A method, system, storage medium and device for reliability modeling of frequency equipped equipment

Abstract

The application discloses a kind of with frequency equipment reliability modeling method, system, storage medium and equipment, comprising the following steps: data acquisition step;Evaluation path selection step: judge whether there is effective prior information available for Bayesian evaluation;Classical evaluation path: if it is judged that there is no effective prior information, based on the field test data, likelihood function is constructed using binomial distribution, the maximum likelihood point estimate of reliability is solved, and based on the relationship between the binomial distribution and beta distribution, the reliability one-sided confidence lower limit R L Under the given confidence γ is calculated;Bayesian evaluation path;Result output step: output evaluation path, reliability point estimate and confidence lower limit evaluation result as the quantification basis of the reliability of the frequency equipment task.The application combines with frequency equipment engineering background analysis to provide a basis for further study of offshore cooperative system reliability evaluation based on the applicability of frequency equipment reliability evaluation method based on success-failure data.

Description

Technical Field

[0001] This invention belongs to the field of reliability technology for multi-stage mission systems, and specifically relates to a reliability modeling method, system, storage medium, and device for frequency-using equipment. Background Technology

[0002] Communication equipment, radar equipment, and navigation equipment perform their respective functions during patrol, reconnaissance, and surveillance missions at sea. Under electromagnetic interference, communication and radar equipment may be burned out by strong electromagnetic pulses or experience performance degradation due to strong electromagnetic interference, preventing them from completing their intended tasks. Due to harsh sea conditions, collecting test data during sea trials is often difficult, and in many cases impractical. However, collecting test data on success or failure through direct observation of test results is relatively easy. This type of data reflects the ability of frequency-using equipment to complete its designated tasks under test conditions and can demonstrate the reliability of the equipment. Success / failure data is an important data type in the field sea trials of frequency-using equipment. Research on reliability assessment methods for frequency-using equipment using binomial distribution is applicable to field sea reliability testing. Summary of the Invention

[0003] The primary objective of this invention is to provide a reliability modeling method, system, storage medium, and device for frequency-use equipment, in order to overcome the aforementioned shortcomings of the prior art.

[0004] To achieve this objective, in a basic implementation scheme, the present invention provides a reliability modeling method for frequency-using equipment, characterized by comprising the following steps: S1. Data acquisition steps: Acquire field test data of the frequency-using equipment to be evaluated. The field test data is success or failure data, including the total number of tests n and the number of successes s. S2. Evaluation path selection steps: Determine whether there is valid prior information that can be used for Bayesian evaluation; S3. Classical Evaluation Path: If it is determined that no valid prior information exists, then based on the field test data, a likelihood function is constructed using the binomial distribution to solve for the maximum likelihood point estimate of the reliability. Based on the relationship between the binomial distribution and the β distribution, the one-sided confidence lower limit R of the reliability at a given confidence level γ is calculated. L ; S4. Bayesian evaluation path: If valid prior information is determined to exist, the following sub-steps are executed: S41. Prior information fusion step: Based on historical test data, simulation data, subsystem test data or expert experience of the same / similar equipment, determine the hyperparameters (s0, f0) of the Beta distribution used to characterize the prior distribution of reliability in Bayesian evaluation; S42. Posterior distribution updating step: fusing the prior distribution and the field test data (s, f) by Bayes' theorem to obtain the posterior distribution of reliability R, wherein the posterior distribution is also a Beta distribution, and the hyperparameters thereof are updated to (s0+s, f0+f); S43. Bayesian lower limit solving step: based on the posterior distribution, calculating the Bayesian confidence lower limit R_L of reliability under a given confidence level γ; S5. Result output step: outputting the evaluation path, reliability point estimation and lower confidence limit evaluation results, which serve as a quantitative basis for the task reliability of the frequency-using equipment.

[0005] Further, in step S41, the effective prior information includes at least one of the following: Uniformly formatted pass-fail statistical data generated by homogeneous or similar frequency-using equipment during factory tests or user use; Equivalent pass-fail data converted based on simulation test or subsystem test data; Interval judgments on the success probability of the equipment made by multiple field experts based on experience, which are converted into equivalent pass-fail data after comprehensive analysis; Based on the effective prior information, the moment estimation method or the maximum entropy method is used to determine the hyperparameters (s0, f0) of the Beta prior distribution.

