A method for evaluating the reliability of prior data for a product.

Abstract

This invention relates to the field of reliability engineering technology, specifically to a method for evaluating the credibility of prior data for a product, comprising the following steps: S1, parameter identification: identifying parameters unrelated to stress and parameters related to stress in the degradation model; S2, consistency relationship construction: constructing the parameter relationship required for consistency of failure mechanisms; S3, consistency judgment: quantifying the deviation between parameter values ​​and reference stress levels; S4, parameter consistency assessment: assessing the degree of consistency between parameter sets under accelerated stress and parameter sets under normal stress, and calculating the credibility of data under corresponding stress levels based on the degree of consistency; S5, credibility evaluation: weighting the importance of data under different stress levels to obtain a comprehensive credibility. This invention quantifies the credibility of prior data and combines it with a hazard coefficient to achieve a weighted calculation of comprehensive credibility, improving the effectiveness and accuracy of accelerated degradation data in reliability modeling.

Description

Technical Field

[0001] This invention relates to the field of reliability engineering technology, and in particular to a method for evaluating the reliability of prior data of a product. Background Technology

[0002] With the rapid development of modern industrial technology, the application demand for high-reliability, long-life products such as aerospace devices, new energy vehicle batteries, and semiconductor chips continues to grow. Traditional natural degradation experiments, due to their long cycle, high cost, and inability to fully simulate the multi-stress coupling effects under actual complex working conditions, can no longer meet the reliability verification needs of these products in rapid iteration and high-intensity usage scenarios. Therefore, accelerated degradation experiments, as an effective means, significantly accelerate the performance degradation process of products by applying controllable stresses such as high temperature and high voltage. They can obtain equivalent long-term degradation data in a shorter time, thereby greatly reducing testing time and cost, and have become an important tool to support the rapid verification and development of high-reliability products.

[0003] In practical reliability modeling, to overcome the scarcity of field degradation data, Bayes' theorem is often used to fuse accelerated degradation experimental data with field operation data to improve model accuracy. However, existing methods have significant drawbacks when processing prior data: the failure mechanism of a product may change with the level of accelerated stress, leading to a mismatch between the obtained prior data and the actual operating conditions, thus affecting the accuracy of subsequent models. When the applied accelerated stress deviates from a reasonable range, the product may trigger a non-original failure mechanism during the experiment, causing the obtained degradation data to no longer be representative. Therefore, the credibility of prior data will be significantly reduced, and it may even mislead the model training results. Summary of the Invention

[0004] This invention provides a method for evaluating the credibility of prior data of a product. It can determine whether degradation data under different stress conditions have the same failure mechanism as those under normal use conditions, and evaluate its credibility by combining mathematical statistics tools. This improves the effectiveness of prior information in the Bayesian modeling process and ensures the accuracy and applicability of the established life model under multi-stress environments.

[0005] A method for evaluating the reliability of prior data for a product includes the following steps:

[0006] S1, Parameter Identification: Based on the theory of constant acceleration factor, identify parameters that are independent of stress and parameters that are related to stress in the product degradation model;

[0007] S2, Consistency Relationship Construction: Constructing the parametric relationships that must be satisfied to ensure consistency in failure mechanisms;

[0008] S3, Consistency Judgment: Based on the established consistency relationship, the consistency analysis of parameter values ​​under different accelerated stresses is performed to quantify the deviation between them and the parameter values ​​under the reference stress level;

[0009] S4, Parameter Consistency Assessment: Based on the consistency discrimination results, assess the degree of consistency between the parameter set under each accelerated stress and the parameter set under normal stress, and calculate the reliability of the data under the corresponding stress level based on the degree of consistency.

[0010] S5, Credibility Evaluation: Based on the credibility under each stress, the importance of the data under different stress levels is weighted by combining the hazard factor to obtain the comprehensive credibility of the degradation data under all accelerated stress conditions.

