Product Reliability Demonstration Test Method Based on Two-Stage Non-Failure Data

Abstract

The present application relates to a product reliability identification test method based on two-stage zero-failure data. The method comprises: for a complex product that is divided into a first stage and a second stage in the product development stage, the first stage product test data is converted into second stage test data by a conversion factor, and then the second stage test data is used as a priori information of the product, and the prior distribution and posterior distribution of the second stage product failure rate are calculated by the Bayesian method, and then the production risk and user risk of the product are calculated based on the prior distribution and the posterior distribution, and finally the reliability of the complex product is identified according to the reliability identification test plan determined by the production risk and the user risk. The adoption of this method can make full use of the failure data and zero-failure data in the product development stage, so that the credibility of the reliability identification test is higher, and through the two types of risks, the selection of the reliability identification test plan is more flexible and has a wider range of use.

Description

Technical Field

[0001] The present application relates to the technical field of reliability identification, and in particular to a product reliability identification test method based on two-stage zero-failure data. Background Art

[0002] Reliability qualification testing is a test conducted during the product development phase to verify whether a product meets reliability requirements. The test results provide a basis for product status assessment. Currently, products that play a vital role in people's lives, such as satellites, automobiles, and drones, are complex products with numerous components, complex processes, and high costs. Reliability requirements for these complex products are increasingly high, making reliability qualification testing essential during the development phase. However, with technological advancements and process maturity, the reliability of complex products is increasing, resulting in a decreasing probability of product failures during development phase testing, and even the generation of zero-failure data during the development phase. Traditional reliability qualification test design relies primarily on failure data from product tests. However, when zero-failure data is generated during development phase testing, traditional test design methods become ineffective. Therefore, research on test qualification design for complex products that generate zero-failure data during development phase testing is urgent. Summary of the Invention

[0003] Based on this, it is necessary to provide a product reliability identification test method based on two-stage zero-failure data, which can use zero-failure data to design reliability identification test plans for complex products to address the above technical problems.

[0004] A product reliability evaluation test method based on two-stage zero-failure data, the method comprising:

[0005] For complex products that are divided into the first and second phases during the product development phase, obtain test data for the first phase product and the second phase product, calculate an estimated failure rate for the first phase product based on the first phase product test data, and calculate a failure probability for the second phase product based on the second phase product test data; where failure data exists for the first phase but not for the second phase;

[0006] A conversion factor is calculated based on the estimated failure rate of the first-stage product and the failure probability of the second-stage product, and the first-stage product test data is converted into the second-stage test data using the conversion factor. The second-stage product failure rate estimate is calculated based on the converted second-stage test data to obtain the second-stage product failure rate estimate. The second-stage product failure rate estimate is used as prior information, and the prior distribution and posterior distribution of the second-stage product failure rate are calculated based on the Bayesian method.

[0007] Calculations are performed based on the prior distribution and posterior distribution of the second-stage product failure rate to determine the production risk and user risk of the complex product. Calculations are performed based on the production risk, user risk, and development requirements for the product failure rate to determine the test cutoff time and test pass conditions for the reliability identification test. The reliability of the complex product is identified based on the reliability identification test plan determined based on the test cutoff time and test pass conditions.

[0008] In one embodiment, the product life of a complex product follows an exponential distribution with a product failure rate of λ, expressed as f(t)=λe -λt , where f(t) is the product life and t represents time.

[0009] In one embodiment, the first phase product test data includes the first phase test sample size, the first phase failure number, the first phase test censoring time, and the first phase failure occurrence time;

[0010] The estimated failure rate of the first-phase products is calculated based on the test data of the first-phase products, including:

[0011] According to the first-stage test sample size, the number of failures in the first stage, the first-stage test censoring time, and the first-stage failure occurrence time, the maximum likelihood estimate of the first-stage product failure rate is obtained, which is expressed as

[0012]

[0013] Among them, L(λ a |t i ) represents the maximum likelihood estimate of the first-stage product failure rate, λ a represents the product failure rate in the first stage, n1 is the test sample size in the first stage, r is the number of failures in the first stage, t a is the censoring time of the first stage of the experiment, t i is the time of occurrence of the i-th fault in the first stage, i = 1, 2, …, r;

