Variable Environment Input Life Assessment Method and System Based on Weibull Distribution

Abstract

The present invention discloses a method and system for evaluating the life of variable environment input based on Weibull distribution. The method includes the following steps: reading in training data and test data; calculating the parameters required for the distribution function at the corresponding temperature of the training data: using the Weibull distribution function as the distribution function of the sensitivity parameter of the electronic instrument to be measured, and obtaining the parameters of the Weibull distribution function under the training data by using the minimum chi-square estimation method; calculating the parameters under the input of the unsteady environment time series: determining the variation law of the parameters of the Weibull distribution function under the input of the unsteady environment time series through the cumulative failure theory and the least square method; calculating the failure probability under the input of the unsteady environment time series: inputting the obtained parameters into the Weibull probability density function to obtain the corresponding probability density function value, and processing it through the probability normalization method to obtain the failure probability. The present invention can accurately estimate the probability that the sensitivity parameter meets the requirements under the time series input.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic digital data processing, and in particular to a variable environment input life evaluation method and system based on Weibull distribution. Background Art

[0002] Traditional probability distribution functions such as Weibull distribution and exponential distribution are important distributions for evaluating reliability systems and predicting lifetimes, and play a crucial role in reliability analysis. However, in practical applications, the environment is often non-steady. When non-steady environmental time series are input, it is difficult to estimate the parameters of the Weibull distribution function (exponential distribution) and its density function, which also affects its application in reliability analysis.

[0003] The Weibull distribution function (exponential distribution) can handle success / failure data but can only predict lifetimes for specific environments. Moreover, traditional lifetime prediction algorithms mainly focus on estimating the lifetime at a certain moment in a steady environment, and it is difficult to combine the lifetime prediction of devices based on non-steady environmental time series input. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a variable environment input life evaluation method and system based on Weibull distribution, which adopts a method combining data analysis and probability distribution function, and can provide a reference for calculating the failure probability under non-steady environment input for subsequent other applications.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A variable environment input life evaluation method based on Weibull distribution includes the following steps:

[0007] S1. Read in training data and test data: Read in success / failure type experiment training data, including the storage time, the number of test samples, and the number of failures of the electronic instrument to be tested under different temperature conditions; read in test data, including non-steady environmental time series, i.e., time series and their corresponding environmental variables;

[0008] S2. Calculate the parameters required for the distribution function at the corresponding temperature of the training data: Use the Weibull distribution function as the distribution function of the sensitivity parameter of the electronic instrument to be tested, and obtain the parameters of the Weibull distribution function under the training data by using the minimum chi-square estimation method;

[0009] S3. Calculate the parameters under non-steady environmental time series input: Determine the variation law of the parameters of the Weibull distribution function under non-steady environmental time series input through Nelson cumulative failure theory and the least squares method;

[0010] S4. Calculate the failure probability under the input of the unsteady environmental time series: Input the parameters of the Weibull distribution function under the input of the unsteady environmental time series obtained in step S3 into the Weibull probability density function to obtain the corresponding probability density function values, and process the probability density function values by the probability normalization method to further obtain the failure probability under the input of the unsteady environmental time series.

[0011] Further, in step S2, the minimum Pearson χ 2 statistic obtained by the minimum chi-square estimation method is used as the true value of the best estimate.

[0012] Further, the Weibull distribution function adopted in step S2 is:

[0013]

[0014] where F(t) is the failure probability, t is the time, η is the location parameter, and m is the shape parameter;

[0015] The form of the χ 2 statistic is:

[0016]

[0017] where is the distribution parameter, represents the failure probability at time t i , n i is the number of experiments, the group frequency is the number of failures, is the number of test samples.

[0018] Further, in step S2, the parameters of the Weibull distribution can be obtained by solving the following system of equations:

[0019]

[0020] After simplifying the above equations, the minimum chi-square estimated value of the distribution parameter is the solution of the following equation:

[0021]

[0022] That is:

[0023]

[0024]

[0025]

[0026]

[0027] Thus, the distribution parameters of the Weibull distribution function at a single temperature are obtained.