[0011] Optionally, the parameter identification in S1 includes:

[0012] S11, Define performance aging amount and change amount: Let the performance aging amount of the product at time t be... The initial conditions are met. The performance aging amount is defined as:

[0013] ;

[0014] S12, Construct a Gamma distribution model for the change: Assume that the performance aging amount follows a gamma distribution, expressed as:

[0015] ;

[0016] in, For shape parameters, For scale parameters, It is a function of time t;

[0017] S13, Deriving the probability distribution function of aging amount: Based on the additivity of the Gamma distribution, the performance aging amount satisfies the distribution... ,but The probability density function is expressed as:

[0018] ;

[0019] S14, Deriving the reliability function: Suppose the product fails when the performance aging reaches a threshold D, then the reliability function is expressed as:

[0020] ;

[0021] in, For gamma function, ;

[0022] S15, Introducing the derivation of variable transformation: ... Substituting into the reliability function, we obtain the closed-form expression of the reliability function, which is expressed as:

[0023] ;

[0024] S16, Constructing the acceleration factor and identifying stress-related and stress-independent parameters: By constructing the relationship between the cumulative distribution functions of products under different stress levels, the acceleration factor is defined, and the correlation between shape parameters, scale parameters and stress is derived, identifying stress-independent and stress-related parameters.

[0025] Optionally, the construction acceleration factor and identification of stress-related and irrelevant parameters in S16 include:

[0026] S161, Define the distribution function and acceleration factor: Let... , For any two stress levels of the product , The cumulative distribution function under the given conditions, then the acceleration factor Represented as ;

[0027] S162, Establish the relationship between distribution functions: Based on the consistency of distribution functions, derive their equivalent expression relationship under the action of the acceleration factor, expressed as:

[0028] ;

[0029] in, , These are stresses , The shape parameters below;

[0030] S163, Constructing the parameter identity condition: Based on the principle of invariant acceleration factor, derive the equivalent expression relation for any... The parametric identity condition that holds is expressed as:

[0031] ;

[0032] S164, Identify stress-dependent and undependent parameters: Based on the constructed parametric identities, identify stress-dependent and undependent parameters, where shape parameters are related to accelerated stress and scale parameters are unrelated to accelerated stress.

[0033] Optionally, the consistency relationship in S2 is constructed by selecting a parametric relationship that satisfies the consistency of the failure mechanism for the parameters to be tested, and based on the fact that the scale parameter remains unchanged under different stress levels, a parametric identity relationship is constructed, expressed as:

[0034] .

[0035] Optionally, the consistency judgment in S3 is based on the statistics of the likelihood ratio test or Wald test to test the difference between the parameter values ​​under different stress levels and the parameter estimates under the benchmark level. If the scale parameters satisfy the constructed consistency relationship, the failure mechanism is considered to be consistent and the data is reliable.

[0036] Optionally, the parameter consistency assessment in S4 includes:

[0037] S41, Construct a parameter distribution model under reference stress: Collect scale parameters from n samples under normal stress level, denoted as... ,by Based on this, a distribution model of the scale parameters is constructed, and the lower confidence level is set as x% quantile and the upper confidence level is (1-x)% quantile, forming the corresponding confidence interval;

[0038] S42, Statistical analysis of sample inclusion rates under other stress levels: Calculate the proportion of samples falling into the target range under different stresses. n at the level Parameter value, denoted as If the number of samples falling within the reference confidence interval is m, then the stress level The parameter value and the sample falling ratio under normal stress are as follows: ;

[0039] S43, Calculation of parameter consistency: Calculate the data reliability at this stress level based on the fall rate. for .

[0040] Optionally, the credibility evaluation in S5 includes:

[0041] S51, Definition of Hazard Factor: Relating the normal stress level to each accelerated stress level. The ratio is defined as the hazard coefficient. ;

[0042] S52, Weighted calculation of overall credibility: The credibility of the data at each stress level is weighted with the hazard coefficient to calculate the overall credibility of the degradation data at all stress levels.

[0043] Optionally, the hazard factor is expressed as:

[0044] .

