A method for predicting the lifespan of avionics products based on Weibull parameters

Abstract

This invention relates to a method for predicting the service life of avionics products based on Weibull parameters. The method includes the following steps: Step 1: Obtaining initial sample data of the avionics product's service life, processing it to obtain a failure dataset; Step 2: Calculating the failure sample level and cumulative failure probability of the initial sample data; Step 3: Fitting the Weibull distribution parameters of the avionics product's service life using the least squares method; Step 4: Plotting the avionics product's service life curve based on the Weibull distribution parameters to achieve service life prediction. This invention is based on a grouped testing method, using failure data from the first failure, significantly shortening the testing time. By classifying and processing the failure samples, and comprehensively applying both failed and non-failed sample data, the cumulative failure probability of the samples is more accurate, further achieving accurate prediction of the avionics product's service life.

Description

Technical Field

[0001] This invention relates to the field of small sample test design and Weibull parameter estimation based on batch initial failure, and specifically to a method for predicting the service life of avionics products based on Weibull parameters. Background Technology

[0002] The Weibull distribution is a widely used probability distribution in failure and lifespan data analysis. Weibull analysis involves probabilistic analysis in graphical form, aiming to find the distribution that best represents the lifespan data of a batch of samples under a given failure mode. Generally, to fit an accurate Weibull distribution curve, a large amount of experimental statistical data is often collected to provide sufficient evidence for Weibull parameter fitting; however, in many cases, insufficient sample size or excessively long experimental periods lead to insufficient statistical data and significant deviations in parameter estimation results. Especially in accelerated aging tests, due to the typically small sample size, at least 63% of the samples generally cannot achieve a good curve fit; furthermore, more than half of the samples experience excessively long failure waiting times, greatly increasing experimental costs. Therefore, deriving characteristic lifespan values ​​and lifespan distribution functions of avionics products based on small sample failure data analysis is of great significance.

[0003] Currently, for statistical analysis of small sample data, the commonly used methods are semi-empirical semi-evaluation method, bootstrap method, virtual augmented sample evaluation method, and Bayesian method.

[0004] The semi-empirical, semi-evaluation method relies on extensive historical testing or information from similar avionics products. It combines field test data with existing information to conduct data analysis and reliability assessments within a certain margin of error. However, this approach is difficult to apply in scenarios lacking historical information and similar avionics products.

[0005] Both the bootstrap method and the virtual augmented sample evaluation method essentially expand limited experimental data. The bootstrap method resamples the original sample data to approximate the original complex statistics through simulation. The virtual augmented sample evaluation method is essentially a sample generation method based on data augmentation and data mining. It uses the results of simulated experiments to replace real experiments, transforming small sample situations into appropriately sized samples for further data processing. However, augmenting new sample data requires two conditions: first, the expected value of the sample must not be changed; second, the standard deviation of similar avionics products must not be altered, which limits its application. Both methods have significant advantages in expanding sample size information, but when parameter estimation is performed in situations where insufficient experimental time leads to excessively small sample sizes, significant biases may occur.

[0006] The Bayesian method is a preliminary estimate of a parameter to be estimated made using prior information. This prior information is then updated with experimental data to obtain the posterior distribution of the parameter. Essentially, the Bayesian method is an information extension, increasing the information content by introducing prior information. However, because prior information lacks quantitative standards and evaluation criteria in practice, the prior distribution is crucial for parameter evaluation in the Bayesian method.

[0007] The aforementioned methods for handling small samples primarily rely on empirical information, prior information, or virtual augmented information to augment data and meet the sample size requirements for parameter estimation. However, when similar avionics products and historical information are lacking and the sample size is too small, it is difficult to augment the data into effective samples. In actual experiments, increasing the sample size and reducing the experimental time are contradictory, and the above methods also struggle to balance the need to reduce experimental time while ensuring high reliability of the sample data. Therefore, it is urgent to research a new method that can overcome these shortcomings. Summary of the Invention

[0008] To address the limitations of the aforementioned methods in estimating Weibull distribution parameters for small samples, this invention provides a small-sample experimental design and Weibull parameter estimation method based on initial batch failures. This method, combined with experimental design, significantly reduces testing time while efficiently and effectively utilizing sample data, resulting in a more accurate Weibull distribution fitting process. Specifically, this invention provides a method for predicting the lifespan of avionics products based on Weibull parameters under small sample conditions. Based on a grouped testing method, it uses failure data from the first failure, greatly shortening the testing time. By classifying failed samples and applying data from both failed and non-failed samples, the cumulative failure probability of the samples is more accurate, further achieving accurate prediction of the lifespan of avionics products.