[0014] By solving the maximum likelihood estimate of the first-stage product failure rate, the estimated value of the first-stage product failure rate is obtained, which is expressed as

[0015]

[0016] In one embodiment, the Phase II product trial data includes the Phase II trial sample size and the Phase II trial censoring time;

[0017] The failure probability of the second-stage product is calculated based on the second-stage product test data, including:

[0018] According to the second stage test sample size n2, the second stage product failure probability is calculated and expressed as

[0019] In one embodiment, calculating a conversion factor based on the estimated failure rate of the first-stage product and the failure probability of the second-stage product, and converting the first-stage product test data into the second-stage test data using the conversion factor includes:

[0020] By considering the life characteristics of the product itself, the estimated failure rate of the first stage product The numerator of the conversion factor is expressed as

[0021] The conversion factor is calculated based on p1 and the second-stage product failure probability p2. The conversion factor is expressed as The first-stage product test data is converted into the second-stage test data through the conversion factor C, which is expressed as

[0022] t j →t 1j =t j C

[0023] Among them, t j Expressed as the first phase product test data, t 1j This is the data from the second phase of the experiment.

[0024] In one embodiment, the estimated value of the second-stage product failure rate is obtained by calculating based on the converted second-stage test data, including:

[0025] According to the second phase test data 1j Calculate and obtain the maximum likelihood estimate of the second-stage product failure rate, which is expressed as

[0026]

[0027] Among them, L(λ b |t k ) represents the maximum likelihood estimate of the second-stage product failure rate, λ b represents the product failure rate in the second stage, t k is the expected failure time of the kth product, t 1i represents the second-stage test data transformed from the first-stage i-th product test data, t b This is the censoring time for the second phase of the trial;

[0028] By solving the maximum likelihood estimate of the second-stage product failure rate, the estimated value of the second-stage product failure rate is obtained, which is expressed as

[0029]

[0030] In one embodiment, the estimated value of the second-stage product failure rate is used as prior information, and a calculation is performed according to the Bayesian method to obtain the prior distribution and posterior distribution of the second-stage product failure rate, including:

[0031] The estimated value of the second-stage product failure rate is used as prior information to calculate the prior distribution mean and the second-order moment of the prior distribution of the second-stage product failure rate according to the Bayesian method;

[0032] The gamma distribution is used to fit the prior distribution of the second-stage product failure rate, and the shape parameters of the gamma distribution are calculated based on the prior distribution mean and the prior distribution second-order moment. and scale parameters According to the shape parameters and scale parameters Determine the prior distribution of the second-stage product failure rate as

[0033] According to the prior distribution of product failure rate in the second stage Calculate the time t′ when the next product failure occurs and obtain the posterior distribution of the second-stage product failure rate as follows:

[0034] In one embodiment, the calculation is performed based on the prior distribution and the posterior distribution of the product failure rate in the second stage to determine the production risk and the user risk of the complex product, including:

[0035] For complex products, the hypothesis test is H0:λ<λ0; H1:λ>λ1, where H0 is the null hypothesis, H1 is the alternative hypothesis, λ0 is the upper limit of the product failure rate, and λ1 is the lower limit of the product failure rate;

[0036] According to the prior distribution and posterior distribution of the second-stage product failure rate, the probability that the second-stage product failure rate has reached λ1 and is rejected by the reliability identification test is taken as the product manufacturer risk, and the probability that the product failure rate is higher than λ0 and passes the reliability identification test is taken as the product user risk. The manufacturer risk and user risk are expressed as

[0037]

[0038]

[0039] Among them, R 生产方 is the producer risk, R 使用方 is the user's risk, T is the test cut-off time of the reliability identification test, It represents the probability of event K occurring for a test with a sample size of N. Event K is that all products in the test pass the reliability identification test. ri It represents the failure time of the i-th product. Since the samples in the same batch are the same product with the same life characteristics, the expected failure time of the product is t r1 =t r2 =...=t rN =t r .

