Product reliability comprehensive evaluation method and system, equipment and medium

Abstract

The present invention provides a comprehensive evaluation method for product reliability, comprising the following steps: step S1: classifying and preprocessing multi-stage and multi-type data; step S2: performing consistency check on the multi-stage and multi-type data after classification and preprocessing; step S3: converting and integrating the multi-stage and multi-type data after consistency check; step S4: determining the prior distribution and hyperparameters according to the data type for the converted and integrated data; step S5: after determining the prior distribution and hyperparameters, performing data fusion and reliability evaluation according to Bayes theory and related models. Starting from the characteristics of each type of data at each stage, the present invention classifies the reliability data existing in actual engineering, provides a classification and preprocessing method for multi-stage and multi-type data, and combines Bayes and related models to propose a set of comprehensive product reliability evaluation processes that integrate multi-stage and multi-type data.

Description

Technical Field

[0001] The present invention relates to the technical field of data analysis and evaluation, and specifically, to a product reliability comprehensive evaluation method and system, equipment, and medium, and in particular to a product reliability comprehensive evaluation method and system, equipment, and medium integrating multiple stages and types. Background Art

[0002] According to the classic reliability theory, to evaluate the reliability level of a product in the actual use environment, it is necessary to make statistical inferences based on the data collected by the product in the field environment, which means that we need a large amount of field data. However, many products do not have a large amount of field data. Therefore, making full use of various types of reliability information collected at various stages of the product life cycle and integrating and evaluating them is an important research direction of reliability analysis.

[0003] Bayesian theory is an effective means to solve the problem of statistical inference of small samples, and it can integrate multiple data for reliability assessment. At present, domestic and foreign literature often only integrates two or a few types of product data when using Bayesian theory for reliability assessment, such as the integration of accelerated life test data and field failure data, and the integration of expert information and field success and failure data. However, in actual engineering, there are a large number of different types of reliability data at different stages, which reflect the reliability level of the product from different aspects and angles. How to integrate field information is also an urgent problem to be solved.

[0004] After searching, the patent document CN110874502A discloses a method for evaluating the reliability of aerospace products based on the conversion of multi-stage test data, including the following steps: conducting a two-stage reliability test of aerospace products, obtaining the product test life data of the first stage and the second stage of aerospace products; converting the product test life data of the first stage; determining the prior distribution of the Weibull life distribution parameters of the second stage, and obtaining the Bayesian posterior distribution kernel function under the joint distribution data; and using the Bayesian MH sampling method to perform interval estimation of reliability. The disadvantage of this prior art is that the reliability data analysis can only be obtained when there is field data. Although the Bayesian theory is also used for reliability evaluation, it only analyzes the life data and is not comprehensive.

[0005] Therefore, it is urgent to design a simple and effective processing method to fuse multi-stage and multi-type reliability data while retaining the content contained in multi-stage and multi-type information as much as possible, so as to give an accurate estimate of the product reliability level. Summary of the invention

[0006] In view of the defects in the prior art, the purpose of the present invention is to provide a comprehensive product reliability evaluation method and system, equipment, and medium. In the absence of sufficient field data, the present invention makes full use of various types of reliability data generated at various stages of the product design, manufacturing, and use process. Under the premise of ensuring data consistency, the reliability data of various types at various stages are classified, preprocessed, integrated, and evaluated to improve the accuracy of reliability evaluation. The present invention solves the problem of integrating multi-stage and multi-type reliability data while retaining the content of multi-stage and multi-type information as much as possible to provide an accurate estimate of the product reliability level.

[0007] A product reliability comprehensive evaluation method provided by the present invention comprises the following steps:

[0008] Step S1: classify and preprocess multi-stage and multi-type data;

[0009] Step S2: Perform consistency check on the multi-stage and multi-type data after classification and preprocessing;

[0010] Step S3: after consistency check, convert and integrate multi-stage and multi-type data;

[0011] Step S4: After converting and integrating multi-stage and multi-type data, determine the prior distribution and hyperparameters according to the data type;

[0012] Step S5: After determining the prior distribution and hyperparameters, data fusion and reliability evaluation are performed according to Bayesian theory and related models.

[0013] Preferably, step S1 includes classifying multi-stage and multi-type data, and the data types are as follows:

[0014] Product field data: lifespan, success / failure and degradation data of the product under actual use or service environment conditions;

[0015] Product heterogeneous environment data: life, success, failure and degradation data of products under different test conditions at different stages of their life cycle and different from the on-site use environment conditions;

[0016] Similar product data: also known as heterogeneous overall data, including similar product field data and similar product heterogeneous environment data. Similar product field data refers to the life, success, failure and degradation data of similar products under the actual use or service environment conditions. Similar product heterogeneous environment data refers to the life, success, failure and degradation data of similar products under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions.

[0017] Component-level data: field data and heterogeneous environment data of each component of the product. Component-level field data refers to the life, success, failure and degradation data of each component of the product under the actual use or service environment conditions. Component-level heterogeneous environment data refers to the life, success, failure and degradation data of each component of the product under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions.

[0018] Expert data: data represented by experts’ empirical estimates of product reliability.