[0045] Optionally, the overall credibility is expressed as:

[0046] .

[0047] The beneficial effects of this invention are:

[0048] This invention constructs a parameter identification method for product degradation models based on the principle of invariant acceleration factor, and combines it with a gamma process modeling framework. This method can effectively distinguish between stress-independent and stress-dependent parameters in product degradation models, thereby clarifying whether prior data has a consistent basis for failure mechanism. This method not only improves the applicability of degradation modeling in multi-stress environments, but also enhances the physical interpretability of accelerated degradation experimental data and reduces the risk of misjudgment under human interference.

[0049] This invention quantifies the credibility of prior data under different stress levels by constructing a consistency discrimination mechanism and a confidence interval evaluation method. Furthermore, it combines the design of hazard coefficients to achieve a comprehensive credibility weighted calculation. This method can optimize and adjust the weights of accelerated degradation data in Bayesian modeling without relying on subjective experience. This method improves the robustness of model inference and ensures the representativeness and reliability of the fused prior information in actual life prediction. It is suitable for the rapid verification and engineering deployment of high-reliability products. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a schematic diagram of the evaluation method flow according to an embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram showing the variation of the operating current of a GaAs laser under ten different accelerating stresses according to an embodiment of the present invention.

[0053] Figure 3 This is a schematic diagram illustrating the principle of determining the degree to which parameter values ​​under different accelerated stresses and parameter values ​​under normal stresses satisfy the equation in an embodiment of the present invention.

[0054] Figure 4 This is a schematic diagram of the accelerated degradation data of carbon film resistors under accelerated stress of 83°C according to an embodiment of the present invention.

[0055] Figure 5 This is a schematic diagram of the accelerated degradation data of carbon film resistors under accelerated stress of 133°C according to an embodiment of the present invention.

[0056] Figure 6 This is a schematic diagram of the accelerated degradation data of carbon film resistors under accelerated stress of 173°C according to an embodiment of the present invention.

[0057] Figure 7 Parameters under normal stress in embodiments of the present invention Schematic diagram of the optimally fitted normal distribution;

[0058] Figure 8 Parameters under normal stress in embodiments of the present invention A schematic diagram of the optimally fitted log-normal distribution;

[0059] Figure 9 Parameters under normal stress in embodiments of the present invention Schematic diagram of the optimal fit exponential distribution;

[0060] Figure 10 Parameters under normal stress in embodiments of the present invention A schematic diagram of the optimally fitted logistic distribution;

[0061] Figure 11 Parameters under normal stress in embodiments of the present invention Schematic diagram of the optimally fitted Logistic distribution;

[0062] Figure 12 This is a schematic diagram illustrating the calculation of the reliability of accelerated stress at 133℃ in an embodiment of the present invention;

[0063] Figure 13 This is a schematic diagram illustrating the calculation of the reliability of accelerated stress at 173°C in an embodiment of the present invention. Detailed Implementation

[0064] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Those skilled in the art may employ other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0065] like Figures 1-13 As shown, a method for evaluating the reliability of prior data for a product includes the following steps:

[0066] 1. Select performance parameters that characterize product degradation. The selection of performance parameters to characterize product degradation should adhere to three main principles: correlation with failure mechanisms, significant parameter changes, and measurability of data. Taking GaAs lasers as an example, their degradation essentially stems from the proliferation of dark line defects in the active region, leading to a decrease in carrier injection efficiency. This process is directly manifested in the continuous increase in the operating current required to maintain constant optical power output. Figure 2 );

[0067] 2. Select an appropriate stochastic process model to model the degradation data. The Wiener process is suitable for quasi-monotonic degradation scenarios with random fluctuations (allowing for positive and negative changes in instantaneous degradation amount) (such as mechanical vibration amplitude drift), while the inverse Gaussian process is used for scenarios with non-negative accumulation and degradation rate dynamically controlled by covariates (such as weld joint damage propagation under thermal cycling stress). The gamma process is suitable for modeling degradation data with monotonically increasing characteristics and non-negative increments, and is especially suitable for describing irreversible cumulative degradation processes. This invention patent uses the gamma process as an example for detailed explanation.

