Quality design method and system considering life-type response of multiple failure modes

Abstract

The application provides a quality design method and system considering life type response of multiple failure modes, and belongs to the technical field of quality design and reliability engineering. The method comprises the following steps: obtaining product life test data; determining an optimal mixed component number and identifying a number of potential failure modes; constructing a mixed censored regression model with the optimal mixed component number; performing parameter estimation by using a Bayesian inference method; constructing a reliability index, a loss index and a model fitness index; taking the reliability index and the loss index as optimization objectives, and taking the model fitness index to adjust the optimization process; determining optimal design values of controllable factors by using a multi-objective optimization algorithm; verifying a scheme and outputting a quality design report. The application solves the problem that the prior art cannot simultaneously process multiple failure mode distribution heterogeneity and right censored data, and significantly improves the reliability and robustness of product life type quality design.

Description

Technical Field

[0001] This invention relates to the fields of quality design and reliability engineering technology, and in particular to a quality design method and system that considers multiple failure modes and lifetime response. Background Technology

[0002] In the field of product reliability engineering and quality design, robust parametric design methods are widely used to determine the optimal values ​​of controllable factors to reduce the sensitivity of product performance to noise factors. However, when product quality characteristics are expressed as time-related lifetime indicators, existing methods face two major statistical challenges: First, lifetime data usually exhibits a highly right-skewed distribution and contains right-censored observations, meaning that some products have not yet failed at the end of the test, and their exact lifetime is unknown; second, products often have multiple physical failure mechanisms, and the lifetime distribution patterns corresponding to different failure modes vary, resulting in multimodal heterogeneity in the overall data. Traditional methods typically assume that product lifetime follows a single Weibull or log-normal distribution and simply process or ignore censored data, which leads to serious biases in model parameter estimation, causing the process parameter combinations recommended based on the model to deviate from the true robust optimal region.

[0003] To address the issue of distributional heterogeneity, mixed distribution models offer an effective modeling tool, representing the overall lifetime distribution as a weighted combination of multiple component distributions, with each component corresponding to a potential failure mode. However, existing mixed models still have significant limitations in the application of quality design. First, the determination of the number of mixed components largely relies on subjective experience or traditional information criteria, failing to fully utilize survival information in censored data. Second, parameter estimation in mixed censored regression models is a complex numerical optimization problem; the mixed censored likelihood function has no analytical solution, and conventional optimization algorithms are prone to divergence or getting trapped in local optima when the censoring ratio is high. Third, existing quality design optimization typically uses mean and variance as single objectives, lacking a multi-objective decision-making mechanism that simultaneously balances reliability and economic loss within a mixed distribution framework, and even more so, lacking a dynamic feedback structure capable of adaptively adjusting optimization strategies based on data quality.

[0004] In summary, existing methods struggle to simultaneously address the heterogeneity of distributions under multiple failure modes, parameter estimation of censored data, and the multi-objective trade-off between reliability and economic loss. Current technologies exhibit significant shortcomings in areas such as mixture component identification, numerical stability of mixed censored regression parameter estimation, and multi-objective optimization decision-making for mixed distributions, necessitating a systematic solution. Summary of the Invention

[0005] The purpose of this invention is to provide a quality design method and system for lifetime response that considers multiple failure modes, in order to solve the problem that the prior art cannot simultaneously handle the distributed heterogeneity and right-censored data under multiple failure modes, and to achieve adaptive multi-objective optimization of reliability and economy.

[0006] To achieve the above objectives, this invention provides a quality design method for lifetime response considering multiple failure modes, comprising the following steps: Step S1: Obtain product life test data and clean and standardize the data; Step S2: Determine the optimal number of mixing components and identify the number of potential failure modes in the lifetime data; Step S3: Construct a mixed censoring regression model with the optimal number of mixed components, and establish the regression relationship between the distribution parameters of each component and the controllable factors; Step S4: For the mixed censored regression model, Bayesian inference is used to estimate the parameters and calculate the estimated values ​​of the model parameters. Step S5: Using the optimal mixture component number and model parameter estimates, construct reliability index, loss index and model fitness index; use reliability index and loss index as optimization objectives, use model fitness index to adjust the optimization process, and use multi-objective optimization algorithm to determine the optimal design value of controllable factors; Step S6: Apply the obtained optimal design values ​​of controllable factors to the product manufacturing process, verify the scheme, and output a quality design report.