[0019] Preferably, step S1 includes preprocessing multi-stage and multi-type data:

[0020] Preprocessing of life data: Use life distribution type test and parameter evaluation method to preprocess and obtain life type and parameter estimation;

[0021] Preprocessing of heterogeneous environmental data: Use environmental factor estimation method to preprocess and give the "environmental factor" of heterogeneous environmental data relative to field data;

[0022] Preprocessing of component-level data: Use system reliability comprehensive method to preprocess and convert component-level data into product data;

[0023] Preprocessing of degradation data: Use degradation modeling method to preprocess and convert degradation data into pseudo-life data;

[0024] Preprocessing of similar product data: Use similarity factor estimation method to preprocess and give the "similarity factor" of similar product data.

[0025] Preferably, step S2 comprises:

[0026] Step S2.1: Perform consistency check on the life distribution type. For life data, determine whether the multi-stage multi-type life data and the product site data obey the same life distribution according to the life type.

[0027] Step S2.2: Perform consistency check on the failure mechanism to determine whether the heterogeneous life data meets the failure mechanism invariance condition, that is, the environmental factor invariance principle.

[0028] Preferably, the conversion and integration of multi-stage and multi-type data in step S3 includes:

[0029] Conversion and integration of heterogeneous environmental data: For environmental factor K i0 ≠1, convert the heterogeneous environment data into field data according to the data type, and then integrate the converted field data;

[0030] Conversion and integration of similar product data: For similarity factor F i0 For similar product data whose value is ≠1, the similar product data is converted into the evaluated product data according to the data type, and then the converted evaluated product data is integrated.

[0031] Preferably, step S4 comprises:

[0032] Step S4.1: Select the prior distribution according to the range of unknown parameters in the overall distribution. The basic method is as follows:

[0033] For parameters with values ​​of [0,1], the Beta distribution Be(a,b) is selected as the prior distribution.

[0034] For parameters with values ​​of (-∞, +∞), the normal distribution N(μ,σ 2 ) as the prior distribution,

[0035] For parameters with values ​​of (0, +∞), the gamma distribution Ga(z,η) or the inverse gamma distribution IGa(z,η) is selected as the prior distribution;

[0036] Step S4.2: Determine the hyperparameters of the prior distribution based on the prior data. The basic method is to use the prior information to generate bootstrap samples, obtain the maximum likelihood estimate sample of the parameters of the distribution corresponding to each sample, calculate the mean and variance of the parameters, which should be equal to the mean and variance of the prior distribution of the corresponding parameters, and obtain the hyperparameters of the prior distribution of the life distribution parameters by solving the simultaneous equations.

[0037] Preferably, step S5 comprises:

[0038] Step S5.1: Determine the likelihood function of each distribution when the overall distribution type and field data are known;

[0039] Step S5.2: According to Bayesian theory, determine the kernel or distribution density function of the posterior distribution;

[0040] Step S5.3: According to the kernel of the posterior distribution, determine the type of the posterior distribution and obtain the posterior distribution density function of the parameter

[0041] Step S5.4: When the posterior distribution density function of the parameters is known, the posterior expected estimate of each reliability evaluation index is calculated according to the overall distribution as its Bayesian estimate.

[0042] A product reliability comprehensive evaluation system provided according to the present invention comprises:

[0043] Module M1: Classify and preprocess multi-stage and multi-type data;

[0044] Module M2: Check the consistency of multi-stage and multi-type data after classification and preprocessing;

[0045] Module M3: Convert and integrate multi-stage and multi-type data after consistency check;

[0046] Module M4: After converting and integrating multi-stage and multi-type data, determine the prior distribution and hyperparameters according to the data type;

[0047] Module M5: After determining the prior distribution and hyperparameters, data fusion and reliability assessment are performed based on Bayesian theory and related models.

[0048] According to a computer-readable storage medium storing a computer program provided by the present invention, the steps of the above method are implemented when the computer program is executed by a processor.

[0049] A product reliability comprehensive evaluation device provided according to the present invention includes the above-mentioned product reliability comprehensive evaluation system or the above-mentioned computer-readable storage medium storing a computer program.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] 1. The present invention classifies the reliability data existing in actual engineering projects based on the characteristics of each type of data at each stage, classifies and preprocesses multi-stage and multi-type data, and combines Bayes and related models to achieve comprehensive product reliability evaluation of multi-stage and multi-type data.

[0052] 2. The present invention can make full use of various reliability information of products during design, manufacturing and use, and can improve the accuracy of reliability evaluation, especially in the absence of sufficient on-site information.

[0053] 3. The present invention makes full use of various types of reliability data generated at various stages of the product design, manufacturing and use process, and classifies, preprocesses, integrates and evaluates various types of reliability data at each stage while ensuring data consistency, thereby further improving the accuracy of reliability evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0055] Figure 1 It is a basic flow chart of the comprehensive evaluation method of product reliability in the present invention;

[0056] Figure 2 A schematic diagram of multi-stage and multi-type data classification in the present invention;

[0057] Figure 3 It is a schematic diagram of the preprocessing process of component-level heterogeneous environment success / failure data in the present invention;

[0058] Figure 4 It is a schematic diagram of the preprocessing process of component-level heterogeneous environment life data in the present invention;

[0059] Figure 5 It is a schematic diagram of the preprocessing process of component-level heterogeneous environment degradation data in the present invention;

[0060] Figure 6 It is a schematic diagram of the preprocessing process of success and failure data of similar products in different environments in the present invention;

[0061] Figure 7 It is a schematic diagram of the preprocessing process of life-type data of similar products in different environments in the present invention;

[0062] Figure 8 It is a schematic diagram of the preprocessing process of the degradation data of similar products in different environments in the present invention;

