Acceleration coefficient interval estimation system

Abstract

The invention discloses an acceleration coefficient interval estimation system, which comprises the following steps of: acquiring sufficient complete failure sample data through a Testto-Failure test, designing a'stress layer and degradation characteristic layer 'double-layered Bootstrap sampling rule, and generating a plurality of groups of failure sample combinations; meanwhile, whole-course degradation data of failure samples under double stress are integrated, a cross-stress integrated joint likelihood function is constructed, the acceleration coefficient of each combination is directly solved, and finally the acceleration coefficient interval is determined through statistical analysis. By the adoption of the technical scheme, the problems that existing acceleration coefficient estimation can only achieve point estimation and lacks effective interval estimation adaptive to Testto-Failure data features, an interval result cannot cover failure scene parameter fluctuation, and error accumulation exists in traditional step-by-step solving are solved, and the accuracy of acceleration coefficient estimation and the interval reference value are improved.

Description

Technical Field

[0001] This invention belongs to the field of accelerated degradation experiment and reliability testing technology, and specifically relates to an acceleration coefficient interval estimation system. Background Technology

[0002] The acceleration factor, as a core parameter connecting data under high accelerated stress and normal stress, directly determines the accuracy of equipment reliability assessment based on the reliability of its estimation results. Test-to-Failure testing, by continuously applying stress until sample failure, can obtain a complete degradation trajectory and failure sample data from initial performance to failure, providing a high-quality data source for acceleration factor estimation. However, existing acceleration factor estimation techniques suffer from the following key limitations: Lack of interval estimation methods: Traditional techniques can only estimate the acceleration factor at the point level through the relationship between stochastic process parameters. There is no interval estimation scheme for test-to-failure failure samples, which makes it impossible to quantify the fluctuation range of the acceleration factor, resulting in a lack of risk boundary reference in subsequent reliability assessment. 1. Inappropriate sampling method: If the existing interval estimation uses simple random sampling, it does not take into account the special characteristics of the "failure sample" in Test-to-Failure. The sampling combination may include non-failure samples, which cannot reflect the parameter fluctuations under the real failure scenario, and the interval results have low reference value. 2. Insufficient interval coverage: Traditional interval estimation is mostly based on theoretical distribution assumptions (such as normal distribution) and does not combine the statistical characteristics of actual test-to-failure data, resulting in large fluctuations in the acceleration coefficient between theoretical intervals and actual failure scenarios, and low coverage. 3. Lack of verification mechanism: There is a lack of validity verification criteria for interval estimation results, making it impossible to determine whether the interval truly covers the true value of the acceleration coefficient, which further reduces the credibility of interval estimation. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides an acceleration coefficient interval estimation system.

[0004] To achieve the above objectives, the present invention provides the following solution: An acceleration coefficient interval estimation system, comprising: The first processing module is used to acquire failed sample data; The second processing module is used to perform Wiener process modeling based on the failure sample data, integrate the degradation increment and failure time of all failure samples under low stress and high stress, and construct a cross-stress integrated joint likelihood function. The third processing module is used to sample the failure sample data through a two-layer bootstrap to obtain multiple sets of failure sample combinations; at the same time, it obtains the acceleration coefficient range based on the integrated joint likelihood function.

[0005] Preferably, the first layer is a stress layer and the second layer is a degradation feature layer.

[0006] Preferably, the second layering rule is as follows: based on the average failure time of all valid samples in each stress layer, the samples are divided into short failure time sub-layers, medium failure time sub-layers, and long failure time sub-layers. If the number of samples in a certain sub-layer is less than 1, it is merged with the adjacent sub-layer to ensure that each sub-layer has valid samples.

[0007] Preferably, the dual-layer Bootstrap sampling is performed by randomly selecting one sample from each sublayer of the low-stress layer, for a total of [number missing]. m ≥2; High-stress layers are extracted according to the same rules. m Each sample was used to form a "low stress and high stress" failure sample combination, and the sampling method was sampling with replacement.

[0008] Preferably, the third processing module samples the failure sample data through a two-layer bootstrap. The two-layer includes a first layer divided according to the accelerated stress level and a second layer divided according to the average failure time of each stress layer. Samples are extracted from the sub-layers of each layer to form multiple sets of failure sample combinations. The acceleration coefficient of each combination is directly solved through the integrated joint likelihood function, and the acceleration coefficient range is obtained through statistical analysis.