[0007] Preferably, the product life test data in step S1 includes the failure time or censoring time of each sample, the censoring indicator variable, and the value of the controllable factor.

[0008] Preferably, the specific method for determining the optimal number of mixture components in step S2 is as follows: A random survival forest model is used to predict the survival of the lifetime data containing censoring indicator variables obtained in step S1. The cumulative risk function of the censored samples is integrated and estimated using each survival tree in the forest to construct a sample dissimilarity matrix that simultaneously reflects the difference between failure time and censoring information. Based on this dissimilarity matrix, the PAM clustering algorithm is used to divide the samples, and the Dunn index and Log-Rank test are combined to evaluate the significant differences in survival distribution among categories under different numbers of clusters. The Dunn index maximization and Log-Rank test are used to further evaluate the differences. Using the minimization of values ​​as the criterion, determine the actual number of multiple failure modes present in the product. And record the Dunn index. .

[0009] Preferably, the mixed censored regression model in step S3 is a mixed Weibull censored regression model, in which each Weibull component corresponds to a failure mode identified in step S2, and the mixed weights of each component are... This indicates the probability of occurrence of the failure mode; the scaling parameter for each component is established with respect to the controllable factor. Log-linear regression model: ; in, For the first The scale parameters of each component Design a matrix for controllable factors. For the first The regression coefficient vector of each component.

[0010] Preferably, the Bayesian inference method in step S4 specifically includes: regressing coefficients for each component. Set a normal prior ,in Let be the identity matrix, and be the shape parameter. Setting gamma a priori , for mixed weights Setting Dirichlet a priori ,in Indicates the first The mixed weights corresponding to each failure mode Indicates that all elements are 1 The dimensional vector; combined with the censored data from step S1, the Markov chain Monte Carlo method is used to sample from the posterior distribution to obtain the posterior sample set of parameters, including the regression coefficients. Shape parameters Mixed weights And the posterior covariance matrix; the mean of the posterior sample is used as the parameter estimate, and the posterior variance is used as a measure of the uncertainty of the parameter estimate.

[0011] Preferably, the product reliability index in step S5 is calculated as follows: ; ; in, This represents the transpose of a vector. This is the vector of controllable factor values. For a pre-defined warranty period; The conditional expected loss metric is calculated as follows: ; in, For the target lifespan, For the first The Weibull probability density function of each component; Model fitness index The calculation method is as follows: ; in, This represents the percentage of deletions. Dunn's Index The posterior covariance matrix for parameter estimation. , , For adaptive weighting coefficients, Represents the trace of a matrix.

[0012] Preferably, in step S5, the reliability index and loss index are used as optimization objectives, and the optimization process is adjusted using the model fitness index. Specifically, the optimization process is as follows: based on the model fitness index... The range of values ​​is used to dynamically determine the correction strategy for product reliability indicators and conditional expected loss indicators; a first critical value is set. =0.3 and the second critical value =0.7; when When using the modified reliability index Compared with the corrected loss index ;when When using the modified reliability index Compared with the corrected loss index ;when At that time, adopt , With the revised and As the input objective function of a multi-objective optimization algorithm.

[0013] Preferably, step S5 also forms a feedback loop: during the iterative solution of the Pareto front using a multi-objective optimization algorithm, every 10 generations, the adaptive weight coefficients are recalculated based on the dispersion of the non-dominated solution set distribution in the current population. , , Substitute the updated weight coefficients back into the model fitness index. The calculation formula is used to obtain the updated version. Then update By incorporating a correction strategy, the objective function for optimization in subsequent algebras is dynamically adjusted.

[0014] Preferably, in step S5, the Bayesian posterior uncertainty is also propagated to the optimization stage: for each set of parameters in the posterior sample set obtained in step S4... Substituting the product reliability index, conditional expected loss index, and model fitness index into the optimization model, multiple Pareto optimal frontiers are obtained. The posterior expectation of the solution at each frontier is then used as the final recommended design scheme. Indicates the sequence number of the posterior sample.

