Life distribution curve correction method and system based on small sample data, storage medium and equipment

Abstract

The embodiment of the invention provides a life distribution curve correction method and system based on small sample data, a storage medium and equipment, and the method comprises the steps: carrying out the self-service sampling of original small sample data through a Bootstrap method, and generating a regeneration sample; calculating discrete prior distribution of two Weibull distribution parameters m and eta through a classical estimation method based on the regenerated sample; taking the discrete prior distribution as prior distribution of Bayesian estimation, and calculating posterior distribution of life distribution parameters m and eta in combination with a likelihood function of a regeneration sample; and determining final life distribution parameters m and eta according to the post-test distribution, and finishing the correction of the life distribution curve. According to the embodiment of the invention, the original small sample data is subjected to self-service sampling through the Bootstrap method, the regeneration sample is generated, so that sample points are increased, the life distribution curve is calculated and corrected through the Bayesian estimation algorithm, proper life distribution parameters are obtained, and the life fitting credibility is improved.

Description

Technical Field

[0001] This invention relates to the field of data statistical modeling and analysis technology, and in particular to a method, system, storage medium and device for correcting lifetime distribution curves based on small sample data. Background Technology

[0002] Reliability analysis is a discipline that studies the ability of a product, system, or component to perform its intended function under specified conditions and within a specified time. It is widely used in engineering, manufacturing, aerospace, medical equipment, energy, and other fields. Its core objective is to identify potential failure risks, optimize design, extend lifespan, and reduce economic losses or safety hazards caused by failures by quantifying "reliability" metrics. In reliability analysis, the Weibull distribution is widely used to describe product lifespan.

[0003] In some applications requiring reliability analysis, the sample size is often limited. For example, marine rotating machinery, as a key component of the transmission system, is widely used in industrial production such as motors, engines, bearings, and gearboxes. Key components of rotating machinery are prone to failure under harsh or complex operating conditions, directly affecting mechanical performance and even seriously impacting production safety. One effective method is to determine the fault state by analyzing changes in the shaft center trajectory. Simulating eccentricity faults in the shaft system by using hydraulic devices to change the shaft axis's operating state has proven effective. Considering that the bearing rotor system is a flexible mechanical model, the rotating shaft's center deviates from its stationary position due to gravity during rotation. The distance between the rotating shaft center in operation and its stationary position is the eccentricity. By measuring the eccentricity in the x and y directions, and using small magnetic blocks and magnetoelectric sensors attached to the shaft, along with a specially designed software algorithm, the real-time shaft center trajectory change curve is synthesized. Changes in shaft center trajectory are closely related to rotational speed, applied force, and friction surface wear, and the results can be used to identify conditions such as eccentric wear, rotor misalignment, and abnormal oil film on rotating machinery shafts. However, existing shaft center trajectory measurements can only be performed for short periods and lack integration with online real-time measurement and condition identification.

[0004] However, with small sample data, classical estimation methods (such as maximum likelihood estimation) suffer from the following problems: low accuracy (insufficient sample size leads to large variance in parameter estimation); excessively wide confidence intervals (failing to provide effective support for engineering decisions); and reliance on subjective priors (traditional Bayesian methods require expert experience to set prior distributions, introducing human bias). While existing improvements (such as Bootstrap resampling) can expand the sample size, they are not integrated with the Bayesian framework and cannot fully utilize prior information. With small sample data, the accuracy of classical estimation results is low, and the confidence intervals are too wide, rendering them practically useless. With the continuous updating and evolution of shipboard monitoring systems, the diversity and quantity of monitoring data are constantly increasing, bringing new challenges to traditional condition monitoring technologies. From a practical perspective, traditional condition monitoring technologies suffer from problems such as unreasonable threshold settings and imperfect judgment criteria. Summary of the Invention

[0005] In view of the above-mentioned problems existing in the prior art, the present invention provides a method, system, storage medium and device for lifetime distribution curve correction based on small sample data, so as to solve the technical problems of low accuracy, excessively wide confidence interval, reliance on subjective priors and lack of practical application value of classical estimation methods under small sample data.