[0009] To achieve the above objectives, the solution adopted by the present invention is as follows:

[0010] A method for predicting the service life of avionics products based on Weibull parameters includes the following steps:

[0011] Step 1: Obtain initial sample data on the lifespan of avionics products, process it, and obtain a failure dataset, specifically:

[0012] Divide the initial sample of total number N into n batches, ensuring that the number of samples in each batch is m. n No fewer than 3 samples; conduct the test sequentially for each batch of samples. When one sample in the batch fails, stop the test for that batch and record the time t when the first sample failure occurs in that batch. n Then, the test was repeated with a new batch of samples until all batches of samples had been tested. The test data was then collected and stored. The time t of each batch of failed samples was recorded. nArranged in chronological order, denoted as T. k Where k represents the order in which the samples fail, and the minimum number of samples that do not fail is denoted as S. k This forms a failure dataset;

[0013] Step 2: Calculate the failure sample level and cumulative failure probability of the initial sample data for avionics products, including the following sub-steps:

[0014] Step 21: The method for calculating the failure sample level of initial sample data for avionics products is as follows:

[0015]

[0016] In the formula: rank k rank represents the rank of the k-th failure sample. k-1 The rank represents the (k-1)th failure level of the sample; N represents the total number of sample data; k-2 S represents the failure level of the (k-2)th sample; k T represents k The minimum number of samples that have not failed at any given time; k represents the time order in which the samples fail.

[0017] Step 22: Calculate the cumulative failure probability of the initial sample data failure samples of the avionics product. The calculation method is as follows:

[0018]

[0019] In the formula: F(T) k ) represents T k The cumulative failure probability of the avionics product failure samples at any given time;

[0020] Step 3: Fit the Weibull distribution parameters of the avionics product lifetime using the least squares method, including the following sub-steps:

[0021] Step 31: The probability distribution function of the lifespan of avionics products is shown below:

[0022]

[0023] In the formula: G(t) represents the probability distribution function value of the avionics product's lifespan; t represents the avionics product's usage time; β represents the shape parameter of the Weibull distribution; η represents the scale parameter of the Weibull distribution; e represents the natural logarithm.

[0024] Taking the logarithm twice on the above equation yields the logarithmic relationship for the probability distribution function of the avionics product's lifespan, as shown below:

[0025]

[0026] In the formula: ln represents the logarithm operation;

[0027] Step 32: By substituting the parameters in the logarithmic calculation of the probability distribution function of avionics product lifespan, and linearizing the complex parameters, a simplified logarithmic calculation of the probability distribution function can be obtained, as shown below:

[0028] y = a + bx;

[0029] In the formula: y represents the dependent variable of the simplified probability distribution function; a represents the intercept of the simplified probability distribution function; b represents the slope of the simplified probability distribution function; x represents the independent variable of the simplified probability distribution function.

[0030] Step 33: Calculate the intercept *a* and slope *b* of the simplified probability distribution function using the least squares method, as shown below:

[0031]

[0032] In the formula: Indicates the first regression coefficient; x represents the second regression coefficient; i Represents the i-th independent variable; y represents the average value of the independent variable; i Represents the i-th dependent variable; The value represents the mean of the dependent variable; n represents the initial batch number of samples.

[0033] Step 34: Substitute the cumulative failure probability of the failed samples calculated in Step 2 into the calculation process in Step 3 to finally obtain the parameter values ​​of the Weibull distribution, as shown below:

[0034]

[0035] In the formula: Represents the shape parameters of the Weibull distribution; The scale parameter of the Weibull distribution is used to represent the scale parameter of the Weibull distribution.

[0036] Step 4: Plot the avionics product lifespan curve based on the parameters of the Weibull distribution to achieve avionics product lifespan prediction. Specifically:

[0037] The shape parameters of the Weibull distribution obtained in step 34 The scale parameter of the Weibull distribution Substitute the data into step 31 to plot the Weibull distribution curve of the avionics product lifespan, and obtain the prediction result of the avionics product lifespan.

[0038] Preferably, in step 21, the first level rank1 of the failure sample level is set to 1, and subsequent failure sample levels are obtained according to the failure sample level calculation method.