[0006] Further, in step S3, the reliability one-sided confidence lower limit R L is calculated according to the field test results in the following cases: When s=n, that is, all tests are successful, the following formula is adopted: R L =(1- γ )1 / n ; wherein n is the total number of field tests, is the given confidence level; When 0<s<n, based on the relationship between binomial distribution and F distribution, R L is obtained by solving the following equation: 1- γ = i R L n-i ; wherein, is the number of successes in the test, is the number of failures in the test, satisfying , or converted to the quantile of F distribution for calculation by using the above relationship.

[0007] Furthermore, if in step S2 it is determined that there is no valid prior information, but the user specifies that a Bayesian framework is used, then an information-free prior distribution is adopted. In the Bayesian evaluation path of step S4, the prior distribution adopts the uninformative prior defined by the Bayesian hypothesis, the reformulation method, or the Box-Tiao method. The calculation of its posterior distribution is the same as in step S42, and the reliability Bayesian confidence lower bound R is calculated based on the posterior distribution. L ; In step S5, multiple R values ​​obtained based on different uninformed priors are processed. L The values ​​are compared and then selected based on engineering experience to output the final evaluation value.

[0008] Furthermore, in step S5, the result output step further includes a reliability decision sub-step: The calculated lower confidence limit R L Compare with the minimum acceptable value R0 required for frequency-using equipment missions; If R L If R0 ≥ 0, the evaluation conclusion is "reliability meets requirements"; If R L If R < R0, the evaluation conclusion is "reliability does not meet requirements", and the evaluation path used is also output to provide a basis for subsequent engineering decisions on whether to conduct additional tests or adopt prior information.

[0009] Another object of the present invention is to provide a reliability modeling system for frequency-using equipment, used to implement the method, characterized in that it includes: The data input module is configured to receive field test data (n, s) of the frequency-using equipment to be evaluated, input by the user. The prior information management library is used to store and manage structured prior information from historical data, simulation data and expert experience, and can associate and extract valid prior information according to equipment model; The evaluation path control module is connected to the prior information management library and is configured to automatically select to trigger the classic evaluation unit or the Bayesian evaluation unit based on whether it is associated with valid prior information. The classic evaluation unit is configured to process the field test data based on the binomial distribution model and calculate the classic point estimate and confidence lower limit of reliability when there is no effective prior information. The Bayesian evaluation unit is configured to, when valid prior information is available, retrieve the corresponding prior distribution hyperparameters from the prior information management library, fuse them with the field test data, update the posterior distribution, and calculate the Bayesian point estimate and confidence lower bound of the reliability. A result generation and output module, configured to integrate the evaluation path, calculation process and final result, and generate an evaluation report, wherein the report includes the adopted evaluation method, point estimate, lower confidence limit and comparison conclusion with a preset threshold.

[0010] Further, the classical evaluation unit has built-in lower confidence limit calculation logics for three cases; The Bayesian evaluation unit is internally provided with a prior distribution hyperparameter analysis module, a posterior distribution updating calculation module and a module for solving a lower confidence limit based on a Beta distribution cumulative distribution function; The three cases refer to the calculation of one-sided lower confidence limit R L , which is divided into the following cases according to field test results: When s=n, that is, all tests are successful, the following formula is adopted: R L =(1- γ )1 / n ; When 0<s<n, based on the relationship between binomial distribution and F distribution, R is obtained by solving the following equation L : 1- γ = i R L n-i or convert it into quantiles of F distribution for calculation by using said relationship.

[0011] Further, the prior information management library is a relational database, wherein each prior information record is associated with equipment model, information type, information intensity, source credibility weight and equivalent (s0, f0) data; the evaluation path control module sets a threshold according to the source credibility weight and information intensity to judge whether the prior information is "valid".

[0012] Another object of the present invention is to provide a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the method steps according to any one of claims 1 to 5.