[0015] This invention also provides a quality design system for lifetime response that considers multiple failure modes, including: The data acquisition and preprocessing module is used to acquire product life test data and clean and standardize the data. The failure mode identification module is used to determine the optimal number of mixture components and identify the number of potential failure modes in the lifetime data. The mixed censoring regression modeling module is used to construct a mixed censoring regression model with the optimal number of mixed components and to establish the regression relationship between the distribution parameters of each component and the controllable factors. The Bayesian parameter estimation module is used to estimate the parameters of a mixed censored regression model using Bayesian inference methods and to calculate the estimated values ​​of the model parameters. The multi-objective optimization design module is used to construct reliability, loss and model fitness indices using the optimal mixture fraction and model parameter estimates; with reliability and loss indices as optimization objectives and model fitness indices to regulate the optimization process, the multi-objective optimization algorithm is used to determine the optimal design value of controllable factors. The scheme verification and output module is used to apply the obtained optimal design values ​​of controllable factors to the product manufacturing process, verify the scheme, and output a quality design report.

[0016] Therefore, the present invention employs the above-described quality design method and system for lifetime response considering multiple failure modes, and the beneficial technical effects are as follows: (1) In view of the problem that the determination of the number of mixed components in the prior art relies on subjective experience and does not make full use of censored information, the present invention combines random survival forest and PAM clustering, uses censored indicator variables to construct sample dissimilarity matrix, and combines Dunn index and Log-Rank test to automatically determine the optimal number of mixed components, realizing data-driven failure mode number identification and avoiding model bias caused by subjective specification.

[0017] (2) In view of the problems of poor numerical stability of mixed censoring regression parameter estimation and difficulty in handling data with high censoring ratio in the prior art, the present invention adopts the Bayesian inference method to set the prior distribution of regression coefficients, shape parameters and mixed weights of each component, and obtains the posterior estimate by MCMC sampling in combination with censored data, and outputs the posterior variance of the parameter as a measure of uncertainty, thereby improving the robustness of parameter estimation in small sample and high censoring ratio scenarios.

[0018] (3) In view of the lack of multiple objective trade-offs between reliability and economy and the lack of adaptive optimization adjustment mechanism in the existing technology, this invention constructs a reliability index, a loss index and a model fitness index. The optimization process is dynamically adjusted by the model fitness index. The priority of the optimization objective is automatically corrected according to the data censoring ratio, component separation degree and parameter estimation variance. The Bayesian posterior uncertainty is propagated to the optimization stage, realizing robust parameter design with adaptive data quality and ensuring the reliability of quality design decisions. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the quality design method for lifetime response considering multiple failure modes as described in this invention; Figure 2 The flowchart for multi-index adaptive optimization. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0022] Example 1 This embodiment uses a life test of a certain type of power module as an example to illustrate the specific implementation process of the method described in this invention. In actual use, this power module may experience two physical failure modes: solder joint fatigue failure (mode 1, caused by temperature cycling) and electrolytic capacitor aging failure (mode 2, caused by prolonged power-on). A total of 120 samples were collected during the test, and the failure time (or censoring time), censoring indicator variable, and three controllable factors were recorded for each sample: soldering temperature (…). (Unit: °C), Working voltage ( (unit: V) and heat dissipation area ( Unit: cm 2 The experiment was terminated at 5000 hours, and any samples that were not expired were considered right-censored. The raw data were standardized and then kept on file.

[0023] like Figure 1 As shown, this method includes the following steps: Step S1: Obtain product life test data (including the failure time or censoring time of each sample, the censoring indicator variable, and the value of the controllable factor), and clean and standardize the data.

[0024] In this embodiment, of the 120 data entries collected, 84 were complete but invalid, and 36 were censored. The censoring ratio is [not specified]. =0.30. Censored data mainly consist of samples with a lifetime exceeding 5000 hours that have not yet failed. The controllable factor values ​​were standardized using Z-score to eliminate the influence of dimensions. Some examples of the original data are shown in Table 1.

[0025] Table 1. Examples of raw experimental data (partial)

[0026] Step S2: Determine the optimal number of mixing components and identify the number of potential failure modes in the lifetime data.