[0039] Preferably, in step 21, S k T represents k The method to obtain the minimum number of samples that have not failed at a given time is: when the nth batch of samples fails at time t n Recorded as T k At that time, the quantity of samples in this batch was also assigned to M. k Where M0 = 0, then T k The maximum number of samples that fail at any given time is Minimum number S of samples that have not failed k The calculation method is as follows:

[0040]

[0041] In the formula: S k T represents k The minimum number of samples that have not failed at any given time; M i This represents the number of samples in the i-th batch.

[0042] Preferably, in step 32, the parameters after logarithmic processing are replaced with variables to complete the linearization of complex parameters, specifically as follows:

[0043]

[0044] Preferably, the method for obtaining the average value of the independent variable in step 33 is as follows:

[0045]

[0046] In the formula: It represents the average value of the independent variable.

[0047] Preferably, the method for obtaining the average value of the dependent variable in step 33 is as follows:

[0048]

[0049] In the formula: This represents the average value of the dependent variable.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] (1) This invention provides a method for predicting the service life of avionics products based on Weibull parameters under small sample conditions. Based on the group test method, it uses the failure data when the first failure occurs, which greatly shortens the test time.

[0052] (2) By classifying and processing the failed samples, this invention comprehensively applies the data of failed samples and the data of non-failed samples, making the cumulative failure probability of the samples more accurate, and further realizing the accurate prediction of the life of avionics products.

[0053] (3) This invention proposes a cumulative failure probability estimation formula based on failure sample level, which realizes the estimation of cumulative failure probability of avionics products under the premise of high utilization of failure data, greatly improves the efficiency of avionics product life estimation, and the adaptability of the method to the usage scenario. Attached Figure Description

[0054] Figure 1 This is a control block diagram of the avionics product lifespan prediction method based on Weibull parameters according to an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of failure records in the experiment of an embodiment of the present invention;

[0056] Figure 3 This is the Weibull distribution curve of the lifespan of an avionics product according to an embodiment of the present invention. Detailed Implementation

[0057] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0058] This invention provides a method for predicting the lifespan of avionics products based on Weibull parameters under small sample conditions. Based on a grouped testing method, it uses failure data from the first failure, significantly shortening the testing time and improving the applicability of this technique. By classifying the failed samples and comprehensively applying data from both failed and non-failed samples, the cumulative failure probability of the samples is more accurate. Furthermore, a lifespan curve is plotted based on Weibull parameters, achieving accurate prediction of the avionics product's lifespan. This technical solution demonstrates good application performance and meets practical application needs. Figure 1 The diagram shown is a control block diagram of the avionics product lifespan prediction method based on Weibull parameters according to an embodiment of the present invention.

[0059] This invention provides a method for predicting the service life of avionics products based on Weibull parameters. To demonstrate the applicability of this invention, it is applied to the prediction of the service life of motor bearings. The service life of bearings often conforms to the Weibull distribution characteristics. Under normal lubrication and processing conditions, bearings can withstand long-term operating loads. However, when individual bearings experience installation problems or material defects, they may fail within a short period of operation. Such failure data can significantly deviate from the life distribution prediction. Therefore, this invention establishes failure sample levels to weight the influencing factors of failure data and constructs a cumulative failure probability calculation formula based on the failure sample levels.

[0060] Specifically, it includes the following steps:

[0061] Step 1: Obtain initial sample data on the lifespan of avionics products, process it, and obtain a failure dataset;

[0062] Divide the initial sample of total number N into n batches, ensuring that the number of samples in each batch is m. n No fewer than 3; the sample grouping is shown in Table 1.

[0063] Table 1 Grouping

[0064]

[0065] The test is conducted sequentially for each batch of samples. When one sample in the batch fails, the test for that batch is stopped, and the time t when the first sample failure occurs in that batch is recorded. n Then, the test was repeated with a new batch of samples until all batches of samples had been tested and the test data was compiled. The time t of failure for each batch of samples was recorded. n Arranged in chronological order, denoted as T. k Where k represents the order in which the samples fail, and the minimum number of samples that do not fail is denoted as S. k The failure data was compiled into a failure dataset. Table 2 shows the failure data for avionics products.