[0068] 3. Based on the theory of constant acceleration factor, parameters independent of stress and parameters related to stress in the product degradation model are identified. Assume the performance aging of the product at time t is... And there are , Let be the change in performance aging. It is assumed that the change follows a gamma distribution, i.e.:

[0069] ;

[0070] In the formula, For shape parameters, For scale parameters, For time t The function.

[0071] Based on the additivity of the Gamma distribution, by The distribution can be obtained as follows:

[0072] , The probability density function is:

[0073] ;

[0074] Assuming the product performance degradation reaches D If failure occurs at any time, the reliability function can be derived from the following:

[0075] ;

[0076] in, For gamma function, ;

[0077] Will Substituting into the reliability function, we get:

[0078] ;

[0079] make ,set up First arrival D The time is the product's lifespan. ,but The distribution function is:

[0080] ;

[0081] set up , For any two stress levels of the product , The cumulative distribution function under the stress level, we take the stress level , The ratio of the time required for products to age to the same degree is set as... relatively acceleration factor The principle of constant acceleration factor means that, Should be for a non-follower , Change, only by , The constant determined by this is defined as:

[0082] ;

[0083] Easy to obtain ,Will Substituting the distribution function, we get:

[0084] ;

[0085] in, , These are stresses , The shape parameters below;

[0086] By the principle that the acceleration factor remains constant, the above equation needs to be applied to any... For an application to be valid, the following conditions must be met:

[0087] ;

[0088] Therefore, the shape parameter of the Gamma process is related to the accelerating stress, while the scale parameter is independent of the accelerating stress.

[0089] 4. Establish a method for judging whether parameter values ​​satisfy the consistency of failure mechanism relationships. The selection of the relationship between the tested parameters should follow the principle of both reflecting changes in the failure mechanism and facilitating the construction of test statistics. From the formula satisfied in point 3, it can be seen that... It can be conveniently used to determine whether the acceleration factor changes under different stress levels, that is, whether the failure mechanism changes; under the same stress level, different These values ​​facilitate the construction of statistics based on likelihood ratio tests or Wald tests. By comparing the differences in parameter estimates between different stress levels and the baseline level, the reliability of data under different stresses can also be quantified. Therefore, the parameters... The parameter test formula for determining whether the failure mechanism of the gamma process has changed, based on the principle of the tested parameter, is as follows: .

[0090] 5. Determine the degree to which the parameter values ​​under different accelerated stresses satisfy the equation with those under normal stress. Use the data collected under normal stress. n Data from one sample were used to obtain data under normal stress. n indivual Parameters, denoted as The goodness-of-fit test method was used to determine this. n indivual The optimal distribution type of the parameters is determined by constructing a qualified interval based on the distribution function, with the lower limit of the interval being... x % quantile, upper limit is (1- x % quantiles. Calculate different stresses. horizontal n indivual Parameter value, denoted as Statistical analysis of stress levels The proportion of parameter values ​​falling within the acceptable range, for example, at stress levels. Below m If the parameter values ​​fall within the acceptable range, then the stress level The degree to which the parameter values ​​under the lower stress and under normal stress satisfy the equation is: Then the stress level Reliability of degraded data for .

[0091] 6. Design of the hazard factor and calculation of the overall reliability. Based on engineering knowledge, the further the accelerated stress level deviates from the normal stress level, the higher the probability of inconsistency in the failure mechanism. Therefore, the hazard factor is designed... To adjust under different stress levels The ratio of the normal stress level to each accelerated stress level is defined as the hazard factor. The calculation method is as follows:

[0092] ;

[0093] The overall reliability of the degradation data obtained from all accelerated stresses is:

[0094] .

[0095] Case Analysis:

[0096] The following will provide a case analysis of this invention. This case is merely to aid in understanding the invention and should not be construed as limiting its scope of application. It should be noted that any modifications and improvements made to the invention without actually departing from its concept are within the protection scope of this invention.