[0027] The specific method for determining the optimal number of mixture components is as follows: A random survival forest model is used to predict the survival of the lifetime data containing censoring indicator variables obtained in step S1. The cumulative risk function of the censored samples is estimated by integrating the data from each survival tree in the forest, constructing a sample dissimilarity matrix that simultaneously reflects the differences in failure time and censoring information. Based on this dissimilarity matrix, the PAM clustering algorithm is used to divide the samples, and the Dunn index and Log-Rank test are combined to evaluate the significant differences in survival distribution among categories under different numbers of clusters. The Dunn index maximization and Log-Rank test are used to further evaluate the results. Using the minimization of values ​​as the criterion, the number of multiple failure modes actually existing in the product is automatically determined. And record the Dunn index. .

[0028] In this embodiment, a random survival forest model is used (setting the number of trees). =500, the number of candidate variables for each node =2) Perform survival prediction on the standardized data to obtain the cumulative risk function estimate for each sample, and then construct... The dissimilarity matrix is ​​calculated. Candidate mixture components are selected with numbers of 2, 3, 4, and 5 respectively. PAM clustering is performed on each candidate value, and the Dunn index corresponding to each candidate value is calculated. and Log-Rank test The values ​​are shown in Table 2.

[0029] Table 2 Clustering evaluation indicators under different candidate component numbers

[0030] Based on maximizing the Dunn index (i.e., the greater the separation between components, the better) and the Log-Rank test The criterion <0.05 indicates that the Dunn exponent is largest when the number of candidate components is 2. The value is significant, therefore the optimal number of mixture components (number of multiple failure modes) is determined. =2, meaning there are two failure modes. The Dunn index recorded at this point is... =0.67, for use in subsequent steps.

[0031] Step S3: Construct a mixed censoring regression model with the optimal number of mixed components, and establish the regression relationship between the distribution parameters of each component and the controllable factors.

[0032] In this embodiment, =2 Construct a two-component mixture Weibull censored regression model. Each component corresponds to a failure mode, and the weights are mixed. , This represents the probability of occurrence of each failure mode. The scaling parameter for each component... , Establish information about controllable factors Log-linear regression model: ; in, For the first The scale parameters of each component Design a matrix for controllable factors. For the first The regression coefficient vector of each component, and The different failure modes are independent of each other; the probability density function of the model explicitly includes censored indicator variables.

[0033] Step S4: For the mixed censored regression model, Bayesian inference is used to estimate the parameters and calculate the estimated values ​​of the model parameters.

[0034] Bayesian inference methods specifically include: regression coefficients for each component. Set a normal prior ,in Let be the identity matrix, and be the shape parameter. Setting gamma a priori , for mixed weights Setting Dirichlet a priori ,in Indicates the first The mixed weights corresponding to each failure mode Indicates that all elements are 1 The dimensional vector; combined with the censored data from step S1, the Markov chain Monte Carlo method is used to sample from the posterior distribution to obtain the posterior sample set of parameters, including the regression coefficients. Shape parameters Mixed weights And the posterior covariance matrix; the mean of the posterior sample is used as the parameter estimate, and the posterior variance is used as a measure of the uncertainty of the parameter estimate.

[0035] Since the likelihood function of a mixed censoring model has no analytical solution, conventional numerical optimization is prone to divergence when the censoring ratio is high. Bayesian inference, through prior information and MCMC sampling, can not only obtain parameter point estimates, but also provide posterior variance as a measure of uncertainty, providing important input for subsequent model fitness indices, especially suitable for scenarios with small samples or high censoring ratios.

[0036] In this embodiment, posterior samples of each parameter are obtained using MCMC sampling (20,000 times in total, discarding the first 5,000 as a warm-up). The posterior mean is taken as the parameter estimate, and the posterior variance is used as the uncertainty measure. The estimation results are shown in Table 3.

[0037] Table 3. Posterior estimation results of parameters of the mixed Weibull regression model

[0038] The trace of the posterior covariance matrix is ​​4.32, which is used as part of the model fitness index.