[0028] Furthermore, in step S3, the mean value of the parameter m under each environmental condition in the environmental fluctuation time series is used as the shape parameter m of the Weibull distribution function under the input of the non-steady environmental time series.

[0029] Furthermore, in step S3, the calculation method of the distribution parameters of the Weibull distribution function under the input of the non-steady environmental condition time series includes:

[0030] Fitting the variation of the location parameter η with the environment according to the Arrhenius life model:

[0031]

[0032] where F(t) is the Weibull distribution function, is the significance level, and T is the temperature;

[0033] By simplification, we have:

[0034]

[0035] From the Arrhenius life model, we have:

[0036]

[0037] Therefore:

[0038]

[0039] After simplification, it becomes:

[0040]

[0041] The temperature sequence under the input time series is fitted with the lnη sequence to obtain the coefficients c and d, and then the distribution parameters corresponding to the environmental conditions under the input of the non-steady environmental condition time series are obtained.

[0042] Furthermore, in step S4, based on the input time series t 1 , t 2 , …, t n and the Weibull distribution function distribution parameters obtained in step S3 To ensure that the total area of the Weibull probability density function under the time series input is equal to 1, t′ is solved by the following formula 2 :

[0043]

[0044] where f 1 (t) and f2 (t) represents the Weibull probability density curve formed by the distribution parameters obtained from the fitting of environmental condition 1 and environmental condition 2 respectively;

[0045] Then, according to the time interval of the input time series, starting from t′ 2 Determine the next time node t′ 3 = t′ 2 +(t3 - t2), and retain the Weibull probability density function values calculated from t′ 2 to t′ 3 for subsequent output of the probability in the time period from t 2 to t 3 ; finally, perform interval integration on the probability density function curve to obtain the failure probability under the input of the non-stationary environmental time series.

[0046] A variable environmental input life assessment system based on the Weibull distribution, comprising:

[0047] A data reading module, used to read in success / failure type experimental training data, including the storage time, the number of test samples, and the number of failures of the electronic instrument to be tested under different temperature conditions; read in test data, including the non-stationary environmental time series, that is, the time series and its corresponding environmental variables;

[0048] A parameter calculation module 1, used to use the Weibull distribution function as the distribution function of the sensitivity parameter of the electronic instrument to be tested, and obtain the parameters of the Weibull distribution function under the training data by using the minimum chi-square estimation method;

[0049] A parameter calculation module 2, used to determine the variation law of the parameters of the Weibull distribution function under the input of the non-stationary environmental time series through the Nelson cumulative failure theory and the least squares method;

[0050] A probability calculation module, used to input the parameters of the Weibull distribution function under the input of the non-stationary environmental time series obtained by the parameter calculation module 2 into the Weibull probability density function to obtain the corresponding probability density function values, and process the probability density function values by the probability normalization method to further obtain the failure probability under the input of the non-stationary environmental time series.

[0051] The beneficial effects of the present invention are as follows:

[0052] 1. Based on the success / failure type data under non-stationary environmental input and using the Weibull distribution function, for the calculation of sensitivity parameters such as life and reliability, it can accurately estimate the probability that the sensitivity parameters meet the requirements under the time series input.

[0053] 2. By predicting the variation of the parameters of the distribution function under the input of the non-stationary environmental time series through experimental data, it can realize the expansion of data application and provide ideas for subsequent applications. Description of the Drawings

[0054] Figure 1 is a flowchart of the variable environment input life assessment method based on Weibull distribution of the present invention.

[0055] Figure 2 is a schematic diagram of the fitting result of temperature and parameter η.

[0056] Figure 3 is a schematic diagram of the probability normalization method.

[0057] Figure 4 is a Weibull probability density function graph.