[0009] Preferably, the first processing module obtains failure sample data through a Test-to-Failure test; As a preferred option, let the parameters under stress be... , Parameters under high stress are obtained through acceleration coefficients A The association is: in, A It is the acceleration coefficient between two different stress levels. The drift coefficient, The diffusion coefficient is denoted as . The constructed unified joint likelihood function is as follows: in, n This represents the number of samples at stress level 1. m This represents the number of samples at stress level 2. Represents stress level 1, the first i The amount of degradation of each sample Represents stress level 2, the second i The amount of degradation of each sample Represents stress level 1, the first i Measurement intervals for the performance of each sample. Represents stress level 2, the second i Measurement intervals for the performance of each sample.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: Data utilization: Relying on Test-to-Failure testing to obtain complete failure trajectory data, abandoning the traditional practice of "extracting part of the degraded data", and fully retaining the entire information of the sample from the initial state to failure; At the solution logic level: breaking through the step-by-step mode of "first fitting the parameters of the single stress model and then deriving the acceleration coefficient through the parameter relationship", we innovatively construct a cross-stress integrated joint likelihood function, which directly links the degradation data and acceleration coefficient under dual stress, avoiding the propagation of parameter fitting error; At the sampling mechanism level: a two-layer Bootstrap sampling method of "stress layer + degradation feature layer" is designed to ensure stress matching and cover different degradation rate scenarios, thus solving the problem that traditional sampling cannot reflect the differences in the characteristics of failed samples.

[0011] This invention obtains sufficient failure sample data through test-to-failure testing, directly solves the acceleration coefficient through cross-stress joint likelihood function, eliminates the single-stress parameter fitting step, reduces error accumulation, and designs an improved Bootstrap sampling rule adapted to failure scenarios. Compared with single-stress stratified sampling, it adds a degradation feature layer division, so that the sampling combination covers the dual scenarios of "stress level + degradation rate", realizes effective coverage of parameter fluctuations in failure scenarios by interval estimation, and provides a quantitative risk boundary basis for equipment reliability assessment. Attached Figure Description

[0012] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a schematic diagram of the acceleration coefficient interval estimation system structure according to an embodiment of the present invention; Figure 2The figures are percentage change curves of test data for three samples at 50V in Example 1 of the present invention; where (a) is the test-to-failure data of sample 1 at 50V, (b) is the test-to-failure data of sample 2 at 50V, and (c) is the test-to-failure data of sample 3 at 50V. Figure 3 The figures are percentage change curves of test data for three samples at 60V in Example 1 of the present invention; where (a) is the test-to-failure data of sample 4 at 60V, (b) is the test-to-failure data of sample 5 at 60V, and (c) is the test-to-failure data of sample 6 at 60V. Figure 4 The data curves of the three samples in Example 1 of this invention after sampling preprocessing at 50V are shown; where (a) is the test-to-failure data of sample 1 after preprocessing at 50V, (b) is the test-to-failure data of sample 2 after preprocessing at 50V, and (c) is the test-to-failure data of sample 3 after preprocessing at 50V. Figure 5 The data curves for the three samples in Example 1 of this invention after sampling preprocessing at 60V are shown below; (a) is the test-to-failure data of sample 4 after preprocessing at 60V, (b) is the test-to-failure data of sample 5 after preprocessing at 60V, and (c) is the test-to-failure data of sample 6 after preprocessing at 60V. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] Example 1 like Figure 1 As shown, the present invention provides an acceleration coefficient interval estimation system, comprising: The first processing module is used to obtain failure sample data through Test-to-Failure testing; The second processing module is used to perform Wiener process modeling based on the failure sample data, integrate the degradation increment and failure time of all failure samples under low stress and high stress, and construct a cross-stress integrated joint likelihood function. The third processing module is used to sample the failure sample data through a two-layer bootstrap method. The two-layer method includes a first layer divided according to the accelerated stress level and a second layer divided according to the average failure time of each stress layer. Samples are extracted from the sub-layers of each layer to form multiple sets of failure sample combinations. The acceleration coefficient of each combination is directly solved by the integrated joint likelihood function, and the acceleration coefficient interval is obtained through statistical analysis. The first layer is the stress layer, and the second layer is the degradation characteristic layer. The division rule of the second layer is: according to the average failure time of all valid samples in each stress layer, the samples are divided into short failure time sub-layers, medium failure time sub-layers, and long failure time sub-layers. If the number of samples in a certain sub-layer is less than 1, it is merged with the adjacent sub-layer to ensure that each sub-layer has valid samples. The two-layer bootstrap sampling method is: randomly selecting 1 sample from each sub-layer of the low stress layer, and the total number of samples is... m ≥2; High-stress layers are extracted according to the same rules. m Each sample was used to form a "low stress and high stress" failure sample combination, and the sampling method was sampling with replacement.