[0063] Fig. 9 It is a schematic diagram of the preprocessing process of product field life data in the present invention. DETAILED DESCRIPTION

[0064] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0065] like Figure 1-Figure 2 As shown, the present invention provides a comprehensive evaluation method for product reliability. Starting from the characteristics of each type of data at each stage, the reliability data existing in actual engineering is classified, and a classification and preprocessing method for multi-stage and multi-type data is given. Combining Bayes and related models, a set of comprehensive product reliability evaluation processes integrating multi-stage and multi-type data is proposed. It includes the following steps:

[0066] Step S1: Classify and preprocess multi-stage and multi-type data, specifically including the following steps:

[0067] Step S1.1: Multi-stage and multi-type data are classified, and the data types are as follows:

[0068] Product field data: lifespan, success / failure and degradation data of the product under actual use or service environment conditions;

[0069] Product heterogeneous environment data: life-type, success-failure and degradation data of products under different test conditions carried out at different stages of their life cycle, which are different from the on-site use environment conditions; each stage includes reliability test, life test, accelerated life test, functional test, environmental test, regular test and other stages.

[0070] Similar product data: also known as heterogeneous overall data, including similar product field data and similar product heterogeneous environment data. Similar product field data refers to the life, success, failure and degradation data of similar products under the actual use or service environment conditions. Similar product heterogeneous environment data refers to the life, success, failure and degradation data of similar products under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions.

[0071] Component-level data: field data and heterogeneous environment data of each component of the product. Component-level field data refers to the life, success, failure and degradation data of each component of the product under the actual use or service environment conditions. Component-level heterogeneous environment data refers to the life, success, failure and degradation data of each component of the product under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions.

[0072] Expert data: data represented by experts’ empirical estimates of product reliability.

[0073] Step S1.2: Preprocess the multi-stage and multi-type data. To facilitate data expression and preprocessing, the above data are further classified. The multi-stage and multi-type data can be divided into four basic data types, namely life data, success data, degradation data, and expert data. The unified formats of the four basic data types are shown in Tables 1 to 4:

[0074] Table 1 Unified format of life type data

[0075] Sample No. Lifespan Type Failure time Censorship time Similarity Factor Environmental factors

[0076] Table 2 Unified format of success / failure data

[0077] Sample No. Number of trials Number of failures Similarity Factor Environmental factors

[0078] Table 3 Unified format of degenerate data

[0079] Sample No. Observation time Performance degradation Similarity Factor Environmental factors

[0080] Table 4 Unified format of expert data

[0081]

[0082] The "life type" in Table 1 is determined by the life distribution type inspection preprocessing module, and the "failure time" and "truncation time" are used to record the sample failure time and truncation time corresponding to different truncation methods (including timed, fixed, fixed total, and random truncation). The "number of tests" and "number of failures" in Table 2 are used to record the total number of tests and failures of sample success and failure data. The "observation time" and "performance degradation amount" in Table 3 are used to record the observation time point and performance degradation amount of sample degradation data. The "point estimate" and "confidence lower limit estimate" of reliability in Table 4 (given confidence level) are subjective estimates of reliability given by experts.

[0083] The "similarity factor" in Table 1, Table 2 and Table 3 is used to reflect the similarity between the evaluated product and the sample, and is determined by the similar product data preprocessing module. When the similarity factor = 1, it means that the technical status of the sample is exactly the same as the evaluated product; when 0 < similarity factor < 1, it means that the reliability of the sample is lower than that of the evaluated product; when the similarity factor > 1, it means that the reliability of the sample is higher than that of the evaluated product.

[0084] The "environmental factor" in Table 1, Table 2 and Table 3 is the environmental conversion factor or acceleration coefficient between heterogeneous environment data and field data. When the environmental factor = 1, it means that the data is field data; when the environmental number > 0 and ≠ 1, it means that the data is heterogeneous environment data.

[0085] After further clarifying the classification, pre-processing is performed on life data, heterogeneous environment data, component-level data, degradation data, and similar product data.

[0086] Preprocessing of life data: Use life distribution type test and parameter evaluation method to preprocess and obtain life type and its parameter estimation; life types include exponential life type, Weibull life type, normal life type, lognormal type, etc.

[0087] Preprocessing of heterogeneous environment data: Use environmental factor estimation method to preprocess and give the "environmental factor" of heterogeneous environment data relative to field data; heterogeneous environment data include product heterogeneous environment data, component-level heterogeneous environment data, and similar product heterogeneous environment data. The environmental factor estimation method is to estimate environmental factors of different distribution types.

[0088] Preprocessing of component-level data: Use system reliability comprehensive methods for preprocessing and convert component-level data into product data; component-level data includes component-level field data and heterogeneous environment data. System reliability comprehensive methods include MML, SR, LM, CMSR, Bayes method, etc.

[0089] Preprocessing of degradation data: Use degradation modeling methods to preprocess and convert degradation data into pseudo-life data; degradation data include product field degradation data, component-level field degradation data, and component-level heterogeneous environment degradation data. Degradation modeling methods include degradation quantity distribution based on degradation quantity distribution, Wiener, Gamma and other random processes.

[0090] Preprocessing of similar product data: Use similarity factor estimation method to preprocess and give the "similarity factor" of similar product data; similar product data include similar product life data, similar product success / failure data, similar product heterogeneous life data and similar product heterogeneous success / failure data. Similarity factor estimation methods include comprehensive evaluation method, expert scoring method, etc.