[0013] Another object of the present invention is to provide a computing device comprising a memory, a processor and a computer program stored in the memory and operable on the processor, wherein the processor, when executing the program, implements the method steps according to any one of claims 1 to 5.

[0014] Beneficial effects of the present invention are: First, a comprehensive reliability assessment system integrating multi-source information, suitable for the characteristics of frequency-using equipment, was established, solving the assessment challenge under small sample conditions. This invention creatively constructs a dual-path adaptive fusion assessment framework combining "classical assessment" and "Bayesian assessment." When effective prior information is lacking, a rigorous classical method is employed; when available historical, simulation, or expert information exists, the Bayesian method quantifies and fuses the prior information in a Beta distribution. This organically combines "dead" field test data with "live" multi-source prior knowledge, significantly improving the accuracy and reliability of reliability assessment results under small sample test conditions. In cases with only a small number of field tests but a large amount of high-confidence simulation data, this method can obtain a tighter (i.e., higher) reliability confidence lower bound than simple field data assessment, thereby reducing unnecessary and costly additional tests while ensuring reliability, and is expected to save more than 30% of test costs.

[0015] Second, it achieves the structured and quantitative integration of prior information, enhancing the scientific rigor and consistency of the evaluation process. This invention proposes specific methods (such as moment estimation and maximum entropy method) for parsing and quantifying multiple types of prior information into Beta distribution hyperparameters (s0, f0). This allows fuzzy expert judgments or heterogeneous experimental data from different sources to be uniformly and systematically encoded into probability distributions. This process makes tacit knowledge explicit and subjective experience objectified, not only enabling Bayesian evaluation but also ensuring the standardization of processes and the comparability of results when different evaluators evaluate different batches of equipment, greatly improving the standardization level of reliability assessment work.

[0016] Third, it provides an engineering decision-making process covering all scenarios, enhancing the practicality and guidance of the evaluation results. The final output of the evaluation process of this invention includes not only point estimates and confidence lower limits of reliability, but also a direct comparison conclusion with the minimum acceptable value R0 of the task requirements ("satisfied" or "unsatisfied"), and clearly indicates the evaluation path used (classical or Bayesian). This provides a clear "yes / no" input for equipment acceptance, type approval, and deployment decisions, solving the long-standing problem of handling ambiguity in engineering applications. When the evaluation conclusion is "unsatisfied," the identified evaluation path can guide engineering decisions in reverse: if it is unsatisfied based on the classical method, additional experiments may be needed; if it is unsatisfied based on the Bayesian method that incorporates weaker prior information, it may indicate the need to re-examine or find stronger prior evidence. This makes the evaluation work form a closed loop from "analysis" to "decision" to "action."

[0017] Fourth, an accumulative and evolvable reliability knowledge base has been constructed to support the systematized development and intelligent evaluation of equipment models. By structurally storing prior information as a database of associated equipment models, information types, and equivalent success and failure data, this invention essentially constructs a continuously growing reliability knowledge base for frequently used equipment. This knowledge base is constantly enriched as the number of models under development increases. When evaluating a new model, the system can automatically match and recommend the historical prior information with the highest similarity, realizing "experience from older equipment empowering the evaluation of new equipment." This marks a leap from "one-time evaluation" to "knowledge-based intelligent and systematized evaluation," significantly improving the starting point and efficiency of reliability evaluation for newly developed equipment.