[0039] Step S5, as follows Figure 2 As shown, reliability, loss and model fitness indices are constructed using the optimal mixture component number and model parameter estimates. The reliability and loss indices are used as optimization objectives, and the model fitness index is used to regulate the optimization process. A multi-objective optimization algorithm is used to determine the optimal design value of the controllable factors.

[0040] The product reliability index is calculated as follows: ; ; in, This represents the transpose of a vector. This is the vector of controllable factor values. The warranty period is predetermined.

[0041] The conditional expected loss metric is calculated as follows: ; in, For the target lifespan, For the first The Weibull probability density function of each component.

[0042] Model fitness index The calculation method is as follows: ; in, The censoring ratio in step S1, Dunn's Index The posterior covariance matrix for parameter estimation. , , For adaptive weighting coefficients, Represents the trace of a matrix.

[0043] Using reliability and loss metrics as optimization objectives, and adjusting the model fitness metric as the optimization process, the specific steps are as follows: Based on the model fitness metric... The range of values ​​is used to dynamically determine the correction strategy for product reliability indicators and conditional expected loss indicators; a first critical value is set. =0.3 and the second critical value =0.7; when When using the modified reliability index Compared with the corrected loss index ;when When using the modified reliability index Compared with the corrected loss index ;when At that time, adopt , With the revised and As the input objective function of a multi-objective optimization algorithm.

[0044] Traditional methods use fixed weights to trade off reliability against loss, failing to capture the reliability of the model estimation. This invention introduces a model fitness index. It integrates the censoring ratio, component separation degree, and parameter estimation variance, when the data quality is poor ( When the data quality is high, the bias is towards minimizing loss to avoid over-reliance on unreliable predictions; when the data quality is high ( The system prioritizes maximizing reliability when the time frame is small. The feedback loop keeps this adjustment ongoing, achieving adaptive multi-objective optimization.

[0045] In this embodiment, a warranty period is set. =2000 hours, target lifespan =3000 hours. Construct each index using the parameter estimates in Table 3. First, calculate the model fitness index: [The remaining text appears to be incomplete and requires further context.] =0.30, =0.67, the trace of the posterior covariance matrix is ​​4.32, and the initial weight coefficients are taken. = = =1 / 3, then: =2.04.

[0046] because =2.04> =0.7 indicates poor data quality (large variance in parameter estimation and poor component separation). Therefore, according to the strategy in claim 7, a modified reliability index is adopted. Compared with the corrected loss index To minimize the optimization bias loss (prioritizing economy).

[0047] Then, the NSGA-II algorithm (population size 50, 200 generations) is used to solve for the Pareto optimal frontier. During the iteration process, the adaptive weight coefficients are recalculated every 10 generations based on the dispersion of the current non-dominated solution set. For example, the first generation calculates... =0.25, =0.35, =0.40, substitute and update This information is then fed back to the correction strategy. After 200 generations of convergence, the solutions on the Pareto front are uniformly distributed.

[0048] Finally, each set of parameters (15,000 sets in total) from the MCMC posterior samples in step S4 is substituted into the optimization model to obtain 15,000 Pareto optimal frontiers. The posterior expectation of the non-dominated solutions on each frontier is taken as the final recommended design scheme. The recommended controllable factor values ​​(standardized values) are as follows: =-0.52 (corresponding to a welding temperature of approximately 238℃). =0.37 (corresponding to an operating voltage of approximately 12.9V). =-0.21 (corresponding to a heat dissipation area of ​​approximately 4.1cm²) 2 The corresponding reliability at this time. =0.76, the expected loss is 1.23 × 10 5 .

[0049] Step S6: Apply the obtained optimal design values ​​of controllable factors to the product manufacturing process, verify the scheme, and output a quality design report.

[0050] The recommended design parameters are: welding temperature 238℃, operating voltage 12.9V, heat dissipation area 4.1cm². 2 The solution was applied to an actual production line, and 30 additional power modules were manufactured for verification testing (5000-hour censoring). Verification results: Of the 30 samples, 27 had complete failure times, 3 were censored, and the average failure time was 3150 hours, far exceeding the warranty period of 2000 hours. The actual reliability estimate was 0.83, which is basically consistent with the model prediction of 0.76. Furthermore, there were no early failures, indicating that the recommended solution effectively balanced the two failure modes.