[0058] Figure 5 is a Weibull probability distribution function graph. Detailed Embodiments

[0059] For a clearer understanding of the technical features, objectives, and effects of the present invention, the detailed embodiments of the present invention are now described. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0060] Embodiment 1

[0061] As Figure 1 shown, this embodiment provides a variable environment input life assessment method based on Weibull distribution, including the following steps:

[0062] S1. Read in training data and test data: Read in success / failure type experiment training data, including the storage time, the number of test samples, and the number of failures of the electronic instrument to be tested under different temperature conditions; read in test data, including the non-steady state environment time series, that is, the time series and its corresponding environmental variables;

[0063] S2. Calculate the parameters required for the distribution function at the corresponding temperature of the training data: Use the Weibull distribution function as the distribution function of the sensitivity parameter of the electronic instrument to be tested, and obtain the parameters of the Weibull distribution function under the training data by using the minimum chi-square estimation method;

[0064] S3. Calculate the parameters under the input of the non-steady state environment time series: Determine the change law of the parameters of the Weibull distribution function under the input of the non-steady state environment time series through Nelson's cumulative failure theory and the least squares method;

[0065] S4. Calculate the failure probability under the input of the unsteady environmental time series: Input the parameters of the Weibull distribution function under the input of the unsteady environmental time series obtained in step S3 into the Weibull probability density function to obtain the corresponding probability density function values, and process the probability density function values by the probability normalization method to further obtain the failure probability under the input of the unsteady environmental time series.

[0066] Specifically, the variable environmental input life assessment method based on the Weibull distribution in this embodiment specifically includes the following steps:

[0067] S1. Read in the training data and test data.

[0068] Read in the success / failure type experiment training data, including the storage time X of the electronic instrument to be tested under different temperature conditions, the number of test samples and the number of failures N f ; Read in the test data, including the unsteady environmental time series, i.e., the time series t 1 , t 2 , …, t n and its corresponding environmental variable condition 1 , condition 2 , …, condition n . Among them, the detection data at different storage times are independent of each other. The following table shows the success / failure type experiment training data as an example.

[0069] Table 1 Success / Failure Type Experiment Training Data

[0070]

[0071]

[0072] S2. Calculate the parameters required for the distribution function at the corresponding temperature of the training data.

[0073] The following takes the calculation of the Weibull distribution function parameters at a single temperature as an example for illustration.

[0074] Take the parameters obtained by minimizing the Pearson χ 2 statistic of the minimum chi-square estimation method as the best estimate of the true value . The Weibull distribution function is as follows:

[0075]

[0076] where F(t) is the failure probability, t is the time, η is the location parameter, and m is the shape parameter;

[0077] The form of the χ 2 statistic is:

[0078]

[0079] wherein is the distribution parameter, represents the failure probability at time t, n i is the number of experiments, and the group frequency i is the number of failures, and is the number of detected samples.

[0080] By deriving and solving the following equations, the parameters of the Weibull distribution can be obtained:

[0081]

[0082] By simplifying the above equations, the minimum chi-square estimated value of the distribution parameter is the solution of the following equation:

[0083]

[0084] That is:

[0085]

[0086]

[0087]

[0088]

[0089] Thus, the distribution parameters of the Weibull distribution function at a single temperature are obtained. Similarly, the distribution parameters of the Weibull distribution function at other temperatures can be obtained.

[0090] S3. Calculate the parameters under the input of the unsteady environmental time series.

[0091] According to the Nelson cumulative failure theory, in this embodiment, the mean value of the parameter m under each environmental condition in the environmental fluctuation time series is used as the shape parameter m of the Weibull distribution function under the input of the unsteady environmental time series. Next, how this embodiment processes the location parameter of the Weibull distribution function under the input of the unsteady environmental condition time series will be described.

[0092] According to the Arrhenius life model, the variation of the location parameter η with the environment is fitted:

[0093]

[0094] where F(t) is the Weibull distribution function, is the significance level, and T is the temperature;

[0095] By simplification, we have:

[0096]

[0097] From the Arrhenius life model, we have:

[0098]

[0099] Therefore:

[0100]

[0101] After simplification, it becomes:

[0102]

[0103] The temperature sequence under the input time series is fitted with the lnη sequence to obtain coefficients c and d, and then the distribution parameters of the corresponding environmental conditions under the input of the time series of unsteady environmental conditions are obtained. The fitting result is as Figure 2 shown.