[0017] As one embodiment of the present invention, the sample and stress settings in the Test-to-Failure test are specifically as follows: ① Target: The electronic component to be tested; ② Grouping Rules: Group by "accelerated stress gradient," with ≥3 samples of the same model configured for each stress level. It must be ensured that all samples fail in the Test-to-Failure test (meeting the Bootstrap sampling requirement for the "failure sample pool"). For example, the optocoupler is set up with two groups: 50V (low acceleration) and 60V (high acceleration), with 3 samples in each group. All 6 samples are tested until failure. The Test-to-Failure test data for the 3 samples at 50V is as follows: Figure 2 As shown, the test-to-failure test data for three samples at 60V are as follows: Figure 3 As shown; ③ Stress Principle: Accelerated stress must not alter the failure mechanism of the component, and the stress level must cause degradation of the sample within the cycle. For example... Figure 2 and Figure 3The degradation trends and degradation rates of the six samples shown did not differ significantly, indicating that the 50V and 60V electrical stresses did not change the failure mechanism of the optocoupler. Furthermore, the key performance parameters of the optocoupler showed obvious degradation trends under both electrical stresses.

[0018] Furthermore, the core requirements for Test-to-Failure testing are as follows: ① Data Recording: Record the entire process including "timestamp, real-time stress value, key performance parameters (such as output current), and failure state," with a focus on marking the failure time and the last set of degradation data before failure for each sample, forming a complete failure data chain, such as... Figure 2 and Figure 3 The figure shows the degradation data recorded from the onset of degradation to failure for the key performance parameter of the optocoupler output stage current. ② Failure Judgment: Clearly define and unify failure thresholds, such as an optocoupler output current dropping to 50% of its initial value or to 5mA, ensuring that the failure modes of all failed samples are consistent (to avoid sampling bias due to differences in failure mechanisms). Figure 2 and Figure 3 The changes in the key performance parameters of all failed samples showed a dramatic increase at the last moment, and the changes were more than 50% greater than the initial values, indicating that the failure modes of all failed samples were consistent. ③ Data filtering: After the test, only the sample data that "completely failed and had the same failure mode" are retained, and the samples that did not fail or had abnormal failure modes are removed. The "effective failure sample pool" of Bootstrap sampling is constructed. After the experiment, all samples under 50V and 60V meet the requirements of "completely failed and had the same failure mode" and do not need to be removed.

[0019] As one embodiment of the present invention, the second processing module performs the following process: Data preprocessing ① Standardization transformation: Calculate the percentage change of key performance parameters (1) in, y i For the first i Percentage change at time point x 0 is the initial value. x i For the first i Time value, eliminating absolute value differences between samples; ② Degradation increment calculation: Based on the Test-to-Failure time series, calculate the degradation increment between adjacent time points. (2) in, It is the firsti+ 1st moment and the first i The increment of the percentage change at time point y i+1 It is the first i+ Percentage change at time 1 y i It is the first i Percentage change at any given time.

[0020] Figure 2 and Figure 3 It is a graph created based on the percentage change of key performance parameters of a sample.

[0021] Wiener process modeling and point estimation solution ① Model parameter correlation: Let the parameters under stress 1 be as follows (Drift coefficient) (Diffusion coefficient), a parameter under high stress, is expressed through the acceleration coefficient. A The association is (3) in, A It is the acceleration coefficient between two different stress levels, and there is no need to solve for the independent parameters under high stress separately; ② Joint Likelihood Function: Integrates the degradation increment and failure time of all failure samples under two stresses to construct a likelihood function. Cross-stress Integrated Joint Likelihood Function: Integrates the full-process degradation increment of all failure samples under low and high stresses to construct an integrated joint likelihood function, directly combining dual-stress data with acceleration coefficients. A The stress model is correlated and does not require a separate single-stress model. (4) in, n This represents the number of samples at stress level 1. m This represents the number of samples at stress level 2. Represents stress level 1, the first i The amount of degradation of each sample Represents stress level 2, the second i The amount of degradation of each sample Represents stress level 1, the first i Measurement intervals for the performance of each sample. Represents stress level 2, the second i Measurement intervals for the performance of each sample; ③ Point estimation solution: The integrated joint likelihood function is optimized using the fminsearch algorithm to directly obtain the point estimate of the acceleration coefficient. As a reference benchmark for Bootstrap interval estimation, it does not require indirect derivation through parameter relationships, where These are point estimates of the acceleration coefficient. (From...) Figure 4 and Figure 5 Two data points are selected from the preprocessed data and input into equation (4) to obtain the point estimate of the acceleration coefficient under the sample combination.