[0097] The case study uses experimental data on a certain type of carbon film resistor provided by Meeker et al. in CSADT. Temperature was used as the accelerated stress in the experiment, with three sets of accelerated stress data at levels of 83℃, 133℃, and 173℃. The data at 83℃ was assumed to be obtained under normal stress. Measurements were taken at 452h, 1030h, 4341h, and 8084h for each set. The measurement index was the percentage increase in the carbon film resistance value. When the percentage increase in resistance value reached 5%, the product experienced degradation failure. Figure 3 The trajectory of carbon film resistivity changes for all samples under each group of accelerated stress is presented. The performance degradation data for each sample are fitted using the Gamma degradation model, and the parameter estimates for the product degradation model are shown in Table 1.

[0098]

[0099]

[0100] Between different accelerating stresses The value changed significantly, while The value did not change significantly, which confirms the parameter Parameters related to accelerating stress The conclusion is unrelated to accelerating stress.

[0101] The optimal fit test method was used to determine the temperature at 83℃. The optimal distribution type for the parameters is determined by fitting the data at 83℃ using the normal, exponential, log-normal, log-logistic, and logistic distributions, respectively. Compare the AD (Anderson-Darling statistic) and P-values ​​for these five distributions. The smaller the AD value and the larger the P-value, the better the data fits the current distribution. For small samples, the P-value may not be stable enough and needs to be judged in conjunction with the AD value.

[0102] Based on the Anderson-Darling (AD) test results, Table 2 summarizes the goodness-of-fit statistics of the five candidate distributions at 83℃. By comparing the combined performance of AD and P values, the optimal fit distribution can be preliminarily determined.

[0103]

[0104] As shown in Table 2, although the AD values ​​of the Logistic and Log-Logistic distributions are slightly lower than those of the Normal distribution (0.254 < 0.272), the P-value of the Normal distribution (0.576) is significantly higher than other distributions, and it clearly demonstrates statistical evidence that the data follows a Normal distribution (P > 0.05). Furthermore, the theoretical background and parameter interpretability of the Normal distribution better meet the needs of practical engineering or scientific scenarios, while the P-value of Logistic distributions only provides a lower limit (> 0.25), failing to quantify its specific significance advantage. Considering the reliability and practical significance of both AD and P-values, the Normal distribution is the optimal choice.

[0105] The data were fitted to a normal distribution with a mean of 7.028 and a standard deviation of 1.879. A qualified interval was constructed, with the lower limit at the 5th percentile and the upper limit at the 95th percentile. Therefore, the qualified interval is: Calculate the values ​​at 133℃ and 173℃ respectively. The probability that the value falls within the acceptable range. For example... Figures 7-11 As shown, 8 out of 10 parameter values ​​at 133℃ fell within the acceptable range, so the probability is... At 173℃, two out of nine parameter values ​​fell within the acceptable range, so the probability is... .

[0106] according to Calculate the hazard factor. , The overall credibility of degraded data .

