Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to claim 1.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the steps of the method of claim 1.

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