[0040] In one embodiment, the reliability evaluation test cutoff time and test pass conditions are determined by calculating the production risk, the user risk, and the product failure rate development requirements. The reliability of the complex product is evaluated based on the reliability evaluation test plan determined based on the test cutoff time and test pass conditions, including:

[0041] Calculate the production risk, user risk and product failure rate requirements to determine the expected failure time of product development based on the production risk requirements or user risk requirements when the product failure rate meets the development requirements. b Determine the test truncation time of the reliability identification test as T;

[0042] Within the test truncation time, the test passing condition of the reliability identification test is selected as zero failure number. According to the test truncation time and the test passing condition, the reliability identification test plan of the complex product is determined to be (T, 0), and the reliability of the complex product is identified through the reliability identification test plan (T, 0).

[0043] The above-mentioned product reliability evaluation test method based on two-stage zero-failure data is aimed at complex products that are divided into the first and second stages during the product development phase. The first-stage product test data is obtained, and the first-stage product test data is converted into the second-stage test data through a conversion factor. The second-stage test data is then used as prior information of the product, and the prior distribution and posterior distribution of the second-stage product failure rate are calculated through the Bayesian method. The manufacturer risk and user risk of the product are then calculated based on the prior distribution and posterior distribution. Finally, the reliability of the complex product is evaluated based on the reliability evaluation test plan determined by the manufacturer risk and user risk. The use of this method can fully utilize the failure data and zero-failure data in the product development phase, making the reliability evaluation test more credible. Moreover, by considering the manufacturer risk and user risk, the selection of the reliability evaluation test plan is more flexible. The appropriate reliability evaluation test plan can be selected according to the specific development requirements, and the scope of application is wider. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 1 is a flow chart of a product reliability evaluation test method based on two-stage zero-failure data in one embodiment;

[0045] Figure 2 This is a graph showing the relationship between producer risk and user risk over time in one embodiment. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0047] In one embodiment, Figure 1 As shown, a product reliability qualification test method based on two-stage zero-failure data is provided, including the following steps:

[0048] Step S1, for a complex product that is divided into the first stage and the second stage in the product development stage, obtain the first stage product test data and the second stage product test data, calculate the first stage product failure rate estimate based on the first stage product test data, and calculate the second stage product failure probability based on the second stage product test data; wherein, failure data exists in the first stage, but no failure data exists in the second stage.

[0049] It is understood that failure data, also known as fault data, is generated during the first phase of product development, while non-failure data is generated during the second phase. Both phases are conducted using a timed truncation test.

[0050] Step S2: Calculate a conversion factor based on the estimated failure rate of the first-stage product and the failure probability of the second-stage product, and convert the first-stage product test data into second-stage test data using the conversion factor. Perform calculations based on the converted second-stage test data to obtain the estimated failure rate of the second-stage product. Use the estimated failure rate of the second-stage product as prior information and perform calculations based on the Bayesian method to obtain the prior distribution and posterior distribution of the second-stage product failure rate.

[0051] It is understandable that traditional reliability assessment methods rely on failure data from product tests to evaluate product reliability. However, since no-failure data is generated in the second phase, it is impossible to directly obtain the reliability of the second-phase product using traditional reliability assessment methods. In addition, since the life characteristics of products at different development stages are related for the same product, the data from the previous phase can often provide effective information for the evaluation of the later phase. Therefore, this application adopts a data conversion method, using a conversion factor to convert the first-phase product test data into second-phase test data, and then uses the converted second-phase test data to evaluate product reliability. This not only integrates the test information of the two phases, but also makes good use of the no-failure data of the second phase.

[0052] Step S3, calculate based on the prior distribution and posterior distribution of the product failure rate in the second stage, determine the production risk and user risk of the complex product, calculate based on the production risk and user risk and the development requirements of the product failure rate, determine the test cut-off time and test pass conditions of the reliability identification test, and identify the reliability of the complex product based on the reliability identification test plan determined by the test cut-off time and test pass conditions.

[0053] In one embodiment, the product life of a complex product follows an exponential distribution with a product failure rate of λ, expressed as f(t)=λe -λt , where f(t) is the product life, t represents time, and the reliability of the product at time t is R(t) = e -λt .