[0107] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0108] 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 principle 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 evaluating the reliability of prior data for a product, characterized in that, Includes the following steps: S1, Parameter Identification: Based on the theory of constant acceleration factor, identify parameters that are independent of stress and parameters that are related to stress in the product degradation model; S2, Consistency Relationship Construction: Constructing the parametric relationships that must be satisfied to ensure consistency in failure mechanisms; S3, Consistency Judgment: Based on the established consistency relationship, the consistency analysis of parameter values ​​under different accelerated stresses is performed to quantify the deviation between them and the parameter values ​​under the reference stress level; S4, Parameter Consistency Assessment: Based on the consistency discrimination results, assess the degree of consistency between the parameter set under each accelerated stress and the parameter set under normal stress, and calculate the reliability of the data under the corresponding stress level based on the degree of consistency. S5, Credibility Evaluation: Based on the credibility under each stress, the importance of the data under different stress levels is weighted by the hazard factor to obtain the comprehensive credibility of the degradation data under all accelerated stress conditions. The consistency judgment in S3 is based on the statistics of the likelihood ratio test or Wald test. It tests the difference between the parameter values ​​under different stress levels and the parameter estimates under the benchmark level. If the scale parameters satisfy the constructed consistency relationship, the failure mechanism is considered to be consistent and the data is reliable. The parameter consistency assessment in S4 includes: S41, Construct a parameter distribution model under reference stress: Collect scale parameters from n samples under normal stress level, denoted as... ,by Based on this, a distribution model of the scale parameters is constructed, and the lower confidence level is set as x% quantile and the upper confidence level is (1-x)% quantile, forming the corresponding confidence interval; S42, Statistical analysis of sample inclusion rates under other stress levels: Calculate the proportion of samples falling into the target range under different stresses. n at the level Parameter value, denoted as If the number of samples falling within the reference confidence interval is m, then the stress level The parameter value and the sample falling ratio under normal stress are as follows: ; S43, Calculation of parameter consistency: Calculate the data reliability at this stress level based on the fall rate. for ; The credibility evaluation in S5 includes: S51, Definition of Hazard Factor: Relating the normal stress level to each accelerated stress level. The ratio is defined as the hazard coefficient. ; S52, Weighted calculation of overall credibility: The credibility of data at each stress level is weighted with the hazard factor to calculate the overall credibility of degradation data at all stress levels; The hazard factor is expressed as: ； The overall credibility is expressed as follows: 。 2. The method for evaluating the credibility of prior data of a product according to claim 1, characterized in that, The parameter identification in S1 includes: S11, Define performance aging amount and change amount: Let the performance aging amount of the product at time t be... The initial conditions are met. The performance aging amount is defined as: ； S12, Construct a Gamma distribution model for the change: Assume that the performance aging amount follows a gamma distribution, expressed as: ； in, For shape parameters, For scale parameters, It is a function of time t; S13, Deriving the probability distribution function of aging amount: Based on the additivity of the Gamma distribution, the performance aging amount satisfies the distribution... ,but The probability density function is expressed as: ； S14, Deriving the reliability function: Suppose the product fails when the performance aging reaches a threshold D, then the reliability function is expressed as: ； in, For gamma function, ; S15, Introducing the derivation of variable transformation: ... Substituting into the reliability function, we obtain the closed-form expression of the reliability function, which is expressed as: ； S16, Constructing the acceleration factor and identifying stress-related and stress-independent parameters: By constructing the relationship between the cumulative distribution functions of products under different stress levels, the acceleration factor is defined, and the correlation between shape parameters, scale parameters and stress is derived, identifying stress-independent and stress-related parameters.

3. The method for evaluating the credibility of prior data of a product according to claim 2, characterized in that, The construction acceleration factor and identification of stress-related and irrelevant parameters in S16 include: S161, Define the distribution function and acceleration factor: Let... , For any two stress levels of the product , The cumulative distribution function under the given condition, then the acceleration factor Represented as ; S162, Establish the relationship between distribution functions: Based on the consistency of distribution functions, derive their equivalent expression relationship under the action of the acceleration factor, expressed as: ； in, , These are stresses , The shape parameters below; S163, Constructing the parameter identity condition: Based on the principle of invariant acceleration factor, derive the equivalent expression relation for any... The parametric identity condition that holds is expressed as: ； S164, Identify stress-dependent and undependent parameters: Based on the constructed parametric identities, identify stress-dependent and undependent parameters, where shape parameters are related to accelerated stress and scale parameters are unrelated to accelerated stress.

4. The method for evaluating the credibility of prior data of a product according to claim 3, characterized in that, The consistency relationship in S2 is constructed by selecting parameter relationships that satisfy the consistency of the failure mechanism for the parameters to be inspected, and based on the fact that the scale parameter remains unchanged under different stress levels, a parameter identity relationship is constructed, expressed as: 。

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