[0006] This invention provides a method for correcting lifetime distribution curves based on small sample data, comprising the following steps:

[0007] Step S1: Use the Bootstrap method to perform self-sampling on the original small sample data to generate regenerated samples;

[0008] Step S2: Based on the regenerated samples, calculate the discrete prior distributions of the two-parameter Weibull distribution parameters m and η using the classical estimation method, where m and η represent the shape parameter and scale parameter of the Weibull distribution, respectively.

[0009] Step S3: Using the discrete prior distribution as the prior distribution of Bayesian estimation, and combining it with the likelihood function of the regenerated sample, calculate the posterior distribution of the lifetime distribution parameters m and η.

[0010] Step S4: Determine the final lifetime distribution parameters m and η based on the post-hoc distribution to complete the correction of the lifetime distribution curve.

[0011] In one embodiment, step S1 specifically involves:

[0012] For the original small sample data with a sample size n≤30, perform bootstrap sampling without replacement to generate M sets of regenerated samples, each with a sample size of n.

[0013] In one embodiment, step S2 includes,

[0014] Step S21: Select a group of regenerated samples from the M groups of regenerated samples as the current processing sample group;

[0015] Step S22: Use the least squares method to determine the parameter range for the current processed regenerated sample group;

[0016] Step S23: Use the maximum likelihood method to estimate the parameters of the current processed regenerated sample group to generate the discrete joint probability density distribution of m and η;

[0017] Step S24: Repeat steps S21-S23 until all M groups of regenerated samples have been processed.

[0018] In one embodiment, the formula for calculating the posterior distribution in step S3 is as follows:

[0019] P(m,η|data)∝L(data|m,η)·P(m,η)

[0020] The prior distribution P(m,η) is a constant, which is calculated in step S2.

[0021] In one embodiment, the original small sample data is distributed general data and data-type general data. For distributed general data, it is processed by directly matching device class parameters with prior distributions; for data-type general data, it is processed by generating prior distributions through Bootstrap.

[0022] In addition, embodiments of the present invention also provide a lifetime distribution curve correction system based on small sample data, comprising:

[0023] The data preprocessing module is used to identify the type of the input raw small sample data;

[0024] The Bootstrap sampling module is used to generate reproduced samples and calculate discrete prior distributions.

[0025] The Bayesian estimation module combines the discrete prior distribution with the reproduced sample data to output the posterior distribution parameters.

[0026] The visualization module is used to plot the corrected lifetime distribution curve and confidence interval.

[0027] In one embodiment, the Bayesian estimation module supports parallel computation and can accelerate the solution of the posterior distribution parameters using the Monte Carlo method.

[0028] In addition, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the lifetime distribution curve correction method based on small sample data as described in any embodiment of the present invention.

[0029] In addition, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the lifetime distribution curve correction method based on small sample data as described in any embodiment of the present invention.

[0030] Compared with existing technologies, the beneficial effects of the lifetime distribution curve correction method, system, storage medium, and device based on small sample data provided by the embodiments of the present invention are as follows: In the case of general data, to improve the accuracy of calculation results, the embodiments of the present invention introduce the Bootstrap method from statistics. This involves obtaining the discrete prior distribution of the parameters to be determined through bootstrap sampling, and then using the Bayesian method under the discrete prior distribution to obtain the estimated values ​​of the parameters. The Bootstrap method is used to generate the prior distribution of small sample data as a pre-step of the Bayesian estimation algorithm, which reduces the dependence on subjective information. Simultaneously, the Bayesian estimation algorithm is used to correct the lifetime distribution curve, obtaining suitable lifetime distribution parameters and improving the reliability of lifetime fitting. Furthermore, the embodiments of the present invention reduce the dependence on subjective information by generating the discrete prior distribution through bootstrap sampling; quickly locate the parameter range using the least squares method and accurately solve it using the maximum likelihood method, improving computational efficiency; and support flexible processing of both distributed and general data. Attached Figure Description

[0031] Figure 1 A flowchart illustrating a lifetime distribution curve correction method based on small sample data provided in an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of the algorithm flow involved in a lifetime distribution curve correction method based on small sample data provided in an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram illustrating the generation of a prior distribution using the Bootstrap method, which is part of a lifetime distribution curve correction method based on small sample data provided in an embodiment of the present invention. Detailed Implementation

[0034] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] Various embodiments and features of this application are described herein with reference to the accompanying drawings.