[0091] The processing flow of various types of data is as follows Figures 3 to 9 shown.

[0092] Step S2: Perform consistency check on the multi-stage and multi-type data after classification and preprocessing; since the field data can truly reflect the reliability level of the product, during the consistency check, the product field data is used as the consistency check benchmark, and the other multi-stage and multi-type data are tested for consistency of life distribution type and failure mechanism with the field data. Only data that pass the consistency check can be used for comprehensive reliability evaluation of the product. The basic method is as follows:

[0093] Step S2.1: For life data, determine whether the multi-stage and multi-type life data (including heterogeneous environment life data, similar product life data, and pseudo life data) and the product field data obey the same life distribution according to the life type.

[0094] Step S2.2: Perform consistency check on the failure mechanism. For heterogeneous life data (environmental factor ≠ 1), a consistency check on the failure mechanism is also required. According to the type of life distribution and its failure mechanism invariance condition, see Table 5, determine whether the heterogeneous life data meets the failure mechanism invariance condition, that is, the environmental factor invariance principle. Only when the failure mechanism invariance condition is met can the heterogeneous environment data and field data be fused.

[0095] Table 5 Common life distribution environmental factors and failure mechanism unchanged conditions

[0096]

[0097] Step S3: After consistency check, convert and integrate multi-stage and multi-type data. Specifically, it includes the following steps:

[0098] Step S3.1: Conversion and integration of heterogeneous environmental data: For environmental factor K i0≠1, convert the heterogeneous data into field data according to the data type, and then integrate the converted field data. The basic method is as follows:

[0099] ①Exponential lifespan data

[0100] Keeping the number of failures z unchanged, the total test time τ is multiplied by the acceleration factor K i0 or its lower confidence limit Right now

[0101]

[0102] The method to integrate all the data converted from different environments is:

[0103] (z′0,τ′0)=(z1,τ1·K 10 )+(z2,τ2·K 20 )+…+(z q ,τ q ·K q0 ) (2)

[0104] ②Other life span data (including Weibull, normal, and lognormal life span data)

[0105] All failure time data and censored data are multiplied by the acceleration factor K i0 or its lower confidence limit Right now

[0106]

[0107] Where: t i For the environment i The test data under , including the failure time or censoring time of each sample.

[0108] The method for synthesizing the converted data of all different environments is:

[0109] t′0=(t′ 10 ,t′ 20 ,…,t′ q0 ) (4)

[0110] ③Success and failure data

[0111] Keep the number of failures f i No change, number of trials n i Multiply by the acceleration factor K i0

[0112]

[0113] The method for synthesizing the converted data of all different environments is:

[0114] (f′0,n′0)=(f′1,n′1)+(f′2,n′2)+…+(f′ q ,n′ q ) (6)

[0115] Step S3.2: Conversion and integration of similar product data: For similarity factor F i0 For similar product data with a value of ≠1, the similar product data is converted into the evaluated product data according to the data type, and then the converted evaluated product data is integrated. The basic method is similar to the conversion and integration method of heterogeneous environment data, the difference is that the environmental factor is replaced by the similarity factor.

[0116] Step S3.3: Based on the data type, the converted and integrated heterogeneous environment data and similar product data are integrated again to obtain the pre-test information of life data and success / failure data.

[0117] Step S4: After converting and integrating multi-stage and multi-type data, determine the prior distribution and hyperparameters according to the data type. Specifically, it includes the following steps:

[0118] Step S4.1: Select the prior distribution π(θ) according to the range of unknown parameters in the overall distribution. The basic method is as follows:

[0119] For parameters with values ​​in [0,1], the beta distribution B(a,b) is used as the prior distribution, and the hyperparameters are (a,b); for parameters with values ​​in (-∞,+∞), the normal distribution N(μ,σ 2 ) as the prior distribution, and the hyperparameters are (μ,σ 2 ); for parameters with values ​​of (0,+∞), the gamma distribution Γ(z,τ) or the inverse gamma distribution IΓ(z,τ) is selected as the prior distribution, and the hyperparameters are (z,τ).

[0120] The density functions, expectations and variances of various prior distributions are shown in Table 6.

[0121] Table 6 Probability density function, kernel, expectation and variance of common prior distributions

[0122]

[0123] Step S4.2: Determine the hyperparameters of the prior distribution based on the prior data. The basic method is to use the prior information to generate bootstrap samples, obtain the maximum likelihood estimate sample of the parameters of the distribution corresponding to each sample, calculate the mean and variance of the parameters, which should be equal to the mean and variance of the prior distribution of the corresponding parameters, and obtain the hyperparameters of the prior distribution of the life distribution parameters by solving the simultaneous equations.

[0124] Specifically, ① select the prior distribution and hyperparameters for exponential life data:

[0125] The conjugate prior distribution of the exponential distribution parameter failure rate λ, λ∈(0,+∞) is the gamma distribution, that is, π(λ)~Γ(z,τ). The hyperparameters (z,τ) represent the number of failures and the total test time of the exponential prior test, respectively, and their values ​​are determined by the prior information.