[0054] In one embodiment, the first phase product test data includes the first phase test sample size, the first phase failure number, the first phase test censoring time, and the first phase failure occurrence time;

[0055] The estimated failure rate of the first-phase products is calculated based on the test data of the first-phase products, including:

[0056] According to the first-stage test sample size, the number of failures in the first stage, the first-stage test censoring time, and the first-stage failure occurrence time, the maximum likelihood estimate of the first-stage product failure rate is obtained, which is expressed as

[0057]

[0058] Among them, L(λ a |t i ) represents the maximum likelihood estimate of the first-stage product failure rate, λ a represents the product failure rate in the first stage, n1 is the test sample size in the first stage, r is the number of failures in the first stage, t a is the censoring time of the first stage of the experiment, ti is the time of occurrence of the i-th fault in the first stage, i=1,2,…,r, and when the time of occurrence of the fault in the first stage is t1, t2,…, t r The censoring time of the first stage experiment is

[0059] By solving the maximum likelihood estimate of the first-stage product failure rate, the estimated value of the first-stage product failure rate is obtained, which is expressed as

[0060]

[0061] In one embodiment, the Phase II product trial data includes the Phase II trial sample size and the Phase II trial censoring time;

[0062] The failure probability of the second-stage product is calculated based on the second-stage product test data, including: calculating based on the second-stage test sample size n2, and obtaining the failure probability of the second-stage product, expressed as

[0063] In one embodiment, calculating a conversion factor based on the estimated failure rate of the first-stage product and the failure probability of the second-stage product, and converting the first-stage product test data into the second-stage test data using the conversion factor includes:

[0064] By considering the life characteristics of the product itself, the estimated failure rate of the first stage product The numerator of the conversion factor is expressed as

[0065] The conversion factor is calculated based on p1 and the second-stage product failure probability p2. The conversion factor is expressed as The first-stage product test data is converted into the second-stage test data through the conversion factor C, which is expressed as

[0066] t j →t 1j =t j C

[0067] Among them, t j Expressed as the first phase product test data, t 1j This is the data from the second phase of the experiment.

[0068] It can be understood that the conversion factor not only takes into account the product test data of each stage of testing, but also takes into account the life characteristics of the product itself.

[0069] In one embodiment, the estimated value of the second-stage product failure rate is obtained by calculating based on the converted second-stage test data, including:

[0070] According to the second phase test data1j Calculate and obtain the maximum likelihood estimate of the second-stage product failure rate, which is expressed as

[0071]

[0072] Among them, L(λ b |t k ) represents the maximum likelihood estimate of the second-stage product failure rate, λ b represents the product failure rate in the second stage, t k is the expected failure time of the kth product, t 1i represents the second-stage test data transformed from the first-stage i-th product test data, t b This is the censoring time for the second phase of the trial;

[0073] By solving the maximum likelihood estimate of the second-stage product failure rate, the estimated value of the second-stage product failure rate is obtained, which is expressed as

[0074]

[0075] In one embodiment, the estimated value of the second-stage product failure rate is used as prior information, and a calculation is performed according to the Bayesian method to obtain the prior distribution and posterior distribution of the second-stage product failure rate, including:

[0076] First, the estimated value of the second-stage product failure rate is calculated as prior information according to the Bayesian method, and the prior distribution mean and the second-order moment of the second-stage product failure rate are obtained, which are expressed as

[0077]

[0078]

[0079] Where u is a constant, is the prior distribution of product failure rate in the second stage.

[0080] Then, the gamma distribution is used to fit the prior distribution of the second-stage product failure rate, and the prior distribution mean E(λ b ) and the second-order moment of the prior distribution E(λ b 2 ) to calculate the shape parameters of the gamma distribution and scale parameters According to the shape parameters and scale parameters Determine the prior distribution of the second-stage product failure rate as Among them, the shape parameter and scale parameters The solution process is expressed as:

[0081]

[0082] Right now

[0083]

[0084] According to the above formula, the shape parameters can be solved and scale parameters The estimated value of is:

[0085]

[0086]

[0087] in, Finally, according to the prior distribution of the second-stage product failure rate Calculate the time t′ when the next product failure occurs and obtain the posterior distribution of the second-stage product failure rate as follows:

[0088] In one embodiment, the calculation is performed based on the prior distribution and the posterior distribution of the product failure rate in the second stage to determine the production risk and the user risk of the complex product, including:

[0089] For complex products, the hypothesis test is H0:λ<λ0; H1:λ<λ1, where H0 is the null hypothesis, H1 is the alternative hypothesis, λ0 is the upper limit of the product failure rate, λ1 is the lower limit of the product failure rate, and the test identification ratio is d, and d=λ1 / λ0;

[0090] According to the prior distribution and posterior distribution of the second-stage product failure rate, the probability that the second-stage product failure rate has reached λ1 and is rejected by the reliability identification test is taken as the product manufacturer risk, and the probability that the product failure rate is higher than λ0 and passes the reliability identification test is taken as the product user risk. The manufacturer risk and user risk are expressed as

[0091]

[0092]

[0093] Among them, R 生产方 is the producer risk, R 使用方 is the user's risk, T is the test cut-off time of the reliability identification test, It represents the probability of event K occurring for a test with a sample size of N. Event K is that all products in the test pass the reliability identification test. riIt represents the failure time of the i-th product. Since the samples in the same batch are the same product with the same life characteristics, the expected failure time of the product is t r1 =t r2 =...=t rN =t r .

[0094] In one embodiment, the reliability evaluation test cutoff time and test pass conditions are determined by calculating the production risk, the user risk, and the product failure rate development requirements. The reliability of the complex product is evaluated based on the reliability evaluation test plan determined based on the test cutoff time and test pass conditions, including:

[0095] Calculate the production risk, user risk and product failure rate requirements to determine the expected failure time of product development based on the production risk requirements or user risk requirements when the product failure rate meets the development requirements. b Determine the test truncation time of the reliability identification test as T;

[0096] Within the test truncation time, the test passing condition of the reliability identification test is selected as zero failure number. According to the test truncation time and the test passing condition, the reliability identification test plan of the complex product is determined to be (T, 0), and the reliability of the complex product is identified through the reliability identification test plan (T, 0).

[0097] It is understandable that during the product development phase, improvements are made only when a product failure occurs during testing. Since there is no failure data product in the second phase of the product test set by this application, it is considered that no product improvement will be made after the end of this phase of the test, that is, the product reliability has not changed after the end of the second phase of the test. Then, when conducting a reliability identification test on the product, this phase of the test can be counted as part of the product reliability identification test. After this phase of the test, a test with a test truncation time of T is conducted. If no failure occurs within the test truncation time, it is considered that the product reliability meets the development requirements. In other words, the reliability identification test plan finally selected is (T, 0).

[0098] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0099] Furthermore, in order to verify the beneficial effects of the method proposed in this application, in a specific embodiment, the test data of a rocket engine component was also tested and verified. The component has a complex composition and can be considered as a complex product whose life follows an exponential distribution. The test data of a rocket engine component is shown in Table 1

[0100] Table 1 Test data of a rocket engine component

[0101] Sample size N <![CDATA[Fault time t i > Censorship time Phase 1 10 316 500 Phase II 10 - 500

[0102] According to the method proposed in this application, the prior distribution of the product failure rate obtained from the two-stage data after data conversion is first obtained as Ga(1,258.3979). If the time of the next failure is t', the posterior distribution of the product is Ga(2,258.3979+t'). Then, assuming that the development requires the failure rate of the product to be no higher than 0.001, that is, λ≤λ0, λ0=0.001, and taking the test identification ratio as d=3, the relationship between the product production risk and the user risk and the test time is obtained as shown in the figure below: Figure 2 As shown. Figure 2 It can be seen that for the manufacturer, the longer the test time, the greater the manufacturer's risk and the higher the test cost. In order to minimize the test cost while controlling the user's risk as much as possible, the maximum acceptable value of the manufacturer's risk is selected as the development requirement, and the corresponding expected failure time is used to calculate the test truncation time. We select the expected failure time when the manufacturer's risk and the user's risk are equal as the test truncation time. When the test sample size N = 1, the manufacturer and user risks are both 0.158, and the expected failure time T = 267, then the test plan can be obtained as (T, 0) = (267, 0). In actual testing, the product can be tested for 267 hours. If no failure occurs within the truncation time, it is considered that the product reliability meets the development requirements and has passed the reliability identification test.

