Reliability Assessment Of Long-life Products Based On Bayesian Theory Under Multi-source Information

Along with science and technology developing unceasingly,higher requirements have been set for the service life and reliability indicators of products applied in important fields that require very high quality.The quality of such products gradually improves during the process of updates and iterations,presenting characteristics such as "long service life,high reliability,and high cost".On the one hand,the amount of failure data that can be obtained from its reliability tests is reduced within a limited time,and the situation of zero-failure data is becoming more common.On the other hand,it is difficult to invest in reliability tests in the form of large samples while considering efficiency and cost,resulting in the reliability test data showing "small sample" characteristics.The traditional reliability assessment method is based on statistical inference methods under large sample test,and a large amount of life data and sample information are prerequisites for improving the accuracy of reliability assessment.For long-life products,traditional reliability assessment methods based on Law of Large Numbers are usually difficult to apply when dealing with small-sample and zero-failure data.The accuracy and belief of reliability assessment results for long-life products are closely related to the realization of their functions and the completion of tasks.The thesis focuses on the "zero-failure" and "small sample" problems occurred in the reliability assessment of long-life products.To improve the accuracy and credibility of the assessment results and fully utilize the multi-source reliability information of long-life products,research is conducted from two aspects: evaluation methods and parameter solving of evaluation indicators.The specific research contents are as follows:(1)The thesis proposes a reliability point estimation and confidence interval estimation method based on maximum entropy and simulated annealing algorithm combined with parameter Bootstrap method,considering the case of zero-failure life test data in response to the current low assessment accuracy and difficulty in obtaining both point estimation and confidence interval estimation of parameters while avoiding inconsistent results in reliability assessment methods with zero-failure data.Firstly,the order characteristic of failure probability size of Weibull distribution is considered,and a hyperparameter optimization model is constructed under the Bayes theory by specifying the range of failure probability values and maximizing the information entropy of prior distribution.Then,simulated annealing algorithm is used to solve the optimization model to avoid getting trapped in local optimal solutions.Next,weighted least squares method is used to obtain the point estimation of reliability,and parameter Bootstrap method is used to re-sample new samples to obtain the confidence interval estimation of reliability.Finally,simulation examples are used to verify the proposed method not only improves the accuracy of reliability point estimation and interval estimation,but also enhances the credibility of evaluation results.(2)The thesis puts forward an improved evidence synthesis method that considers evidence conflict and uncertainty in response to the challenges faced by Bayes-like methods in dealing with small-sample failure data,including the difficulty in incorporating prior information to determine the prior distribution,and the inefficiency in handling cognitive uncertainty and information conflicts among different reliability information sources.The proposed method first uses the maximum difference measurement method to identify evidence conflicts and determine which sources of evidence have higher conflict levels.Then,the conflicting evidence is corrected using the improved conflict correction factor and uncertainty correction factor,and the optimal comprehensive weight is obtained based on Game theory.Finally,simulation examples are used to verify that the proposed method can alleviate evidence conflicts to a certain extent and reduce the uncertainty of fusion results.(3)The thesis provides a small-sample reliability Bayesian fusion assessment method for long-life products in response to the small samples,insufficient data from a single information source,and low credibility of individual information sources for longlife products.The proposed method takes into account the phenomenon of multiple sources of information coexisting.Firstly,a fusion model is established for degradation data and right-censored life data.Secondly,the parameters of the reliability distribution are estimated using the Markov chain Monte Carlo method based on the fusion model.Thirdly,simulation examples are presented to demonstrate the advantages of the proposed method in dealing with small sample data and the necessity of considering right-censored data.Finally,the proposed method is applied to the reliability assessment of a harmonic reducer as a representative of long-life products,and the effectiveness of the proposed method is verified.The advantages of using the improved evidence fusion method to fuse prior information and construct prior distributions are further demonstrated,which proves the engineering applicability of the proposed method in addressing the "zero-failure" and "small sample" problems in the reliability assessment of long-life products.