[0126] The method to determine the hyperparameters (z, τ) is as follows:

[0127] Using prior information and the Bootstrap method, we obtain several estimates of the failure rate, denoted as Calculate the prior mean and the prior variance And let them be equal to the expectation and variance of the gamma distribution Γ(z,τ), solve the system of simultaneous equations, and get the estimated values ​​of the hyperparameters:

[0128]

[0129] ②Select prior distribution and hyperparameters for normal or lognormal data:

[0130] Parameters μ and σ of a normal or lognormal distribution 2 When unknown and related, its parameters (μ,σ 2 ) is the normal-inverse gamma distribution, that is, v0,μ0, k0 is a hyperparameter determined by prior data.

[0131] Determining Hyperparameters The method is as follows:

[0132] For the mean, we first use the prior information and Bootstrap method to get the prior mean of the mean μ. The difference between the test and the pre-test Let them be equal to the prior distribution of μ respectively The expectation and variance of

[0133]

[0134] Similarly, for the variance, the variance σ is obtained using prior information and the Bootstrap method. 2 The pre-test mean The difference between the test and the pre-test Let them be equal to σ 2 The prior distribution of The expectation and variance of

[0135]

[0136] Combining the above two equations, we can get

[0137]

[0138] ③ Select the prior distribution and hyperparameters for Weibull lifetime data:

[0139] The parameters of the Weibull distribution are (m, η). According to the value range of m, it is discussed in two cases:

[0140] Case 1: If it is known that the failure rate is decreasing, then 0 < m < 1. Select the beta distribution as the prior distribution of m, that is, take m ∼ β(a, b), λ = (1 / η) m ∼ Γ(z, τ), then under the assumption that m and λ are independent of each other, their prior distribution is:

[0141] π(λ, m) ∝ λ z-1 e -τλ m a-1 (1 - m) b-1 (10)

[0142] The determination methods of hyperparameters (a, b) and (z, τ) are as follows:

[0143] For the parameter m, use the prior information and the Bootstrap method to obtain the prior mean and variance Respectively make them equal to the expectation and variance of the prior distribution m ∼ β(a, b) of m, that is

[0144]

[0145] Solve the above equations to obtain the hyperparameters (a, b):

[0146]

[0147] Similarly, for the parameter λ, use the prior information and the Bootstrap method to obtain the prior mean of λ and variance Respectively make them equal to the expectation and variance of the prior distribution λ = (1 / η) m ∼ Γ(z, τ), that is

[0148]

[0149] Solve the above equations to obtain the hyperparameters (z, τ):

[0150]

[0151] Case 2: If it is known that the failure rate is increasing, then m > 1. Then the following prior distribution can be selected so that m′ = m - 1 follows a gamma distribution. Since m > 1, let the prior distribution of m′ = m - 1 be a gamma distribution, that is, take m′ = m - 1 ∼ Γ(a, b), λ = (1 / η)m ~Γ(d,τ), then under the assumption that m and λ are independent, their prior distribution is

[0152] π(λ,m)∝λ z-1 e -τλ (m-1) a-1 e -b(m-1) (14)

[0153] The hyperparameters (a, b) and (z, τ) are determined in the same way as in case 1.

[0154] ④Select prior distribution and hyperparameters for success / failure data:

[0155] The parameter of binomial distribution is success rate or reliability R: the conjugate prior distribution is beta distribution, that is, π(R)~B(a0,b0), and the hyperparameters a0 and b0 represent the number of successes and failures of the prior test, respectively, and their values ​​are determined by the prior information. Prior distribution density function:

[0156]

[0157] The method to determine the hyperparameters (a0, b0) is as follows:

[0158] Using prior information and the Bootstrap method, we can obtain several estimates of the success probability (reliability), denoted as Calculate the prior mean and the prior variance And let them be equal to the expectation and variance of the Beta distribution B(α,β), and use the following equations to get the hyperparameters (a0,b0):

[0159]

[0160] ⑤ When the prior information is expert information, the method of selecting the prior distribution is as follows:

[0161] When the field data are of the success-failure type, the Beta distribution is selected as the prior distribution;

[0162] When the field data are of life span type, the negative log-gamma distribution is selected as the prior distribution.

[0163] Methods for determining hyperparameters:

[0164] Point estimates of reliability from known experts and the lower confidence limit R 0L (confidence 1-β), when the prior distribution of R is Beta distribution, the hyperparameters (a, b) are determined by the following equations:

[0165]

[0166] When the prior distribution of R is a negative log-gamma distribution, let the task time t0, τ be the total test time, then the equivalent number of tasks is η = τ / t0. The hyperparameters (z, η) are determined by the following equations:

[0167]

[0168] Step S5: After determining the prior distribution π(θ) and hyperparameters, data fusion and reliability evaluation are performed according to Bayesian theory and related models. Specifically, the steps are as follows:

[0169] Step S5.1: When the overall distribution type and field data are known, determine the likelihood function p(x|θ) of each distribution.

[0170] The likelihood functions of various population distributions are shown in Table 7.

[0171] Table 7 Likelihood functions of common population distributions

[0172]

[0173] Step S5.2: According to Bayesian theory, determine the kernel or distribution density function of the posterior distribution.

[0174] The posterior distribution density function is:

[0175]

[0176] Where c = 1 / ∫ Θ p(x|θ)π(θ)dθ is a regularization constant that is independent of θ, and p(x|θ)π(θ) is the kernel of the posterior distribution, that is,

[0177] π(θ|x)∝p(x|θ)π(θ)

[0178] Step S5.3: According to the kernel of the posterior distribution, determine the type of the posterior distribution and obtain the posterior distribution density function of the parameter.

[0179] Specifically, ①For the binomial distribution, the test data is: (n,s), where n is the number of trials and s is the number of successes.