[0104] S4. Calculate the failure probability under the input of the unsteady environmental time series.

[0105] Due to the change of environmental conditions under the input time series, the parameters corresponding to the Weibull function in the unsteady environment also change accordingly. Directly using the distribution function parameters corresponding to the environmental conditions in the Weibull distribution function will result in the sum of the calculated probability values not being equal to 1 for the entire time series. To solve this problem, this embodiment considers starting from the Weibull probability density function and calculating the probability under the input of the time series environmental conditions through the following method.

[0106] Based on the input time series t 1 , t 2 , …, t n and the Weibull distribution function distribution parameters obtained in step S3 such as Figure 3 are the Weibull probability density functions for two environmental conditions. To ensure that the total area of the Weibull probability density function under the time series input is equal to 1, use the following formula to solve for t′ 2 :

[0107]

[0108] where f 1 (t) and f 2 (t) respectively represent the Weibull probability density curves formed by the distribution parameters obtained from the fitting of environmental condition 1 and environmental condition 2.

[0109] Then, according to the time interval of the input time series, determine the next time node t′ from t′ 2 such that t′ 3 = t′2 +(t3 - t2), and for t' 2 from t' 3 The obtained Weibull probability density function values are retained for t 2 to t 3 The probabilities for the time period are output later; finally, the interval integral of the probability density function curve is performed to obtain the failure probability under the input of the unsteady environmental time series, as Figure 4 and Figure 5 shown.

[0110] Embodiment 2

[0111] Based on Embodiment 1, this embodiment:

[0112] This embodiment provides a variable environmental input life evaluation system based on the Weibull distribution, including:

[0113] A data reading module for reading in success - failure type experimental training data, including the storage time of the electronic instrument to be tested under different temperature conditions, the number of test samples, and the number of failures; reading in test data, including the unsteady environmental time series, that is, the time series and its corresponding environmental variables;

[0114] A parameter calculation module one for using the Weibull distribution function as the distribution function of the sensitivity parameter of the electronic instrument to be tested, and obtaining the parameters of the Weibull distribution function under the training data by using the minimum chi - square estimation method;

[0115] A parameter calculation module two for determining the variation law of the parameters of the Weibull distribution function under the input of the unsteady environmental time series through the Nelson cumulative failure theory and the least - squares method;

[0116] A probability calculation module for inputting the parameters of the Weibull distribution function under the input of the unsteady environmental time series obtained by the parameter calculation module two into the Weibull probability density function to obtain the corresponding probability density function values, and processing the probability density function values through the probability normalization method to further obtain the failure probability under the input of the unsteady environmental time series.

[0117] It should be noted that for the foregoing method embodiments, for the sake of simple description, they are expressed as a series of action combinations. However, those skilled in the art should know that this application is not limited by the described action sequence, because according to this application, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

Claims

1. A method for evaluating the life of variable environment input based on Weibull distribution, characterized in that, it includes the following steps: S1. Read in training data and test data: Read in success / failure type experimental training data, including the storage time, the number of test samples, and the number of failures of the electronic instrument to be tested under different temperature conditions; Read in test data, including non-steady environment time series, that is, the time series and its corresponding environmental variables; S2. Calculate the parameters required for the distribution function at the corresponding temperature of the training data: Take the Weibull distribution function as the distribution function of the sensitivity parameter of the electronic instrument to be tested, and use the minimum chi-square estimation method to obtain the parameters of the Weibull distribution function under the training data; S3. Calculate the parameters under the input of non-steady environment time series: Determine the change law of the parameters of the Weibull distribution function under the input of non-steady environment time series through Nelson's cumulative failure theory and the least squares method; S4. Calculate the failure probability under the input of non-steady environment time series: Input the parameters of the Weibull distribution function under the input of non-steady environment time series obtained in step S3 into the Weibull probability density function to obtain the corresponding probability density function value, and process the probability density function value through the probability normalization method to further obtain the failure probability under the input of non-steady environment time series.