[0066] Table 2 Failure data for avionics products

[0067] Sample number / i 1 2 3 4 5 6 7 8 9 10 Test time / h 100 100 100 100 100 250 250 250 250 450 Whether it is invalid or not × × × Sample number / i 11 12 13 14 15 16 17 18 19 20 Test time / h 450 450 450 450 800 800 800 1300 1300 1300 Whether it is invalid or not × ×

[0068] Step 2: Calculate the failure sample level and cumulative failure probability of the initial sample data for avionics products, which includes the following sub-steps:

[0069] Step 21: Since only one sample in each batch failed, the actual failure of all samples actually exists. Figure 2 As shown, the first failure of the second batch of samples is not necessarily the second failure of the entire sample; therefore, the weight of each failure data is adjusted by classifying the failure sample levels.

[0070] The method for calculating the failure sample level of initial sample data for avionics products is as follows:

[0071]

[0072] In the formula: rank k rank represents the rank of the k-th failure sample. k-1 The rank represents the (k-1)th failure level of the sample; N represents the total number of sample data; k-2 S represents the failure level of the (k-2)th sample;k T represents k The minimum number of samples that have not failed at any given time; k represents the time order in which the samples fail.

[0073] Table 3 shows the summary table of failure data:

[0074] Table 3 Failure Data Compilation Table

[0075] Sample number / i Failure time / h Failure Sample Level Number Remaining sample volume 1 100 1 19 6 250 2 14 10 273 3 10 15 289 4 5 18 333 5 2

[0076] The first level of the failure sample level, rank1, has a value of 1. Subsequent failure sample levels are obtained according to the failure sample level calculation method. Table 4 shows the failure sample levels for each sample.

[0077] Table 4 Failure Levels of Each Sample

[0078]

[0079] When the nth batch of samples expires at time t n Recorded as T k At that time, the quantity of samples in this batch was also assigned to M. k Where M0 = 0, then T k The maximum number of samples that fail at any given time is Minimum number S of samples that have not failed k The calculation method is as follows:

[0080]

[0081] In the formula: S k T represents k The minimum number of samples that have not failed at any given time; M i This represents the number of samples in the i-th batch.

[0082] Step 22: Determine the cumulative failure probability of the initial sample data failure samples of the avionics product. The method for obtaining this probability is as follows:

[0083]

[0084] In the formula: F(T) k ) represents T k The cumulative failure probability of the avionics product failure samples at any given time.

[0085] Table 5 Cumulative failure probability of failed samples

[0086]

[0087] Step 3: Fit the Weibull distribution parameters of the avionics product lifetime using the least squares method;

[0088] Step 31: Since the failure probability of this avionics product follows a Weibull parameter distribution, the probability distribution function of the avionics product's lifetime is as follows:

[0089]

[0090] In the formula: G(t) represents the probability distribution function value of the avionics product lifespan; t represents the usage time of the avionics product; β represents the shape parameter of the Weibull distribution; η represents the scale parameter of the Weibull distribution; and e represents the natural logarithm.

[0091] Taking the logarithm twice on the above equation yields the logarithmic relationship for the probability distribution function of the lifespan of avionics products, as shown below:

[0092]

[0093] In the formula: ln represents the logarithm operation;

[0094] Step 32: By substituting the parameters in the logarithmic calculation of the probability distribution function of avionics product lifespan, and linearizing the complex parameters, a simplified logarithmic calculation of the probability distribution function can be obtained, as shown below:

[0095] y = a + bx;

[0096] In the formula: y represents the dependent variable of the simplified probability distribution function; a represents the intercept of the simplified probability distribution function; b represents the slope of the simplified probability distribution function; and x represents the independent variable of the simplified probability distribution function.

[0097] The parameters after logarithmic processing are then subjected to variable substitution to linearize complex parameters, specifically:

[0098]

[0099] Table 6 shows the parameterized sample data.

[0100] Table 6. Parameterized Sample Data

[0101] <![CDATA[x1]]> 4.60517 <![CDATA[y1]]> -2.971437 <![CDATA[x2]]> 5.52146 <![CDATA[y2]]> -2.064132 <![CDATA[x3]]> 5.60947 <![CDATA[y3]]> -1.407396 <![CDATA[x4]]> 5.66642 <![CDATA[y4]]> -0.682584 <![CDATA[x5]]> 5.80814 <![CDATA[y5]]> 0.199274

[0102] Step 33: Calculate the intercept *a* and slope *b* of the simplified probability distribution function using the least squares method, as shown below:

[0103]

[0104] In the formula: Represents the first regression coefficient. This represents the second regression coefficient. x iRepresents the i-th independent variable; represents the average of the independent variables; yi represents the i-th dependent variable; represents the mean of the dependent variable; n represents the initial batch number of samples.