[0180] Parameters: Reliability R, R∈[0,1], its conjugate prior distribution is Beta distribution, that is, π(R)~Be(s0,f0), and the hyperparameters s0 and f0 represent the number of successes and failures of the prior test, respectively, and their values ​​are determined by the prior information.

[0181] Prior distribution density function

[0182]

[0183] The likelihood function is

[0184]

[0185] Kernel of the posterior distribution

[0186] π(R|n,s)∝p(n,s|R)π(R)

[0187] The posterior distribution of R is also a Beta distribution, that is, π(R|n,s)~Be(s0+s,f0+f), and its pdf is

[0188]

[0189] ②Exponential distribution

[0190] Test data: (z, τ), z = r is the number of failures, τ = T r The total test time

[0191] Parameters: failure rate λ, λ∈(0,+∞), its conjugate prior distribution is the gamma distribution, that is, π(λ)~Ga(z0,τ0), the hyperparameters z0,τ0 represent the number of failures and the total test time of the exponential prior test, respectively, and their values ​​are determined by the prior information.

[0192] The likelihood function is:

[0193] p(z,τ|λ)=

[0194] λ posterior distribution: also a gamma distribution, that is, its pdf is

[0195]

[0196] ③Normal distribution and lognormal distribution

[0197] Test data:

[0198] Normal x (1) ≤x (2) ≤…≤x (n)

[0199] Lognormal lnx (1) ≤lnx (2) ≤…≤lnx (n)

[0200] If it is life data, it should be greater than 0. Only the case of complete samples is considered here.

[0201] Parameters: There are three cases:

[0202] Case (I): μ is unknown (σ 2 Known)

[0203] The prior conjugate distribution of μ is a normal distribution, that is, Hyperparameter μ0, They represent the mean and variance of the pre-test data, respectively, and are estimated from the pre-test data.

[0204] The kernel of the prior distribution is:

[0205]

[0206] The likelihood function is:

[0207]

[0208] The conjugate posterior distribution of μ is still a normal distribution, that is, in:

[0209]

[0210]

[0211]

[0212] Case (2): σ 2 Unknown (μ is known)

[0213] σ 2 The prior conjugate distribution of is the inverse gamma distribution, that is, π(σ 2 )~IGa(a,b), the hyperparameters a and b are estimated by prior data.

[0214] Prior distribution density function:

[0215]

[0216] Likelihood function:

[0217]

[0218] σ 2 The conjugate posterior distribution of is still the inverse gamma distribution

[0219]

[0220]

[0221] Case (III): μ and σ 2 Unknown and relevant

[0222] Parameters (μ,σ 2 ) is the normal-inverse gamma distribution, that is, v0,μ0, k0 is a hyperparameter determined by prior data.

[0223] in: Right now

[0224]

[0225]

[0226] Then the joint prior distribution

[0227]

[0228] The likelihood function is

[0229]

[0230] Then the joint posterior distribution is also normal-inverse gamma distribution

[0231]

[0232] in:

[0233]

[0234] The posterior distribution of μ is v degrees of freedom n The Student's t distribution is

[0235] σ 2 The posterior distribution of is the inverse gamma distribution, that is,

[0236] ④ Weibull distribution

[0237] Test data:

[0238] t1≤t2≤…≤t r , that is, the first r failure times of n samples

[0239] Distribution function of the two-parameter Weibull distribution:

[0240]

[0241] Parameters: Discussed in the following three cases:

[0242] Case (1): shape parameter m is known, η is unknown

[0243] The test data can be expressed as Then these data are from the exponential distribution Exp(λ), λ=(1 / η) m The first r order statistics of , then the posterior distribution of parameter λ can be given by exponential distribution.

[0244] Case (2): The failure rate is decreasing, that is, 0<m<1, and Beta distribution is selected as the prior distribution of m.

[0245] Take m~β(a,b), λ=(1 / η) m ~Γ(d,τ), then under the assumption that m and λ are independent, the prior distribution is

[0246] π(λ,m)∝λ d-1 e -τλ m a-1 (1-m) b-1

[0247] Given the experimental sample data, the likelihood function is

[0248]

[0249] in: Indicates is the total test time for the failure time.

[0250] Then the joint posterior distribution of m and λ is

[0251]

[0252] Right now

[0253]

[0254] Where: C1 is a constant independent of m and λ, and its value is

[0255]

[0256] It can be obtained that the posterior distribution of m is

[0257]

[0258] The posterior distribution of λ is

[0259]

[0260] Case (III): The failure rate is increasing, that is, m>1, then the following prior distribution can be selected to make m′=m-1 obey the gamma distribution, that is, m′=m-1~Γ(a,b), and select λ=(1 / η) m ~Γ(d,τ), then under the assumption that m and λ are independent, the prior distribution is

[0261] π(λ,m)∝λ d-1 e -τλ (m-1) a-1 e -b(m-1)

[0262] Given the experimental sample data, the likelihood function is

[0263]

[0264] in: Indicates is the total test time for the failure time.

[0265] Then the joint posterior distribution of m and λ is

[0266]

[0267] Right now

[0268]

[0269] Where: C2 is a constant independent of m and λ, and its value is

[0270]

[0271] It can be obtained that the posterior distribution of m is

[0272]

[0273] The posterior distribution of λ is

[0274]

[0275] Step S5.4: When the posterior distribution density function of the parameters is known, the posterior expected estimate of each reliability evaluation index is calculated according to the overall distribution as its Bayesian estimate.