[0022] As one embodiment of the present invention, the third processing module performs the following process: Design of two-layer Bootstrap sampling rules ① Dual-layer innovation: To address the shortcomings of traditional Bootstrap sampling in not fully exploring the differences in degradation rates of Test-to-Failure samples, data quality heterogeneity, and the diversity of failure modes, an improved "dual-layer" mechanism is designed. ② Basis for layering: The first layer (stress layer) is divided into low-stress and high-stress layers according to the accelerated stress level to ensure stress matching of the sampling combination. Each layer contains only "valid failure samples," for example... Figure 4 and Figure 5 The data can be divided into two layers according to the stress layer: S1, S2, S3 and S4, S5, S6. The second layer (degradation characteristic layer) is based on the average failure time of all valid samples within each stress layer. μ The core criterion for classification is that this criterion is easy to calculate and strongly correlates with the degree of degradation. The specific classification method is as follows: the samples are divided into short failure time sub-layers according to their failure time. T ≤0.3 μ ), and the intermediate failure time sublayer (0.3) μ ≤ T ≤0.7 μ ), long failure time sublayer ( T ≥0.7 μ Two sub-layers, of which, T This is the sample's expiration time; if the number of samples in a sublayer is less than 1, it is merged with the adjacent sublayer to ensure that each sublayer has valid samples. For the low-stress layers (S1, S2, S3), S3 is assigned to the short failure time sublayer, S1 to the medium failure time sublayer, and S2 to the long failure time sublayer. Selecting a sample from each characteristic layer will result in the combination of (S1, S2), (S1, S3), and (S2, S3). For the high-stress layers (S4, S5, S6), S6 is assigned to the short failure time sublayer, S4 to the medium failure time sublayer, and S5 to the long failure time sublayer. Selecting a sample from each characteristic layer will result in the combination of (S4, S5), (S4, S6), and (S5, S6). ③ Sampling method: "Two-stratified sampling with replacement" is adopted - first, the stress level is divided into a low-stress layer and a high-stress layer (first stratum). Then, for the valid failure samples in each stress layer, one sample is randomly selected from each sub-layer of the stress layer. The total number of samples is... m ≥2, forming a "low stress + high stress" failure sample combination. Figure 4 and Figure 5 Taking the data as an example, the following can be generated: [(S1,S2,S4,S5),(S1,S2,S4,S6),(S1,S2,S5,S6),(S1,S3,S4,S5),(S1,S3,S4 ,S6),(S1,S3,S5,S6),(S2,S3,S4,S5),(S2,S3,S4,S6),(S2,S3,S5,S6)] 9 combinations.

[0023] Calculation of multiple combination acceleration coefficients For each Bootstrap sampling combination, the point estimate of the corresponding acceleration coefficient is calculated using the likelihood function. Let's assume it's the first... k The acceleration coefficient point estimate obtained from the combination of "low stress + high stress" failure samples is _____. ; (5) in, represent In the k Point estimates for combinations, such as the acceleration coefficient point estimates for the combination (S1, S2, S4, S5). for A Point estimate of the acceleration coefficient for the combination of 1, (S1, S2, S4, S6) for A Point estimates of the acceleration coefficient for combinations of 2, (S1, S2, S5, S6) for A Point estimates of the acceleration coefficient for combinations of 3, (S1, S3, S4, S5) for A Point estimates of the acceleration coefficient for combinations of 4, (S1, S3, S4, S6) for A Point estimates of the acceleration coefficient for combinations of 5, (S1, S3, S5, S6) for A Point estimates of the acceleration coefficient for combinations of 6, (S2, S3, S4, S5) for A Point estimates of the acceleration coefficient for combinations of 7, (S2, S3, S4, S6) for APoint estimates of the acceleration coefficient for the combination of 8, (S2, S3, S5, S6) for A 9.