[0051] The final output quality design report includes: the optimal number of mixing components. =2 and its corresponding failure mode explanation, recommended design values ​​for each controllable factor, confidence intervals for reliability and loss indices, trajectory graph of model fitness index changes, and verification conclusions.

[0052] Table 4 Comparison of Recommended Design Scheme and Original Scheme

[0053] Table 4 shows that the recommended solution of this invention is superior to the original solution in terms of both reliability and loss, and the verification results further prove the effectiveness of the method.

[0054] Example 2 Quality design systems considering lifetime response with multiple failure modes include: The data acquisition and preprocessing module is used to acquire product life test data and clean and standardize the data. The failure mode identification module is used to determine the optimal number of mixture components and identify the number of potential failure modes in the lifetime data. The mixed censoring regression modeling module is used to construct a mixed censoring regression model with the optimal number of mixed components and to establish the regression relationship between the distribution parameters of each component and the controllable factors. The Bayesian parameter estimation module is used to estimate the parameters of a mixed censored regression model using Bayesian inference methods and to calculate the estimated values ​​of the model parameters. The multi-objective optimization design module is used to construct reliability, loss and model fitness indices using the optimal mixture fraction and model parameter estimates; with reliability and loss indices as optimization objectives and model fitness indices to regulate the optimization process, the multi-objective optimization algorithm is used to determine the optimal design value of controllable factors. The scheme verification and output module is used to apply the obtained optimal design values ​​of controllable factors to the product manufacturing process, verify the scheme, and output a quality design report.

[0055] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0056] Therefore, the present invention adopts the above-mentioned quality design method and system for life-type response that considers multiple failure modes, which can simultaneously handle the heterogeneity of multiple failure mode distribution and right-censored data in product life testing, realize adaptive multi-objective optimization of reliability and economy, and improve the reliability and robustness of quality design decisions.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A quality design method for lifetime response considering multiple failure modes, characterized in that, Includes the following steps: Step S1: Obtain product life test data and clean and standardize the data; Step S2: Determine the optimal number of mixing components and identify the number of potential failure modes in the lifetime data; Step S3: Construct a mixed censoring regression model with the optimal number of mixed components, and establish the regression relationship between the distribution parameters of each component and the controllable factors; Step S4: For the mixed censored regression model, Bayesian inference is used to estimate the parameters and calculate the estimated values ​​of the model parameters. Step S5: Using the optimal mixture component number and model parameter estimates, construct reliability index, loss index and model fitness index; use reliability index and loss index as optimization objectives, use model fitness index to adjust the optimization process, and use multi-objective optimization algorithm to determine the optimal design value of controllable factors; Step S6: Apply the obtained optimal design values ​​of controllable factors to the product manufacturing process, verify the scheme, and output a quality design report.

2. The quality design method for lifetime response considering multiple failure modes according to claim 1, characterized in that, The product life test data in step S1 includes the failure time or censoring time of each sample, the censoring indicator variable, and the value of the controllable factor.

3. The quality design method for lifetime response considering multiple failure modes according to claim 1, characterized in that, The specific method for determining the optimal number of mixture components in step S2 is as follows: use the random survival forest model to perform survival prediction on the lifetime data containing censoring indicator variables obtained in step S1, and use the cumulative risk function of each survival tree in the forest to perform integrated estimation of the censored sample, and construct a sample dissimilarity matrix that can simultaneously reflect the difference between failure time and censoring information. Based on the dissimilarity matrix, the PAM clustering algorithm was used to divide the samples. The Dunn index and Log-Rank test were combined to evaluate the significant differences in survival distributions among different cluster numbers. The Dunn index maximization and Log-Rank test were used to further analyze the differences. Using the minimization of values ​​as the criterion, determine the actual number of multiple failure modes present in the product. And record the Dunn index. .

4. The quality design method for lifetime response considering multiple failure modes according to claim 1, characterized in that, In step S3, the mixed censored regression model is a mixed Weibull censored regression model. Each Weibull component in this model corresponds to a failure mode identified in step S2, and the mixed weights of each component are... This indicates the probability of occurrence of the failure mode; the scaling parameter for each component is established with respect to the controllable factor. Log-linear regression model: ； in, For the first The scale parameters of each component Design a matrix for controllable factors. For the first The regression coefficient vector of each component.