[0018] Fifth, the evaluation process is automated and made more efficient through software and systematization. The method of this invention is software-based into an evaluation system integrating data input, path determination, automatic calculation, and report generation functions. Users only need to input field test data and select / confirm prior information; the system can automatically select the optimal evaluation path, complete all complex calculations, and generate a standardized evaluation report. This frees reliability engineers from tedious mathematical calculations, allowing them to focus more on engineering judgments, reducing the manual time spent on a single evaluation from hours to minutes, and completely eliminating calculation errors. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a schematic diagram illustrating the reliability definition of frequency-using devices constructed for embodiments of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Please refer to Figure 1 and Figure 2 The purpose of this invention is to provide a reliability modeling method for frequency-using equipment, comprising the following steps: S1. Data acquisition steps: Acquire field test data of the frequency-using equipment to be evaluated. The field test data is success or failure data, including the total number of tests n and the number of successes s. S2. Evaluation path selection steps: Determine whether there is valid prior information that can be used for Bayesian evaluation; S3. Classical Evaluation Path: If it is determined that no valid prior information exists, then based on the field test data, a likelihood function is constructed using the binomial distribution to solve for the maximum likelihood point estimate of the reliability. Based on the relationship between the binomial distribution and the β distribution, the one-sided confidence lower limit R of the reliability at a given confidence level γ is calculated. L ; S4. Bayesian evaluation path: If valid prior information is determined to exist, the following sub-steps are executed: S41. Prior information fusion step: Based on historical test data, simulation data, subsystem test data or expert experience of the same / similar equipment, determine the hyperparameters (s0, f0) of the Beta distribution used to characterize the prior distribution of reliability in Bayesian evaluation; S42. Posterior distribution update step: The prior distribution and the field test data (s, f) are fused using Bayes' theorem to obtain the posterior distribution of the reliability R. The posterior distribution is also a Beta distribution, and its hyperparameters are updated to (s0+s, f0+f). S43. Steps for solving the Bayesian lower bound: Based on the posterior distribution, calculate the reliability Bayesian confidence lower bound R at a given confidence level γ. L ; S5. Results Output Steps: Output the evaluation path, reliability point estimation, and confidence lower limit evaluation results as a quantitative basis for the reliability of the frequency-using equipment mission.

[0023] The technical solution of the present invention will now be described through specific embodiments.

[0024] Step 1: Defining the Reliability of Frequency-Using Equipment The reliability of frequency-using equipment can be defined in two ways: Firstly, frequency-using equipment operates in complex electromagnetic environments and needs to perform specified functions according to task requirements. These functions are characterized by performance indicators and are affected by the electromagnetic environment. If a drop in equipment performance indicators to a threshold or below is considered a "failure," then the reliability of frequency-using equipment in an electromagnetic environment refers to its ability to perform its specified functions within a specified electromagnetic environment and time period. Its quantitative measure can be expressed as probability. For example... Figure 2 As shown on the left, when setting electromagnetic interference The following is a repeated test on one device. Next time, obtain Performance metrics data Using probability distribution Fitting. Obtaining performance metric thresholds. Afterwards, if If the frequency-using equipment is "working normally", then the reliability of the frequency-using equipment is: in, This indicates that when the performance threshold is At that time, the reliability of frequency-using equipment, , is a random variable Value greater than threshold The probability, For performance indicators The probability density function.

[0025] Secondly, such as Figure 2 As shown on the right, with a fixed signal strength Under certain conditions, examine the distribution of interference thresholds when the equipment is in a critical state between "normal" and "fault". Given a signal strength... The equipment is working normally. Adjust interference. The intensity of the interference puts the equipment in a critical state between operation and failure; at this point, the interference level... This is the interference threshold. Repeat. In this experiment, the frequency-using equipment was observed. The results of this experiment yielded... Critical interference threshold , interference threshold Using probability distribution Fitting to obtain the interference threshold of frequency-using equipment The distribution function. Determine the electromagnetic environment stress level J of the frequency-using equipment based on the scenario and task. The interference of the electromagnetic environment in which the frequency-using equipment is located. Greater than the threshold When frequency-using equipment cannot perform its intended function and is in a "fault" state, interference occurs. Less than the threshold At this time, the frequency-using equipment can perform its specified functions and is in a "normal" state. Under this condition, the reliability of the frequency-using equipment is defined as follows: Step 2: Determine the functions that the main frequency-using equipment needs to perform and the success or failure criteria. In practical tasks, the main frequency-using equipment needs to perform the following functions and the success or failure criteria are as follows: Radar equipment: For radar, shore-based systems often deploy large phased array radars for searching and tracking targets. These radars are required to be able to detect targets within a certain range. If they cannot search for or stably track targets within a certain range, the equipment is considered to be faulty. GJB 2944-97 stipulates that if, after jamming, a track cannot be established within a certain range, the track is interrupted, or the established track is incorrect, then the jamming is considered effective within that range.