[0024] The specific process is as follows: ① Data extraction: Extract the Test-to-Failure degradation increment and failure time of low-stress and high-stress samples in the current combination, for example... Figure 2 and Figure 3 It's the process of data extraction. Figure 4 and Figure 5 This involves preprocessing the extracted data; ② Modeling and solving: Constructing the joint likelihood function of the combination, and obtaining the point estimate of the combination-specific acceleration coefficient through maximum likelihood estimation. For example, according to Figure 4 and Figure 5 Data obtained , ,..., It refers to the modeling and solving process; ③ Result storage: recording all combinations This forms a set of acceleration coefficients ( , , ..., )( n (The total number of sample combinations). For example, ... , ,..., Store as ( , , ..., This refers to the process of storing the results.

[0025] Acceleration coefficient range determined Data sorting refers to sorting the stored set of speedup factors ( , , ..., The sequences are rearranged according to their numerical values ​​to generate a new ordered sequence. , ,..., ); The next step is the interval boundary selection operation, where the basic interval is defined as follows: In a sorted sequence, select the minimum value within that sequence. and maximum value These two values ​​are then used as the two endpoints of the closed interval, thus forming a complete closed interval. This method of constructing basic intervals has clear application scenarios, and is especially suitable for practical needs that require high interval coverage.

[0026] As one embodiment of the present invention, it further includes: a fourth processing module, used to accelerate the verification of coefficient interval estimation, specifically executing the following process: Baseline acceleration coefficient acquisition Record the actual failure time of each sample under different stress levels, and obtain the baseline acceleration factor. (6) in, This represents the actual mean failure time of test-to-failure samples under high accelerated stress levels. This represents the actual average failure time of test-to-failure samples under low accelerated stress levels. The reference acceleration factor represents two stress levels; Validation metrics ① Interval coverage rate: judgment Whether it falls within the Bootstrap estimation range, a coverage rate of ≥90% is considered acceptable; ② Reasonableness of interval width: The difference between the midpoint value of the interval and the benchmark value should be less than 50% of the interval length to avoid the interval being too wide and losing its reference value or too narrow and failing to cover fluctuations.

[0027] Example: The following section uses optocouplers as the test object to elaborate on the implementation process of acceleration coefficient interval estimation based on dual-stress hierarchical bootstrap sampling, and verifies the feasibility of the method: 1 Test-to-Failure Experiment and Failure Sample Preparation (Bootstrap Sampling Basics) ① Sample grouping: Select 6 optocouplers from the same batch and divide them into two groups - low stress group (50V accelerating voltage, samples S1-S3) and high stress group (60V accelerating voltage, samples S4-S6), with 3 samples in each group, to ensure that all are tested until failure; ② Test parameters: Apply a constant current of 10mA to the input side and apply a corresponding accelerating voltage to the output side, and collect leakage current data once per second; ③ Failure determination: Failure is determined when the leakage current changes sharply, and the failure time is recorded: Low stress group failure time: S1 (304406s), S2 (366342s), S3 (30998s); High stress group failure time: S4 (123580s), S5 (183378s), S6 (21171s); ④ Sample screening: All 6 samples were "stress degradation failures" with no abnormal failure modes, and an "effective failure sample pool" was constructed.

[0028] 2. Acceleration Coefficient Point Estimation Data preprocessing ①Standardization: Using the initial leakage current of 0.140mA as a baseline, calculate the percentage change at each time point. For example, if the leakage current of S1 is 0.143mA at 10800s, the percentage change is... y =(0.143-0.140) / 0.140×100%=2.14%.

[0029] ② Incremental calculation: Obtain the percentage change for all samples. .

[0030] ③ Sampling Processing: During the experiment, a high leakage current sampling frequency was set to capture changes in leakage current when samples failed. However, this resulted in a lot of repetitive data without any change. To reduce the amount of data processing, the original test data can be sampled, with a sampling interval of [missing information]. f .

[0031] (7) Point estimation solution Construct the joint likelihood function and optimize it using the fminsearch algorithm to obtain: =8.87×10 -8 , =9.80×10 -5 , A point =3.0454 (point estimate).

[0032] 3. Two-tiered Bootstrap sampling interval estimation Sampling combination generation Using "double-layered sampling with replacement" – first divide the stress into low-stress layers and high-stress layers (first layer) according to stress level, and then randomly select one sample from each sub-layer of the stress layer for the effective failure samples in each stress layer. The following samples are selected: [S1S2, S4S5], [S1S2, S4S6], [S1S2, S5S6], [S1S3, S4S5], [S1S3, S4S6], [S1S3, S5S6], [S2S3, S4S5], [S2S3, S4S6], [S2S3, S5S6].