[0103] Furthermore, in order to test the advancedness of the method proposed in this application, it is compared with the standard timed truncation test scheme provided in China's current reliability evaluation test standard GJB-899A. The reliability evaluation test scheme is shown in Table 2.

[0104] Table 2 Comparison of reliability identification test schemes

[0105]

[0106] It can be seen that under the same development requirements and identification ratio, the test truncation time of the reliability identification test scheme obtained in this application is shorter, and in terms of test risk, the risks for both the user and the manufacturer of this application are lower. In terms of the process of obtaining the reliability identification test scheme, the reliability identification test scheme obtained in this application is obtained after comprehensively utilizing the test data of the previous stage of the product and the zero-failure data of the test, and the result is more credible; in terms of the risk of the identification test, the risk definition in this application does not adopt the traditional test risk definition, but adopts the Bayesian risk definition, which can make full use of the prior information of the product; in terms of test cost, under the same risk, the reliability identification test scheme obtained in this application has a shorter test time and lower test cost. In addition, the reliability identification test scheme obtained in this application is more flexible, and the appropriate reliability identification test scheme can be selected according to the specific development requirements (see Table 3 for test schemes at different risks).

[0107] Table 3 Experimental plans at different risks

[0108]

[0109] Table 4 Identification test plan for sample size 5 and 10

[0110]

[0111] Based on the results of the above case studies, it can be concluded that the reliability identification test method designed in this application generally has the following advantages over the classic timed truncation test method: (1) Since the failure data and no-failure data in the development phase are fully utilized, its credibility is higher; (2) Compared with the GJB scheme, the test scheme obtained in this application has a shorter test time, lower cost, and lower risk; (3) Compared with the classic test scheme that fixes two types of risks to obtain the test scheme, the test scheme of this application can flexibly select the test scheme according to different risk requirements. In addition, according to the method proposed in this application, the test time can be shortened by increasing the test sample size. Taking the above case as an example, the identification test schemes when the sample size is 5 and 10 can be obtained, as shown in Table 4.

[0112] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0113] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A product reliability evaluation test method based on two-stage zero-failure data, characterized in that: The method comprises: For a complex product that is divided into a first stage and a second stage during the product development phase, obtain product test data for the first stage and product test data for the second stage, calculate an estimated failure rate for the first stage product based on the first stage product test data, and calculate a failure probability for the second stage product based on the second stage product test data; wherein failure data exists for the first stage but not for the second stage; Calculating a conversion factor based on the estimated failure rate of the first-stage product and the failure probability of the second-stage product, and converting the first-stage product test data into second-stage test data using the conversion factor, performing calculations based on the converted second-stage test data to obtain an estimated failure rate of the second-stage product, and using the estimated failure rate of the second-stage product as prior information to perform calculations based on the Bayesian method to obtain a prior distribution and a posterior distribution of the second-stage product failure rate; Calculating based on the prior distribution and posterior distribution of the product failure rate in the second phase to determine the manufacturer risk and user risk of the complex product, calculating based on the manufacturer risk and user risk and the development requirements of the product failure rate to determine the test cutoff time and test pass conditions for the reliability identification test, and identifying the reliability of the complex product based on the reliability identification test plan determined by the test cutoff time and test pass conditions; The estimated value of the second-stage product failure rate is obtained by calculating the second-stage test data obtained after conversion, including: Based on data from the Phase II trial Calculate and obtain the maximum likelihood estimate of the second-stage product failure rate, which is expressed as: ； in, represents the maximum likelihood estimate of the second-stage product failure rate, represents the second-stage product failure rate, It is k The expected time of failure of each product, represents the second-stage test data transformed from the first-stage i-th product test data, This is the censoring time for the second phase of the trial; For product life, Indicates time; is the sample size for the first phase of the trial, The sample size for the second phase of the trial; By solving the maximum likelihood estimate of the second-stage product failure rate, the estimated value of the second-stage product failure rate is obtained, which is expressed as: ； in, is the conversion factor, is the number of failures in the first stage, The censoring time for the first phase of the experiment is Represents the first phase product test data.

2. The method according to claim 1, characterized in that The product life of the complex product is subject to the product failure rate The exponential distribution of .