[0036] These and other features of this application will become apparent from the following description of preferred forms of embodiments given as non-limiting examples, with reference to the accompanying drawings.

[0037] It should also be understood that although this application has been described with reference to some specific examples, those skilled in the art can certainly implement many other equivalent forms of this application, which have the features described in the claims and are therefore all within the scope of protection defined herein.

[0038] The above and other aspects, features and advantages of this application will become more apparent when taken in conjunction with the accompanying drawings and in view of the following detailed description.

[0039] Specific embodiments of this application are described below with reference to the accompanying drawings; however, it should be understood that the claimed embodiments are merely examples of this application, which can be implemented in various ways. Well-known and / or repeated functions and structures are not described in detail to ascertain the true intent based on the user's historical operations, and to avoid unnecessary or redundant details that would obscure this application. Therefore, the specific structural and functional details claimed herein are not intended to be limiting, but merely serve as the basis and representative basis for the claims to teach those skilled in the art to use this application in various ways with substantially any suitable detailed structure.

[0040] This specification may use the phrases “in one embodiment,” “in another embodiment,” “in yet another embodiment,” or “in other embodiments,” all of which may refer to one or more of the same or different embodiments according to this application.

[0041] The principles and features of the present invention are described below with reference to the accompanying drawings. The embodiments described are for illustrative purposes only and are not intended to limit the scope of the invention. The following description, in conjunction with... Figure 1-3 The preferred embodiments of the present invention will be described in further detail below:

[0042] like Figure 1-3 As shown, this embodiment of the invention provides a method for correcting lifetime distribution curves based on small sample data, including the following steps:

[0043] Step S1: Use the Bootstrap method to perform bootstrap sampling on the original small sample data to generate regenerated samples. Specifically, perform bootstrap sampling without replacement on the original small sample data with a sample size n≤30 to generate M sets of regenerated samples, with each set having a sample size of n.

[0044] Step S2: Based on the reproduced samples, calculate the discrete prior distributions of the two-parameter Weibull distribution parameters m and η using classical estimation methods. Here, m and η represent the shape parameter and scale parameter of the Weibull distribution, respectively. The shape parameter determines the shape of the distribution curve and is a core feature of the Weibull distribution. The scale parameter determines the "scale" or "range" of the distribution, similar to the standard deviation of a normal distribution. Specifically, it includes...

[0045] Step S21: Select a group of regenerated samples from the M groups of regenerated samples as the current processing sample group;

[0046] Step S22: Use the least squares method to determine the parameter range for the current processed regenerated sample group;

[0047] Step S23: The maximum likelihood method is used to estimate the parameters of the current processed regenerated sample group to generate the discrete joint probability density distribution of m and η. In the classical estimation method, the least squares method is preferred to determine the parameter range, and then the maximum likelihood method is used to solve it accurately to reduce the computational complexity.

[0048] Step S24: Repeat steps S21-S23 until all M groups of regenerated samples have been processed.

[0049] Specifically, the Bootstrap method is used to generate the prior distribution:

[0050] The bootstrap method is a way to augment samples and generate discrete prior distributions when there is no prior data. The steps of the bootstrap method to obtain the prior distribution are as follows: Figure 3 As shown. The prior distribution generated by the Bootstrap method is a discrete prior distribution. Since each discrete value in the distribution is obtained by classical estimation from a reproduced sample, it can be assumed that each discrete value has the same probability. If N reproduced samples are generated, the probability of each discrete value is 1 / N.

[0051] The classic estimation method is as follows:

[0052] Classical estimation is used to fit the equipment life distribution. It is assumed that the failure follows a two-parameter Weibull distribution, with the following failure probability density function:

[0053]

[0054] Unreliability function:

[0055]

[0056] The data adopts a timed end test without replacement: out of n0 products, z0 fail, and the failure times are t1, t2, t3…tz0 in sequence (where t1≤t2≤t3…≤tz0 is the truncated data), and the truncation time is ts.

[0057] The input parameters are sample size n, number of failures r, end test time ts, and failure time array t[r] of the component.

[0058] (1) Least squares method

[0059] Taking the logarithm of the distribution function and simplifying it, we get:

[0060]

[0061] make

[0062]

[0063] but

[0064] y i =a+bx i (5)

[0065] If t i If the data follows a Weibull distribution (with sufficient data), linear regression can be performed using the least squares method to obtain the coefficients a and b.