[0105] The method for obtaining the average of the independent variables is as follows:

[0106]

[0107] In the formula: It represents the average value of the independent variable.

[0108] The method for obtaining the mean of the dependent variable is as follows:

[0109]

[0110] In the formula: This represents the average value of the dependent variable.

[0111] Step 34: Substitute the cumulative failure probability of the failed samples calculated in Step 2 into the calculation process in Step 3 to finally obtain the parameter values ​​of the Weibull distribution, as shown below:

[0112]

[0113] In the formula: Represents the shape parameters of the Weibull distribution; This represents the scale parameter of the Weibull distribution.

[0114] Step 4: Plot the lifespan curve of avionics products based on the parameters of the Weibull distribution to achieve lifespan prediction of avionics products;

[0115] The shape parameters of the Weibull distribution obtained in step 34 The scale parameter of the Weibull distribution Substitute the data into step 31 to plot the Weibull distribution curve of the avionics product lifespan, and obtain the prediction result of the avionics product lifespan.

[0116] The final Weibull distribution parameters obtained in this case are: like Figure 3 The figure shown is a lifespan curve of avionics products plotted based on Weibull parameters according to an embodiment of the present invention. Because the present invention provides a sample lifespan prediction method based on the first failure of a batch, it significantly reduces the overall lifespan testing time for avionics products. In this case, the total testing time for collecting all required sample data using this method was 3912 hours, as shown in Table 7.

[0117] Table 7. Full Sample Test Time

[0118]

[0119] The prerequisite for using semi-empirical semi-evaluation methods, bootstrap methods, virtual augmented sample evaluation methods, or Bayesian methods to predict avionics lifespan is obtaining the failure times of all samples. Assuming the predicted Weibull distribution curve of the avionics product's lifespan conforms to the actual lifespan distribution, and taking a maximum lifespan of 500 hours and a minimum lifespan of 1 hour, three sets of virtual full-sample lifetimes conforming to the Weibull probability distribution of this avionics product were obtained using commercial software MATLAB. The results are shown in Table 8, representing three possible full-sample failure lifetimes obtained in the experiment.

[0120] Table 8 Sample Virtual Lifetime

[0121]

[0122]

[0123] As can be seen from Table 8, the total test time for all samples in each virtual lifetime group is much longer than the test time in this invention, and some even require less than two-thirds of the test time for virtual lifetime group b. This is extremely important for lifetime testing, which requires a long testing period to obtain failure data.

[0124] In summary, the prediction results of the avionics product lifespan prediction method based on Weibull parameters in this case study demonstrate its excellent effectiveness.

[0125] (1) The present invention provides a method for predicting the service life of avionics products based on Weibull parameters under small sample conditions. Based on the group test method, the failure data at the first failure is used, which greatly shortens the test time and makes the technical method more widely applicable.

[0126] (2) The embodiments of the present invention classify and process the failed samples, and comprehensively apply the data of failed samples and the data of non-failed samples, so that the cumulative failure probability of the samples is more accurate. Furthermore, the life curve is plotted based on the Weibull parameter, and the life of avionics products is accurately predicted.

[0127] (3) The present invention proposes a cumulative failure probability estimation formula based on failure sample level, which realizes the estimation of cumulative failure probability of avionics products under the premise of high utilization of failure data, greatly improves the efficiency of avionics product life estimation, and the adaptability of the method to the application scenario; by comparing the calculation results of this method with other methods, it is proved that the application effect of this technical solution is good and can meet the actual application needs.