[0026] Communication equipment: All information in the entire system needs to be transmitted to each other through communication equipment. The connection should be guaranteed to be normal over a certain distance. When the communication distance, packet loss rate, and latency of the communication equipment do not meet the requirements, the equipment can be judged to be faulty.

[0027] Navigation equipment: Navigation equipment must be powered on at all times during a mission to acquire a position. If the position accuracy output by the receiver does not meet the requirements, the equipment can be considered to have failed.

[0028] Step 3: Compile success and failure reliability data: This study considers various types of frequency-using equipment, disregarding their specific performance indicators and focusing solely on their ability to complete the task. It then analyzes individual frequency-using devices... Secondary test or The devices conduct experiments simultaneously, treating each experiment as an independent Bernoulli trial, with two states: 1 (success) and 0 (failure).

[0029] Will The number of times the frequency-controlled equipment successfully completed its mission function in this experiment Number of failures As a basis for equipment reliability assessment, the general form of reliability data is... ,use express The number of times the frequency-controlled equipment successfully performs the mission's specified functions in this test will be... If treated as a random variable, then Follows a binomial distribution. in, These are the Newtonian binomial coefficients, binomial distribution parameters. It is the probability that the frequency-using equipment will successfully complete the task in a single test, that is, the reliability of the frequency-using equipment task.

[0030] Step 4: Conduct reliability assessments of frequency-using equipment using multiple methods: Step 4.1: Classical Reliability Assessment Method for Frequency-Using Equipment Based on Binomial Distribution The frequency-controlled equipment underwent reliability testing, and success / failure test data were obtained. , The number of successes in the experiment. Given the total number of trials, we obtain the likelihood function. Taking the logarithm of both sides of the above equation, we get: right Differentiating the equation and setting the result to zero, we obtain the likelihood equation: Solving the above equation yields the reliability. The maximum likelihood point estimate, Total number of trials Reliability at a given time With the number of successful trials Increase and grow, for experimental data Given a confidence level Confidence lower limit for: In the formula: This represents the number of failed trials.

[0031] when hour, ;when hour, ;when When the time is right, use the following method to solve it. Because the binomial distribution and The distribution has the following relationship: In the formula: Since it is a Beta function, we can obtain: In the formula: .in Let be the two shape parameters of the Beta distribution, both of which are positive real numbers.

[0032] and Distribution quantiles and The distribution quantiles also have the following relationship: in, Let be the two shape parameters of the Beta distribution (both positive numbers). In success-or-failure data scenarios, is typically taken as . (Number of successes) (Increase the number of failures by 1).

[0033] From this, we can deduce... The solution formula is: In the formula The quantiles of the distribution can be obtained by looking up a table.

[0034] Step 4.2: Bayesian Reliability Assessment Method for Frequency-Using Equipment Based on Binomial Distribution To address the sparsity of experimental data, the Bayes assessment method integrates historical information, information on similar products, and domain expert experience by adopting a prior distribution to update the post-test distribution, thereby expanding the amount of information and improving the accuracy of reliability assessment results for frequency-using equipment. This method has been widely used in reliability engineering.

[0035] If it is known that the frequency-using equipment has success and failure test data. When using the Bayes method to assess the reliability of success-or-failure products, the Beta distribution can be used as the prior distribution of the reliability R. The probability density function of the Beta distribution is... The two test data are , The probability of an experiment failing is the number of failures. Then reliability The posterior probability density function is obtained from Bayes' theorem: The reliability can be obtained from the above formula. The point estimate and lower confidence limit are as follows: In the formula: Let be the distribution function of the prior Beta distribution. and These are the hyperparameters of the prior distribution, obtained from prior information. In engineering, hyperparameters... and This can be interpreted as: This can be approximated as the number of successful equipment tests. This can be approximated as the number of equipment test failures. In engineering, various prior information, such as equipment development and testing information (e.g., simulation, subsystem testing), expert experience information, or information on similar equipment, is generally used to determine hyperparameters in order to obtain the prior distribution of the equipment success rate (i.e., the success rate level).