2. The method for evaluating the life of variable environment input based on Weibull distribution according to claim 1, characterized in that, In step S2, the parameter obtained by minimizing the Pearson χ - statistic of the minimum chi - square estimation method 2 is used as the best estimate of the true value .

3. The method for evaluating the life of variable environment input based on Weibull distribution according to claim 2, characterized in that, the Weibull distribution function adopted in step S2 is: where F(t) is the failure probability, t is the time, η is the location parameter, and m is the shape parameter; χ 2 The form of the statistic is: wherein is a distribution parameter, represents the failure probability at time t, n i is the number of experiments, and the group frequency i is the number of failures, and is the number of test samples.

4. The method for evaluating the life of variable environment input based on Weibull distribution according to claim 3, characterized in that, in step S2, the parameters of the Weibull distribution can be obtained by solving the following equations: Simplify the above equations, and the minimum chi-square estimation value of the distribution parameters is the solution of the following equation: That is: Thus, the distribution parameters of the Weibull distribution function at a single temperature are obtained.

5. The method for evaluating the life of variable environment input based on Weibull distribution according to claim 4, characterized in that, in step S3, the mean value of the parameter m under each environmental condition is used as the shape parameter m of the Weibull distribution function under the input of non-steady environment time series in the environmental fluctuation time series.

6. The method for evaluating the life of variable environment input based on Weibull distribution according to claim 5, characterized in that, in step S3, the calculation method of the distribution parameters of the Weibull distribution function under the input of non-steady environment condition time series includes: Fitting the change of the location parameter η with the environment according to the Arrhenius life model: where F(t) is the Weibull distribution function, α is the significance level, and T is the temperature; By simplification, there is: From the Arrhenius life model, there is: Therefore: After simplification, it is: Temperature sequence under the input time series Coefficients c and d are obtained by fitting with the lnη sequence, and then the distribution parameters of the corresponding environmental conditions under the input of the unsteady environmental condition time series are obtained 7. The method for evaluating the life of variable environment input based on Weibull distribution according to any one of claims 1-6, characterized in that, In step S4, based on the input time series t 1 , t 2 , …, t n and the distribution parameters of the Weibull distribution function obtained in step S3 To ensure that the total area of the Weibull probability density function under the time series input is equal to 1, use the following formula to solve for t′ by inverse solution 2 : where f 1 (t) and f 2 (t) respectively represent the Weibull probability density curves formed by the distribution parameters obtained by fitting environmental condition 1 and environmental condition 2; According to the time interval of the input time series, starting from t′ 2 determine the next time node t′ 3 = t′ 2 +(t 3 - t 2 ), and retain the Weibull probability density function values calculated from t′ 2 to t′ 3 for subsequent output of the probability during the time period from t 2 to t 3 ; finally, perform interval integration on the probability density function curve to obtain the failure probability under the input of the unsteady environment time series.

8. A system for evaluating the life of variable environment input based on Weibull distribution, characterized in that, it includes: A data reading module for reading in success / failure type experimental training data, including the storage time, the number of test samples, and the number of failures of the electronic instrument under test at different temperature conditions; Read in test data, including unsteady environment time series, that is, time series and their corresponding environmental variables; A parameter calculation module 1 for using the Weibull distribution function as the distribution function of the sensitivity parameter of the electronic instrument under test and obtaining the parameters of the Weibull distribution function under the training data by using the minimum chi-square estimation method; A parameter calculation module 2 for determining the variation law of the parameters of the Weibull distribution function under the input of the unsteady environment time series through the Nelson cumulative failure theory and the least squares method; A probability calculation module for inputting the parameters of the Weibull distribution function under the input of the unsteady environment time series obtained by the parameter calculation module 2 into the Weibull probability density function to obtain the corresponding probability density function value, and processing the probability density function value by the probability normalization method to further obtain the failure probability under the input of the unsteady environment time series.

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