3. The method according to claim 2, characterized in that The first phase product test data includes the first phase test sample size, the number of failures in the first phase, the first phase test censoring time, and the first phase failure occurrence time; The estimated failure rate of the first phase products is calculated based on the test data of the first phase products, including: The maximum likelihood estimate of the first-stage product failure rate is calculated based on the first-stage test sample size, the first-stage failure number, the first-stage test censoring time, and the first-stage failure occurrence time, and is expressed as: in, represents the maximum likelihood estimate of the first-stage product failure rate, represents the first-stage product failure rate, is the sample size for the first phase of the trial, is the number of failures in the first stage, The censoring time for the first phase of the experiment is For the first stage i Time of the first fault occurrence, ; By solving the maximum likelihood estimate of the product failure rate in the first stage, the estimated value of the product failure rate in the first stage is obtained, which is expressed as: 。 4. The method according to claim 3, characterized in that Phase II product trial data include Phase II trial sample size and Phase II trial censoring time; The failure probability of the second-stage product is calculated based on the second-stage product test data, including: According to the sample size of the second phase of the trial Calculate and get the failure probability of the second stage product, expressed as .

5. The method according to claim 4, characterized in that Calculating a conversion factor based on the estimated failure rate of the first-stage product and the failure probability of the second-stage product, and converting the first-stage product test data into second-stage test data using the conversion factor, including: By considering the life characteristics of the product itself, the estimated failure rate of the first stage product The numerator of the conversion factor is expressed as ; According to the and the second-stage product failure probability Calculate the conversion factor, which is expressed as , through the reduction factor The first phase product test data is converted into the second phase test data, which is expressed as: in, Represented as the first phase product test data, This is the data from the second phase of the experiment.

6. The method according to claim 1, characterized in that The estimated value of the second-stage product failure rate is used as prior information and the Bayesian method is used to calculate the prior distribution and posterior distribution of the second-stage product failure rate, including: The estimated value of the failure rate of the second-stage products is used as prior information to calculate according to the Bayesian method, and the prior distribution mean and the second-order moment of the prior distribution of the failure rate of the second-stage products are obtained; The gamma distribution is used to fit the prior distribution of the second-stage product failure rate, and the shape parameters of the gamma distribution are calculated based on the prior distribution mean and the second-order moment of the prior distribution. and scale parameters , according to the shape parameters and scale parameters Determine the prior distribution of the second-stage product failure rate as ; According to the prior distribution of product failure rate in the second stage and the time when the next product failure occurs Calculation is performed to obtain the posterior distribution of the second-stage product failure rate: .

7. The method according to claim 6, characterized in that Calculations are performed based on the prior and posterior distributions of the product failure rate in the second phase to determine the manufacturer and user risks of complex products, including: For complex products, the hypothesis test is ,in, is the null hypothesis, For the alternative hypothesis, is the upper limit of product failure rate, is the lower limit of product failure rate; According to the prior distribution and posterior distribution of the second-stage product failure rate, the second-stage product failure rate has reached The probability of being rejected by the reliability identification test is regarded as the manufacturer's risk of the product, and the product failure rate is higher than The probability of passing the reliability identification test is taken as the user risk of the product. The manufacturer risk and the user risk are expressed as: in, For the production side risk, For the user's risk, T represents the test truncation time of the reliability identification test, For a sample size of N Trials, events K Probability of occurrence, event K To ensure that all products in the test have passed the reliability identification test, Indicates the i The failure time of each product. Since the samples in the same batch are of the same product and have the same life characteristics, the expected failure time of the product is .

8. The method according to claim 1, characterized in that The manufacturer's risk, the user's risk, and the product failure rate development requirements are calculated to determine the test cutoff time and test pass conditions for the reliability identification test. The reliability of the complex product is identified based on the reliability identification test plan determined by the test cutoff time and test pass conditions, including: Calculate the production risk, user risk and product failure rate requirements and determine the expected failure time of product development based on the production risk requirements or user risk requirements when the product failure rate meets the development requirements. Determine the test cut-off time of the reliability identification test as ; Within the test truncation time, the reliability identification test pass condition is selected as zero failure number. According to the test truncation time and test pass condition, the reliability identification test plan of the complex product is determined as follows: and passed the reliability identification test plan Qualify the reliability of complex products.

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