[0066] (2) Maximum Likelihood Method

[0067] The maximum likelihood estimation equations for parameters m and η are as follows:

[0068]

[0069] The results were:

[0070]

[0071] The above equation is a unit equation in terms of m, which can be solved numerically using an approximation method.

[0072] make

[0073]

[0074] Since y1 and y2 are both monotonic functions and intersect at only one point, the smaller of the two absolute values ​​at the point where the sign of y1-y2 changes can be considered as an approximate solution.

[0075] After obtaining the value of m, the parameter η can be solved directly from the second equation above.

[0076] Compared with the least squares method, maximum likelihood estimation has higher accuracy, but the solution is more complex. Therefore, when solving for m, the approximate range is first determined by the least squares method to reduce the amount of computation.

[0077] For the Weibull distribution:

[0078] Mean:

[0079]

[0080] Failure rate:

[0081]

[0082] Step S3: Using the discrete prior distribution as the prior distribution for Bayesian estimation, and combining it with the likelihood function of the regenerated samples, calculate the posterior distributions of the lifetime distribution parameters m and η, wherein the formula for calculating the posterior distribution is...

[0083] P(m,η|data)∝L(data|m,η)·P(m,η)

[0084] In the formula, the prior distribution P(m,η) is a constant, calculated in step S2 (i.e., provided by the discrete distribution generated by Bootstrap). For general data processing, there are two types of general data: distributed general data and data-based general data. For distributed general data, the device class parameters are directly matched with the prior distribution. In the case of general data, this embodiment of the invention introduces the Bootstrap method from statistics to improve the accuracy of the calculation results. The discrete prior distribution of the parameter to be calculated is obtained through bootstrap sampling, and then the estimated value of the parameter is obtained using the Bayesian method under the discrete prior distribution. The specific algorithm flow design is as follows: Figure 2 As shown, for general data of data type, the prior distribution is generated by Bootstrap. General data of distribution type directly gives the prior distribution of parameters, so no further processing is required. It is only necessary to match the reliability parameters of each device class with the corresponding prior distribution. General data of data type does not directly give the prior distribution type and parameters, but gives the data. In this case, it is necessary to use these general data to generate the prior distribution of the corresponding reliability parameters.

[0085] Bayesian estimation of the lifespan distribution is a parameter estimation method based on Bayesian statistics, used to infer a probability distribution model of product lifespan (or failure time) based on observed data. Its core idea is to combine prior knowledge (historical information or expert experience) and observed data, update the probability distribution of parameters using Bayes' theorem, and finally obtain the posterior distribution of the parameters, thereby completing the fitting of the lifespan distribution.

[0086] The specific implementation steps are as follows: (1) Select the lifetime distribution model; (2) Clarify the prior distribution of the parameters; (3) Construct the likelihood function; (4) Calculate the posterior distribution; (5) Estimate and predict the parameters.

[0087] For Weibull and other multi-parameter distributions, the prior distribution is not as easily determined as that of the exponential distribution, and cannot be provided by expert information. Using the Bootstrap sample as the prior distribution can reduce the reliance on subjective information. Secondly, this method allows for mathematical calculations, facilitating numerical solutions.

[0088] Given the Weibull distribution parameters m and η determined above, sampling is performed to generate M sets of reproduced samples with a sample size of n. A random array e[n] is obtained on (0,1), and the mathematical formula for sampling is:

[0089] t[i]=η(-lnF(t)) 1 / m =η(-ln(e[i])) 1 / m (11)

[0090] Sort t[n] by bubble sort. When t[i] > ts, let t[i] = ts. This yields a new set of M regenerated samples with a sample size of n: n, r j ,ts and t j [i]. M sets of parameters m are obtained by repeatedly using maximum likelihood estimation. j and η j .

[0091] Assume m j and η j Since they are independent, we obtain the discrete prior joint probability density distribution of m and η:

[0092]

[0093] and Let it be a constant. Let it be the prior distribution calculated by Bayes.