[0276] Specifically, ①For the binomial distribution, the Bayesian estimate (posterior expectation) of R:

[0277]

[0278] ②Exponential distribution

[0279] Bayesian estimate (posterior expectation) of λ:

[0280]

[0281] Bayesian estimate of mean life span (posterior expectation):

[0282]

[0283] Bayesian estimate (posterior expectation) of reliability at task time t0:

[0284]

[0285] ③Normal distribution and lognormal distribution

[0286] Situation (I)

[0287] Bayesian estimate of μ:

[0288]

[0289] Point estimate of reliability at task time t0:

[0290]

[0291] Situation 2

[0292] σ 2 Bayesian estimation of :

[0293]

[0294] Bayesian estimate (posterior expectation) of reliability at task time t0:

[0295]

[0296] Where: c1 is s 2 The normalization constant involved.

[0297] Situation (III)

[0298] The expected posterior estimate of μ is:

[0299]

[0300] σ 2 The expected posterior estimate of :

[0301]

[0302] Bayesian estimation in R:

[0303]

[0304] Where: c2 is a s 2 The related constants.

[0305] ④ Weibull distribution

[0306] Situation (I)

[0307] Same as exponential distribution.

[0308] Situation 2

[0309] Bayesian estimate of m:

[0310]

[0311] Bayesian estimation of λ:

[0312]

[0313] Bayesian estimation of reliability:

[0314]

[0315] Situation (III)

[0316] Bayesian estimate of m:

[0317]

[0318] Bayesian estimation of λ:

[0319]

[0320] Bayesian estimation of reliability:

[0321]

[0322] The present invention also provides a product reliability comprehensive evaluation system, comprising:

[0323] Module M1: Classify and preprocess multi-stage and multi-type data;

[0324] Module M2: Check the consistency of multi-stage and multi-type data after classification and preprocessing;

[0325] Module M3: Convert and integrate multi-stage and multi-type data after consistency check;

[0326] Module M4: After converting and integrating multi-stage and multi-type data, determine the prior distribution and hyperparameters according to the data type;

[0327] Module M5: After determining the prior distribution and hyperparameters, data fusion and reliability assessment are performed based on Bayesian theory and related models.

[0328] The present invention further provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0329] The present invention further provides a product reliability comprehensive evaluation device, including the above-mentioned product reliability comprehensive evaluation system or the above-mentioned computer-readable storage medium storing a computer program.

[0330] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0331] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A comprehensive product reliability evaluation method, characterized in that: The steps include: Step S1: classify and preprocess multi-stage and multi-type data; Step S2: Perform consistency check on the multi-stage and multi-type data after classification and preprocessing; Step S3: after consistency check, convert and integrate multi-stage and multi-type data; Step S4: for the converted and integrated data, determine the prior distribution and hyperparameters according to the data type; Step S5: After determining the prior distribution and hyperparameters, data fusion and reliability evaluation are performed according to Bayesian theory and related models; The step S1 includes classifying multi-stage and multi-type data, and the data types are as follows: Product field data: lifespan, success / failure and degradation data of the product under actual use or service environment conditions; Product heterogeneous environment data: life, success, failure and degradation data of products under different test conditions at different stages of their life cycle and different from the on-site use environment conditions; Similar product data: also known as heterogeneous overall data, including similar product field data and similar product heterogeneous environment data. Similar product field data refers to the life, success, failure and degradation data of similar products under the actual use or service environment conditions. Similar product heterogeneous environment data refers to the life, success, failure and degradation data of similar products under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions. Component-level data: field data and heterogeneous environment data of each component of the product. Component-level field data refers to the life, success, failure and degradation data of each component of the product under the actual use or service environment conditions. Component-level heterogeneous environment data refers to the life, success, failure and degradation data of each component of the product under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions. Expert data: data represented by experts’ empirical estimates of product reliability; The step S1 includes preprocessing multi-stage and multi-type data: Preprocessing of life data: Use life distribution type test and parameter evaluation method to preprocess and obtain life type and parameter estimation; Preprocessing of heterogeneous environmental data: Use environmental factor estimation method to preprocess and give the "environmental factor" of heterogeneous environmental data relative to field data; Preprocessing of component-level data: Use system reliability comprehensive method to preprocess and convert component-level data into product data; Preprocessing of degradation data: Use degradation modeling method to preprocess and convert degradation data into pseudo-life data; Preprocessing of similar product data: Use similarity factor estimation method to preprocess and give the "similarity factor" of similar product data; The step S2 comprises: Step S2.1: Perform consistency check on the life distribution type. For life data, determine whether the multi-stage multi-type life data and the product site data obey the same life distribution according to the life type. Step S2.2: Perform consistency test on the failure mechanism to determine whether the heterogeneous life data meets the failure mechanism invariance condition, that is, the environmental factor invariance principle; The conversion and integration of multi-stage and multi-type data in step S3 includes: Conversion and integration of heterogeneous environmental data: For environmental factors The heterogeneous environment data are converted into field data according to the data type, and then the converted field data are integrated; Conversion and integration of similar product data: For similarity factors similar product data, convert the similar product data into the evaluated product data according to the data type, and then integrate the converted evaluated product data; The step S4 comprises: Step S4.1: Select the prior distribution according to the range of unknown parameters in the overall distribution. The basic method is as follows: for For the parameter of value, use Beta distribution As a prior distribution, for For the parameter of value, select normal distribution As a prior distribution, for For the parameter of value, gamma distribution is used or inverse gamma distribution as a prior distribution; Step S4.2: Determine the hyperparameters of the pre-test distribution based on the pre-test data. The basic method is to use the pre-test information to generate bootstrap samples, obtain the maximum likelihood estimate sample of the parameter corresponding to the distribution of each sample, calculate the mean and variance of the parameter, which should be equal to the mean and variance of the pre-test distribution of the corresponding parameter, and obtain the hyperparameters of the pre-test distribution of the life distribution parameters by solving the simultaneous equations. The step S5 comprises: Step S5.1: Determine the likelihood function of each distribution when the overall distribution type and field data are known; Step S5.2: According to Bayesian theory, determine the kernel or distribution density function of the posterior distribution; Step S5.3: According to the kernel of the posterior distribution, determine the type of the posterior distribution and obtain the posterior distribution density function of the parameter Step S5.4: When the posterior distribution density function of the parameters is known, the posterior expected estimate of each reliability evaluation index is calculated according to the overall distribution as its Bayesian estimate.