[0036] (1) Prior information is available Various frequency-using equipment undergoes extensive verification tests during its development. Similar or identical equipment also generates a wealth of historical data from its use. In addition, there is the experience and information from industry experts. All of this data can serve as prior information for equipment reliability assessment. For reliability assessment of products with varying success or failure probabilities, one can focus on the success and failure statistics from manufacturers' tests and user usage of similar or identical products, as well as experts' experienced judgments on the probability of product success or failure. and The data.

[0037] Then, based on the obtained field test data The posterior distribution of reliability can be obtained according to the formula, and then the lower confidence limit of the reliability of the frequently used equipment can be derived from the formula. .

[0038] (2) No prior information is available When there is no prior experience or historical information to refer to, i.e., when prior information about the frequency-using equipment cannot be obtained, it is necessary to assess the reliability of the frequency-using equipment in the absence of prior information.

[0039] 1) Common Reliability Uninformed prior distribution There are three types: ①Bayes hypothesis That is, the parameter is of Distribution, often denoted as .

[0040] ②reformation method This prior density is generalized and is often denoted as . .

[0041] ③Box-Tiao method This prior density is also generalized and is often denoted as... .

[0042] 2) Obtaining on-site success and failure test data In the case of a distribution without prior information, the reliability is... Bayes' precise lower bound The solution is as follows: ① Regarding the Bayes hypothesis, we have in It is a Beta function with incomplete regularization.

[0043] ② Regarding the reformulation method, there are ③ Regarding the Box-Tiao method, there are The quantiles of the F-distribution can be used to represent this. In the formula: It has degrees of freedom. F-distribution Quantiles can be found in a table.

[0044] Of the three uninformative prior probability density functions mentioned above, This is not a normal density function and cannot be applied when the number of successes or failures in a field experiment is zero. Based on the aforementioned uninformed prior distribution density function, and using the obtained field experiment data... The reliability can be obtained. The posterior distribution is then used to derive the lower confidence limit of the reliability of the equipment task based on the formula. Based on engineering practice and with specific analysis of each situation, the following three types of reliability confidence limits were obtained. Make a choice.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Those skilled in the art should understand that modifications can be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reliability modeling method for frequency-using equipment, characterized in that, Includes the following steps: S1. Data acquisition steps: Acquire field test data of the frequency-using equipment to be evaluated. The field test data is success or failure data, including the total number of tests n and the number of successes s. S2. Evaluation path selection steps: Determine whether there is valid prior information that can be used for Bayesian evaluation; S3. Classical Evaluation Path: If it is determined that no valid prior information exists, then based on the field test data, a likelihood function is constructed using the binomial distribution to solve for the maximum likelihood point estimate of the reliability. Based on the relationship between the binomial distribution and the β distribution, the one-sided confidence lower limit R of the reliability at a given confidence level γ is calculated. L ; S4. Bayesian evaluation path: If valid prior information is determined to exist, the following sub-steps are executed: S41. Prior information fusion step: Based on historical test data, simulation data, subsystem test data or expert experience of the same / similar equipment, determine the hyperparameters (s0,f0) of the Beta distribution used to characterize the prior distribution of reliability in Bayesian evaluation; S42. Posterior distribution update step: The prior distribution and the field test data (s, f) are fused using Bayes' theorem to obtain the posterior distribution of the reliability R. The posterior distribution is also a Beta distribution, and its hyperparameters are updated to (s0+s,f0+f). S43. Steps for solving the Bayesian lower bound: Based on the posterior distribution, calculate the reliability Bayesian confidence lower bound R at a given confidence level γ. L ; S5. Results Output Steps: Output the evaluation path, reliability point estimation, and confidence lower limit evaluation results as a quantitative basis for the reliability of the frequency-using equipment mission.

2. The method according to claim 1, characterized in that, In step S41, the valid prior information includes at least one of the following: Success and failure statistics generated in a uniform format during manufacturer testing or user use of the same or similar frequency-using equipment; Equivalent success or failure data calculated based on simulation test or subsystem test data; Based on the experience of multiple experts in the field, the range of success probability of equipment was judged and transformed into equivalent success and failure data after comprehensive analysis; Based on the effective prior information, the hyperparameters (s0, f0) of the Beta prior distribution are determined using the method of moments or the maximum entropy method.