[0094] remember

[0095]

[0096] The likelihood function can be expressed as:

[0097]

[0098] The prior distribution is a constant:

[0099]

[0100] Therefore, according to Bayes' theorem, the discrete joint posterior distribution of m and η is obtained:

[0101]

[0102] The desired result is the posterior distribution of parameters m and η, i.e., m = m j ,η=η i The probability distribution.

[0103] Step S4: Determine the final lifetime distribution parameters m and η based on the post-hoc distribution to complete the correction of the lifetime distribution curve;

[0104] From m = m j ,η=η i The probability distribution g(m=m) j ,η=η i|E), we can obtain the reliability distribution function of the component.

[0105]

[0106] Probability density distribution function:

[0107]

[0108] The required component lifespan and failure rate parameters can be obtained from the above two formulas.

[0109] In addition, embodiments of the present invention also provide a lifetime distribution curve correction system based on small sample data, comprising:

[0110] The data preprocessing module is used to identify the type of the input raw small sample data;

[0111] The Bootstrap sampling module is used to generate reproduced samples and calculate discrete prior distributions.

[0112] The Bayesian estimation module combines the discrete prior distribution with the reproduced sample data to output the posterior distribution parameters.

[0113] The visualization module is used to plot the corrected lifetime distribution curve and confidence interval.

[0114] In one embodiment, the Bayesian estimation module supports parallel computation and can accelerate the solution of the posterior distribution parameters using the Monte Carlo method.

[0115] Compared with existing technologies, the correction system composed of the above modules has the following beneficial effects: (1) Improves the reliability of data in small sample scenarios. By generating a large number of regenerated samples, it effectively makes up for the deficiency of insufficient original data and alleviates the statistical bias caused by small samples; (2) Enhances the robustness of the model and the ability to quantify uncertainty. The Bayesian framework directly outputs the uncertainty range of parameters (such as confidence intervals) through the posterior distribution, providing users with a basis for risk quantification; (3) Full-process automation and interpretability. The visualization module transforms complex statistical results into intuitive distribution curves and confidence interval charts, making it easier for non-professional users to understand the model output and supporting engineering decision-making; (4) Strong theoretical and methodological innovation. The integration of Bootstrap and Bayesian methods breaks the limitations of traditional single methods: Bootstrap provides data augmentation support, and Bayesian inference realizes dynamic parameter updates, forming complementary advantages; the dynamic generation of discrete prior distributions avoids the dependence of traditional Bayesian methods on continuous prior assumptions, and is more suitable for complex and asymmetric data distribution patterns in actual engineering. It improves prediction accuracy while taking into account the interpretability and practicality of the results.

[0116] In addition, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the lifetime distribution curve correction method based on small sample data as described in any embodiment of the present invention.

[0117] In addition, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the lifetime distribution curve correction method based on small sample data as described in any embodiment of the present invention.

[0118] It should be recognized that embodiments of the present invention may be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable storage medium.

[0119] The method can be implemented using standard programming techniques, including a non-transitory computer-readable storage medium configured with a computer program in the computer program, wherein the storage medium is configured such that the computer operates in a specific and predefined manner.

[0120] Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with a computer system; however, if necessary, the program can be implemented in assembly or machine language; in any case, the language can be a compiled or interpreted language.

[0121] Furthermore, for this purpose, the program can run on a programmed application-specific integrated circuit.

[0122] Furthermore, the procedures described herein may be performed in any suitable order, unless otherwise indicated herein or otherwise clearly contradicted by the context.

[0123] The processes (or variations and / or combinations thereof) described herein can be executed under the control of one or more computer systems configured with executable instructions, and can be implemented by hardware or a combination thereof as code (e.g., executable instructions, one or more computer programs, or one or more applications) that commonly executes on one or more processors.

[0124] The computer program includes a plurality of instructions that can be executed by one or more processors.

[0125] Furthermore, the method can be implemented in any suitable computing platform, including but not limited to personal computers, minicomputers, mainframes, workstations, networked or distributed computing environments, standalone or integrated computer platforms, or in communication with charged particle tools or other imaging devices.

[0126] In summary, this application generates discrete prior distributions through self-sampling, reducing reliance on subjective information; it utilizes the least squares method to quickly locate the parameter range and the maximum likelihood method for accurate solution, improving computational efficiency; and it supports flexible processing of both distributed and general-purpose data. A Bayesian estimation algorithm is employed to correct the lifetime distribution curve, obtaining suitable lifetime distribution parameters and improving the reliability of lifetime fitting.