5. The quality design method for lifetime response considering multiple failure modes according to claim 4, characterized in that, The Bayesian inference method in step S4 specifically includes: regressing coefficients for each component. Set a normal prior ,in Let be the identity matrix, and be the shape parameter. Setting gamma a priori , for mixed weights Setting Dirichlet a priori ,in Indicates the first The mixed weights corresponding to each failure mode Indicates that all elements are 1 The dimensional vector; combined with the censored data from step S1, the Markov chain Monte Carlo method is used to sample from the posterior distribution to obtain the posterior sample set of parameters, including the regression coefficients. Shape parameters Mixed weights And the posterior covariance matrix; the mean of the posterior sample is used as the parameter estimate, and the posterior variance is used as a measure of the uncertainty of the parameter estimate.

6. The quality design method for lifetime response considering multiple failure modes according to claim 5, characterized in that, The product reliability index is calculated in step S5 as follows: ； ； in, This represents the transpose of a vector. This is the vector of controllable factor values. For a pre-defined warranty period; The conditional expected loss metric is calculated as follows: ； in, For the target lifespan, For the first The Weibull probability density function of each component; Model fitness index The calculation method is as follows: ； in, This represents the percentage of deletions. Dunn's Index The posterior covariance matrix for parameter estimation. , , For adaptive weighting coefficients, Represents the trace of a matrix.

7. The quality design method for lifetime response considering multiple failure modes according to claim 6, characterized in that, Step S5 uses reliability and loss metrics as optimization objectives, and adjusts the optimization process using model fitness metrics. Specifically, the optimization process is as follows: based on the model fitness metrics... The range of values ​​is used to dynamically determine the correction strategy for product reliability indicators and conditional expected loss indicators; a first critical value is set. =0.3 and the second critical value =0.7; when When using the modified reliability index Compared with the corrected loss index ;when When using the modified reliability index Compared with the corrected loss index ;when At that time, adopt , With the revised and As the input objective function of a multi-objective optimization algorithm.

8. The quality design method for lifetime response considering multiple failure modes according to claim 7, characterized in that, Step S5 also forms a feedback loop: during the iterative solution of the Pareto front using a multi-objective optimization algorithm, the adaptive weight coefficients are recalculated every 10 generations based on the dispersion of the non-dominated solution set distribution in the current population. , , ; Substitute the updated weight coefficients back into the model fitness index. The calculation formula is used to obtain the updated version. Then update By incorporating a correction strategy, the objective function for optimization in subsequent algebras is dynamically adjusted.

9. The quality design method for lifetime response considering multiple failure modes according to claim 5, characterized in that, Step S5 also propagates the Bayesian posterior uncertainty to the optimization stage: for each set of parameters in the posterior sample set obtained in step S4... Substituting the product reliability index, conditional expected loss index, and model fitness index into the optimization model, multiple Pareto optimal frontiers are obtained. The posterior expectation of the solution at each frontier is then used as the final recommended design scheme. Indicates the sequence number of the posterior sample.

10. A quality design system for lifetime response considering multiple failure modes, characterized in that, include: The data acquisition and preprocessing module is used to acquire product life test data and clean and standardize the data. The failure mode identification module is used to determine the optimal number of mixture components and identify the number of potential failure modes in the lifetime data. The mixed censoring regression modeling module is used to construct a mixed censoring regression model with the optimal number of mixed components and to establish the regression relationship between the distribution parameters of each component and the controllable factors. The Bayesian parameter estimation module is used to estimate the parameters of a mixed censored regression model using Bayesian inference methods and to calculate the estimated values ​​of the model parameters. The multi-objective optimization design module is used to construct reliability, loss and model fitness indices using the optimal mixture fraction and model parameter estimates; with reliability and loss indices as optimization objectives and model fitness indices to regulate the optimization process, the multi-objective optimization algorithm is used to determine the optimal design value of controllable factors. The scheme verification and output module is used to apply the obtained optimal design values ​​of controllable factors to the product manufacturing process, verify the scheme, and output a quality design report.

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