[0128] 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 by those skilled in the art to the technical solutions of the present invention 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. A method for predicting the service life of avionics products based on Weibull parameters, characterized in that, It includes the following steps: Step 1: Obtain initial sample data on the lifespan of avionics products, process it, and obtain a failure dataset, specifically: Divide the initial sample of total number N into n batches, ensuring that the number of samples in each batch is m. n No fewer than 3 samples; conduct the test sequentially for each batch of samples. When one sample in the batch fails, stop the test for that batch and record the time t when the first sample failure occurs in that batch. n Then, the test was repeated with a new batch of samples until all batches of samples had been tested. The test data was then collected and stored. The time t of each batch of failed samples was recorded. n Arranged in chronological order, denoted as T. k Where k represents the order in which the samples fail, and the minimum number of samples that do not fail is denoted as S. k This forms a failure dataset; Step 2: Calculate the failure sample level and cumulative failure probability of the initial sample data for avionics products, including the following sub-steps: Step 21: The method for calculating the failure sample level of initial sample data for avionics products is as follows: In the formula: rank k rank represents the rank of the k-th failure sample. k-1 The rank represents the (k-1)th failure level of the sample; N represents the total number of sample data; k-2 S represents the failure level of the (k-2)th sample; k T represents k The minimum number of samples that have not failed at any given time; k represents the time order in which the samples fail. Step 22: Calculate the cumulative failure probability of the initial sample data failure samples of the avionics product. The calculation method is as follows: In the formula: F(T) k ) represents T k The cumulative failure probability of the avionics product failure samples at any given time; Step 3: Fit the Weibull distribution parameters of the avionics product lifetime using the least squares method, including the following sub-steps: Step 31: The probability distribution function of the lifespan of avionics products is shown below: In the formula: G(t) represents the probability distribution function value of the avionics product's lifespan; t represents the avionics product's usage time; β represents the shape parameter of the Weibull distribution; η represents the scale parameter of the Weibull distribution; e represents the natural logarithm. Taking the logarithm twice on the above equation yields the logarithmic relationship for the probability distribution function of the avionics product's lifespan, as shown below: In the formula: ln represents the logarithm operation; Step 32: By substituting the parameters in the logarithmic calculation of the probability distribution function of avionics product lifespan, and linearizing the complex parameters, a simplified logarithmic calculation of the probability distribution function can be obtained, as shown below: y = a + bx; In the formula: y represents the dependent variable of the simplified probability distribution function; a represents the intercept of the simplified probability distribution function; b represents the slope of the simplified probability distribution function; x represents the independent variable of the simplified probability distribution function. Step 33: Calculate the intercept *a* and slope *b* of the simplified probability distribution function using the least squares method, as shown below: In the formula: Indicates the first regression coefficient; x represents the second regression coefficient; i Represents the i-th independent variable; y represents the average value of the independent variable; i Represents the i-th dependent variable; The value represents the mean of the dependent variable; n represents the initial batch number of samples. Step 34: Substitute the cumulative failure probability of the failed samples calculated in Step 2 into the calculation process in Step 3 to finally obtain the parameter values ​​of the Weibull distribution, as shown below: In the formula: Represents the shape parameters of the Weibull distribution; The scale parameter of the Weibull distribution is used to represent the scale parameter of the Weibull distribution. Step 4: Plot the avionics product lifespan curve based on the parameters of the Weibull distribution to achieve avionics product lifespan prediction. Specifically: The shape parameters of the Weibull distribution obtained in step 34 The scale parameter of the Weibull distribution Substitute the data into step 31 to plot the Weibull distribution curve of the avionics product lifespan, and obtain the prediction result of the avionics product lifespan.

2. The method for predicting the service life of avionics products based on Weibull parameters according to claim 1, characterized in that, In step 21, the first level of the failure sample level, rank1, is set to 1. Subsequent failure sample levels are obtained according to the failure sample level calculation method in step 21.

3. The method for predicting the service life of avionics products based on Weibull parameters according to claim 1, characterized in that, In step 21, S k T represents k The specific method for obtaining the minimum number of samples that have not failed at a given time is as follows: when the nth batch of samples fails at time t... n Recorded as T k At that time, the quantity of samples in this batch was also assigned to M. k Where M0 = 0, then T k The maximum number of samples that fail at any given time is Minimum number of samples S that have not failed k The calculation method is as follows: In the formula: S k T represents k The minimum number of samples that have not failed at any given time; M i This represents the number of samples in the i-th batch.

4. The method for predicting the service life of avionics products based on Weibull parameters according to claim 1, characterized in that, In step 32, variable substitution is performed on the logarithmically processed parameters to linearize the complex parameters, specifically as follows:

5. The method for predicting the service life of avionics products based on Weibull parameters according to claim 1, characterized in that, The method for obtaining the average value of the independent variable in step 33 is as follows: In the formula: It represents the average value of the independent variable.

6. The method for predicting the service life of avionics products based on Weibull parameters according to claim 1, characterized in that, The method for obtaining the average value of the dependent variable in step 33 is as follows: In the formula: This represents the average value of the dependent variable.

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