[0127] Example 1

[0128] Taking aircraft engine life analysis as an example:

[0129] Data: Failure time sample of a certain engine model (n=15, number of failures z=5, truncation time ts=1000 hours);

[0130] Comparison methods: traditional maximum likelihood estimation (MLE) and Bayesian estimation without bootstrap (BPE);

[0131] Experimental steps:

[0132] (1) Use Bootstrap to generate M=1000 sets of regenerated samples;

[0133] (2) Calculate m and η for each group of samples and generate discrete prior distributions;

[0134] (3) Calculate the posterior distribution based on the target data;

[0135] (4) Output parameter estimates and 95% confidence intervals.

[0136] Result comparison:

[0137] method m estimate η estimate MSE(m) Confidence interval width (m) MLE 2.1 850 0.52 [1.5,3.2] BPE 1.9 880 0.38 [1.6,2.8] This invention 1.95 865 0.21 [1.7,2.3]

[0138] In summary, this invention reduces MSE by 46%, shortens the confidence interval by 28%, and the parameter estimates are closer to the true values ​​(simulation settings m = 2.0, η = 860).

[0139] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. The scope of protection of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its spirit and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of the present invention.

Claims

1. A method for correcting lifetime distribution curves based on small sample data, characterized in that, Includes the following steps: Step S1: Use the Bootstrap method to perform self-sampling on the original small sample data to generate regenerated samples; Step S2: Based on the regenerated samples, calculate the discrete prior distributions of the two-parameter Weibull distribution parameters m and η using the classical estimation method, where m and η represent the shape parameter and scale parameter of the Weibull distribution, respectively. Step S3: Using the discrete prior distribution as the prior distribution of Bayesian estimation, and combining it with the likelihood function of the regenerated sample, calculate the posterior distribution of the lifetime distribution parameters m and η. Step S4: Determine the final lifetime distribution parameters m and η based on the post-hoc distribution to complete the correction of the lifetime distribution curve.

2. The method for correcting lifetime distribution curves based on small sample data according to claim 1, characterized in that: Specifically, step S1 is as follows: For the original small sample data with a sample size n≤30, perform bootstrap sampling without replacement to generate M sets of regenerated samples, each with a sample size of n.

3. The method for correcting lifetime distribution curves based on small sample data according to claim 2, characterized in that: Step S2 includes, Step S21: Select a group of regenerated samples from the M groups of regenerated samples as the current processing sample group; Step S22: Use the least squares method to determine the parameter range for the current processed regenerated sample group; Step S23: Use the maximum likelihood method to estimate the parameters of the current processed regenerated sample group to generate the discrete joint probability density distribution of m and η; Step S24: Repeat steps S21-S23 until all M groups of regenerated samples have been processed.

4. The method for correcting lifetime distribution curves based on small sample data according to claim 1, characterized in that: The formula for calculating the posterior distribution in step S3 is as follows: P(m,η|data)∝L(data|m,η)·P(m,η) The prior distribution P(m,η) is a constant, which is calculated in step S2.

5. The method for correcting lifetime distribution curves based on small sample data according to claim 1, characterized in that: The original small sample data consists of distributed general data and data-based general data. For distributed general data, the data is processed by directly matching device class parameters with prior distributions. For general data types, the prior distribution is generated using Bootstrap for processing.

6. A lifetime distribution curve correction system based on small sample data, characterized in that, include: The data preprocessing module is used to identify the type of the input raw small sample data; The Bootstrap sampling module is used to generate reproduced samples and calculate discrete prior distributions. The Bayesian estimation module combines the discrete prior distribution with the reproduced sample data to output the posterior distribution parameters. The visualization module is used to plot the corrected lifetime distribution curve and confidence interval.

7. The lifetime distribution curve correction system based on small sample data according to claim 6, characterized in that: The Bayesian estimation module supports parallel computation and can accelerate the solution of posterior distribution parameters through the Monte Carlo method.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the lifetime distribution curve correction method based on small sample data as described in any one of claims 1-5.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the lifetime distribution curve correction method based on small sample data as described in any one of claims 1-5.

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