Reliability Evaluation Of The Products With Zero-failure Data And Small Sample Based On Bayes Method And Its Improvement

In order to improve the accuracy of reliability evaluation,a large number of life data and sample information are needed.However,with development of manufacturing technology in China,the quality and reliability of most products have been improved accordingly,resulting in less life data available in a limited time,which results in more zero-failure data got by researchers in life tests.At the same time,for some high-cost products,large sample life test will cause a lot of labor and financial losses.Generally speaking,small sample of failure data and zero-failure data are becoming more and more common in life test,while the classical statistics reliability evaluation method faces the problems of low accuracy.Therefore,the accuracy of evaluation results can't satisfy the practical demands of engineering.Thus,it is of great research significance and engineering value to study the reliability evaluation method with small sample and zerofailure data in order to obtain more accurate evaluation results.Therefore,in order to make full use of the information from small sample of failure data and zero-failure data,so as to improve the accuracy of products reliability.this paper takes Weibull distribution as an example,and studies the reliability evaluation of small sample,zero failure data and mixed life test data respectively.The specific contents are as follows:(1)To deal with the problems of small sample size and the difficulty in determining the prior distribution of Bayes method,a reliability evaluation method based on Bayes theory and improved bootstrap method is proposed in this paper.Firstly,the B-spline function is constructed and sampled according to the life data.Secondly,the K-means clustering algorithm is used to cluster each group of resampling data to remove the outliers that affect the evaluation accuracy.Thirdly,the least square method is used to estimate the distribution parameters of each group because there aren't many data in each group.Finally,in the case of insufficient product prior information,in order to further improve the reliability evaluation accuracy,the lognormal distribution is used to fit the above groups of parameter estimates and regard them as the parameter prior distribution.The posterior distribution of parameters is obtained by fusing the existing life data,and the posterior distribution is solved by Markov Monte Carlo method.The proposed method is applied to simulation examples and practical cases,and compared with other literature methods,the evaluation results verify the applicability of the proposed method.(2)In order to solve the problem of inaccurate estimation of failure probability when there are zero-failure data only,a matching distribution curve method based on improved hierarchical Bayes estimation is proposed in this paper.The method is proposed by combining the characteristics of Weibull distribution and incomplete Beta distribution to construct hierarchical Bayes prior distribution,which makes up for the conservative problem of failure probability estimation in traditional Bayes method.Firstly,the failure probability range is calculated according to the characteristics of Weibull distribution,and then the incomplete Beta prior distribution is constructed.Secondly,the value range of hyper parameters in incomplete Beta prior distribution is determined according to expert experience or historical information.The posterior distribution of failure probability is solved by Bayes formula,and the posterior distribution is used to calculate failure probability at each censoring time.Finally,the unknown parameters in the life distribution are estimated by the weighted least square method.At the same time,the robustness of the proposed method is verified,that is,the proposed method can still keep a relatively high reliability evaluation accuracy when the prior information is inaccurate.The proposed method is applied to simulation examples and practical cases,and compared with other literature methods,the evaluation results verify the feasibility of the proposed method.(3)Aiming at the problem of low accuracy and existing limitations of Bayes method in estimating the failure probability with mixed test data,a matching distribution curve method based on maximum information entropy is proposed in this paper.Firstly,the corresponding prior beta distribution of failure probability is constructed at different truncation times.Secondly,the optimization model is established by maximizing the prior distribution information entropy.The constraints of the model are determined according to the order of failure probability and the characteristics of Weibull distribution(the corresponding constraints can also be constructed for other life distributions).Thirdly,considering that there is no effective prior information of the product,the simulated annealing algorithm is used to solve the optimization model and determine the hyperparametric value of each prior beta distribution in turn.Finally,the posterior distribution of failure probability is solved by Bayes conjugate prior distribution theory.After calculating the failure probability value at each truncation time,the life distribution parameters are estimated by the least square method to determine the reliability curve.The proposed method is applied to simulation examples and practical cases,and compared with other literature methods,the evaluation results verify the feasibility and effectiveness of the proposed method.