3. The method according to claim 1, characterized in that, In step S3, the reliability one-sided confidence lower limit R L The calculations, based on the results of field tests, are divided into the following categories: When s=n, meaning all are successful, the formula is used: R L =(1- γ )1 / n ;in n This represents the total number of field tests. For a given confidence level; When 0<s<n, based on the relationship between the binomial distribution and the F distribution, R is obtained by solving the following equation L : 1- γ = i R L n-i ； in, The number of successes in the experiment. The number of failures in the experiment, satisfying... , Alternatively, the relationship can be converted into the quantiles of the F-distribution for calculation.

4. The method according to claim 1, characterized in that, If in step S2 it is determined that there is no valid prior information, but the user specifies that a Bayesian framework is used, then the no-information prior distribution is used. In the Bayesian evaluation path of step S4, the prior distribution adopts the uninformative prior defined by the Bayesian hypothesis, the reformulation method, or the Box-Tiao method. The calculation of its posterior distribution is the same as in step S42, and the reliability Bayesian confidence lower bound R is calculated based on the posterior distribution. L ; In step S5, multiple R values ​​obtained based on different uninformed priors are processed. L The values ​​are compared and then selected based on engineering experience to output the final evaluation value.

5. The method according to claim 1 or 4, characterized in that, In step S5, the result output step further includes a reliability decision sub-step: The calculated lower confidence limit R L Compare with the minimum acceptable value R0 required for frequency-using equipment missions; If R L If R ≥ R0, the evaluation conclusion is "reliability meets requirements"; If R L If R < R0, the evaluation conclusion is "reliability does not meet requirements", and the evaluation path used is also output to provide a basis for subsequent engineering decisions on whether to conduct additional tests or adopt prior information.

6. A reliability modeling system for frequency-using equipment, used to implement the method according to any one of claims 1-5, characterized in that, include: The data input module is configured to receive field test data (n, s) of the frequency-using equipment to be evaluated, input by the user. The prior information management library is used to store and manage structured prior information from historical data, simulation data and expert experience, and can associate and extract valid prior information according to equipment model; The evaluation path control module is connected to the prior information management library and is configured to automatically select to trigger the classic evaluation unit or the Bayesian evaluation unit based on whether it is associated with valid prior information. The classic evaluation unit is configured to process the field test data based on the binomial distribution model and calculate the classic point estimate and confidence lower limit of reliability when there is no effective prior information. The Bayesian evaluation unit is configured to, when valid prior information is available, retrieve the corresponding prior distribution hyperparameters from the prior information management library, fuse them with the field test data, update the posterior distribution, and calculate the Bayesian point estimate and confidence lower bound of the reliability. The results generation and output module is configured to integrate the evaluation path, calculation process and final results to generate an evaluation report. The report includes the evaluation method used, point estimates, confidence limits and comparison conclusions with preset thresholds.

7. The system according to claim 6, characterized in that: The classic evaluation unit has built-in confidence lower limit calculation logic for three cases; The Bayesian evaluation unit has a built-in module for analyzing the hyperparameters of the prior distribution, a module for calculating the update of the posterior distribution, and a module for solving the confidence lower limit based on the cumulative distribution function of the Beta distribution. The three cases represent the one-sided confidence lower limit R of reliability. L The calculations, based on the results of field tests, are divided into the following categories: When s=n, meaning all are successful, the formula is used: R L =(1- γ )1 / n ; When 0<s<n, based on the relationship between the binomial distribution and the F distribution, R is obtained by solving the following equation L : 1- γ = i R L n-i ； Alternatively, the relationship can be converted into the quantiles of the F-distribution for calculation.

8. The system according to claim 6, characterized in that, The prior information management database is a relational database, in which each prior information record is associated with equipment model, information type, information strength, source credibility weight, and equivalent (s_0, f_0) data; the evaluation path control module sets a threshold based on the source credibility weight and information strength to determine whether the prior information is "valid".

9. 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 method steps as described in any one of claims 1-5.

10. A computing 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 method steps as described in any one of claims 1-5.

Images