2. A product reliability comprehensive evaluation system, characterized in that: include: Module M1: Classify and preprocess multi-stage and multi-type data; Module M2: Check the consistency of multi-stage and multi-type data after classification and preprocessing; Module M3: Convert and integrate multi-stage and multi-type data after consistency check; Module M4: After converting and integrating multi-stage and multi-type data, determine the prior distribution and hyperparameters according to the data type; Module M5: After determining the prior distribution and hyperparameters, data fusion and reliability assessment are performed based on Bayesian theory and related models; The module M1 includes classifying multi-stage and multi-type data, and the data types are as follows: Product field data: lifespan, success / failure and degradation data of the product under actual use or service environment conditions; Product heterogeneous environment data: life, success, failure and degradation data of products under different test conditions at different stages of their life cycle and different from the on-site use environment conditions; Similar product data: also known as heterogeneous overall data, including similar product field data and similar product heterogeneous environment data. Similar product field data refers to the life, success, failure and degradation data of similar products under the actual use or service environment conditions. Similar product heterogeneous environment data refers to the life, success, failure and degradation data of similar products under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions. Component-level data: field data and heterogeneous environment data of each component of the product. Component-level field data refers to the life, success, failure and degradation data of each component of the product under the actual use or service environment conditions. Component-level heterogeneous environment data refers to the life, success, failure and degradation data of each component of the product under different test conditions carried out at various stages of the life cycle that are different from the field use environment conditions. Expert data: data represented by experts’ empirical estimates of product reliability; The module M1 includes preprocessing of multi-stage and multi-type data: Preprocessing of life data: Use life distribution type test and parameter evaluation method to preprocess and obtain life type and parameter estimation; Preprocessing of heterogeneous environmental data: Use environmental factor estimation method to preprocess and give the "environmental factor" of heterogeneous environmental data relative to field data; Preprocessing of component-level data: Use system reliability comprehensive method to preprocess and convert component-level data into product data; Preprocessing of degradation data: Use degradation modeling method to preprocess and convert degradation data into pseudo-life data; Preprocessing of similar product data: Use similarity factor estimation method to preprocess and give the "similarity factor" of similar product data; The module M2 comprises: Conduct consistency check on the life distribution type. For life data, determine whether the multi-stage and multi-type life data and product site data follow the same life distribution according to the life type. Conduct consistency test on failure mechanism to determine whether the life data in different environments meet the failure mechanism invariance condition, that is, the principle of invariance of environmental factors; The conversion and integration of multi-stage and multi-type data in the module M3 includes: Conversion and integration of heterogeneous environmental data: For environmental factors The heterogeneous environment data are converted into field data according to the data type, and then the converted field data are integrated; Conversion and integration of similar product data: For similarity factors similar product data, convert the similar product data into the evaluated product data according to the data type, and then integrate the converted evaluated product data; The module M4 comprises: The prior distribution is selected according to the value range of the unknown parameter in the overall distribution. The basic method is as follows: for The parameter for taking values ​​is Beta distribution. As a prior distribution, for For the parameter of value, select normal distribution As a prior distribution, for For the parameter of value, gamma distribution is used or inverse gamma distribution as a prior distribution; According to the pre-test data, the hyperparameters of the pre-test distribution are determined. The basic method is to use the pre-test information to generate bootstrap samples, obtain the maximum likelihood estimate sample of the parameters of the corresponding distribution of each sample, calculate the mean and variance of the parameters, which should be equal to the mean and variance of the pre-test distribution of the corresponding parameters, and obtain the hyperparameters of the pre-test distribution of the life distribution parameters by solving the simultaneous equations. The module M5 comprises: Determine the likelihood function of each distribution when the overall distribution type and field data are known; According to Bayesian theory, determine the kernel or distribution density function of the posterior distribution; According to the kernel of the posterior distribution, the type of the posterior distribution is determined, and the posterior distribution density function of the parameter is obtained. When the posterior distribution density function of the parameters is known, the posterior expected estimate of each reliability evaluation index is calculated according to the overall distribution as its Bayesian estimate.

3. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to claim 1 are implemented.

4. A product reliability comprehensive evaluation device, characterized in that: It includes the product reliability comprehensive evaluation system as described in claim 2 or the computer-readable storage medium storing a computer program as described in claim 3.

Images