[0033] Calculation of multiple combination acceleration coefficients For each combination of repetition points estimation process, calculate the acceleration factor. : Combination 1 ([S1S2, S4S5]): =3.5088, Combination 2 ([S1S2, S4S6]): =3.9984, Combination 3 ([S1S2, S5S6]): =3.3126, Combination 4 ([S1S3, S4S5]): =4.2105, Combination 5 ([S1S3, S4S6]): =3.1746, Combination 6 ([S1S3, S5S6]): =4.2105, Combination 7 ([S2S3, S4S5]): =3.0454, Combination 8 ([S2S3, S4S6]): =3.1746, Combination 9 ([S2S3, S5S6]): =3.8095. The resulting set of acceleration coefficients is: (3.5088, 3.9984, 3.3126, 4.2105, 3.1746, 4.2105, 3.0454, 3.1746, 3.8095).

[0034] Interval determination ① Data sorting: The ordered sequence is [3.0454, 3.1746, 3.1746, 3.3126, 3.5088, 3.8095, 3.9984, 4.2105, 4.2105]; ②Basic interval: A min =3.0454, A max =4.2105, the interval is [3.0454, 4.2105].

[0035] 4. Interval verification Calculation of reference acceleration factor Additional testing of the mean time to failure (T) of 3 50V samples 50V =141186s and the average failure time T of three 60V samples 60V =39386s, A ref =141186 / 39386≈3.5847.

[0036] Verification results ①Interval coverage: A ref =3.5847 falls within the basic interval [3.0454, 4.2105], with 100% coverage; ② Reasonableness of interval width: The midpoint value of the basic interval width is 3.62795, and the difference between it and the estimated value of the point is 3.5847, which is 0.04325. The difference accounts for 1.19% of the basic interval, which is less than 50%, thus meeting the requirements.

[0037] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. An acceleration coefficient interval estimation system, characterized in that, include: The first processing module is used to acquire failed sample data; The second processing module is used to perform Wiener process modeling based on the failure sample data, integrate the degradation increment and failure time of all failure samples under low stress and high stress, and construct a cross-stress integrated joint likelihood function. The third processing module is used to sample the failure sample data through a two-layer bootstrap to obtain multiple sets of failure sample combinations; at the same time, it obtains the acceleration coefficient range based on the integrated joint likelihood function.

2. The acceleration coefficient interval estimation system as described in claim 1, characterized in that, The first layer is the stress layer, and the second layer is the degradation feature layer.

3. The acceleration coefficient interval estimation system as described in claim 2, characterized in that, The second stratification rule is as follows: based on the average failure time of all valid samples in each stress layer, the samples are divided into short failure time sub-layers, medium failure time sub-layers, and long failure time sub-layers. If the number of samples in a certain sub-layer is less than 1, it is merged with the adjacent sub-layer to ensure that each sub-layer has valid samples.

4. The acceleration coefficient interval estimation system as described in claim 3, characterized in that, The dual-layer Bootstrap sampling method involves randomly selecting one sample from each sublayer of the low-stress layer, for a total of [number missing]. m ≥2; High-stress layers are extracted according to the same rules. m A total of 10 samples were used to form a "low stress and high stress" failure sample combination, and the sampling method was sampling with replacement.

5. The acceleration coefficient interval estimation system as described in claim 4, characterized in that, The third processing module samples the failure sample data through a dual-layer bootstrap. The dual-layer includes a first layer divided according to the accelerated stress level and a second layer divided according to the average failure time of each stress layer. Samples are extracted from the sub-layers of each layer to form multiple sets of failure sample combinations. The acceleration coefficient of each combination is directly solved through the integrated joint likelihood function, and the acceleration coefficient interval is obtained through statistical analysis.

6. The acceleration coefficient interval estimation system as described in claim 5, characterized in that, The first processing module obtains failure sample data through Test-to-Failure testing.

7. The acceleration coefficient interval estimation system as described in claim 6, characterized in that, Let the parameters under stress be , Parameters under high stress are obtained through acceleration coefficients A The association is: in, A It is the acceleration coefficient between two different stress levels. The drift coefficient, The diffusion coefficient is denoted as . The constructed unified joint likelihood function is as follows: in, n This represents the number of samples at stress level 1. m This represents the number of samples at stress level 2. Represents stress level 1, the first i The amount of degradation of each sample Represents stress level 2, the second i The amount of degradation of each sample Represents stress level 1, the first i Measurement intervals for the performance of each sample Represents stress level 2, the second i Measurement intervals for the performance of each sample.

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