Research On Performance Degradation Reliability Modeling And Assessment Method Based On Bayesian Updation And Copula Theory

Traditional reliability assessment methods are established on the basis of failure lifetime data. For high reliability and long lifetime products, it is difficult to obtain enough failure lifetime data via life test or accelerated life test in a short time. Meanwhile, degradation data can provide useful information for the reliability assessment. In the last decades, reliability modeling and analysis based on performance degradation has become a hot point of reliability assessment for highly reliable and long life products. Focusing on the reliability assessment of highly reliable products, this thesis uses the approaches including stochastic process, Bayesian method, Copula theory, shock theory and Markov Chain Monte Carlo (MCMC) algorithm comprehensively, the following aspects are considered, including real time reliability evaluation, multidimensional performance degradation characteristic modeling and dependent competing failure modeling, et al. The main contributions of the dissertation are as follows:(1) Real time reliability assessment with random effect Wiener process. First, the population product degradation path is characterized by random effect Wiener process, and the model can capture unit to unit variation. MCMC method is used to estimate the unknown parameters and the best fitting degradation model is obtained by using the Deviance Information Criterion (DIC) criterion, then the population product reliability assessment is studied. In individual product reliability assessment, a Bayesian method is proposed to integrate the population degradation information and the individual degradation data, and the reliability assessment and its residual use life of particular individual can be obtained. A lasers data is given as an example to demonstrate the usefulness and validity of the proposed model and method.(2) Real time reliability assessment with random effect linear independent increment process. When degradation path has linear mean and linear standard deviation functions, the linear independent increment process is presented to model the performance degradation data. The population degradation path is characterized by random effect linear independent increment process, and the model can capture unit to unit variation. Considering the likelihood function is complicated, MCMC method is used to estimate the unknown parameters. By using Bayesian updated method, the real time reliability evaluation of individual product are obtained. The proposed models and methods are validated through a wheel wear data example.(3) Reliability modeling methods of bivariate nonlinear diffusion degradation process is studied. For the products with bivariate nonlinear degradation paths, random effect nonlinear diffusion process and Copula function are used to describe the degradation failure processes and their correlativity, where random effects are used to capture the unit to unit difference, and the new model provides technical support of the reliability analysis under multiple performance degradation characteristics. The fatigue cracks development of the alloy products is given to demonstrate the usefulness and validity of the proposed model and method.(4) Reliability modeling approaches of bivariate nonlinear Gamma degradation process is studied. For the complexity products with bivariate nonlinear strictly monotone degradation paths, the nonlinear Gamma process and Copula function are used to describe the degradation failure process and their correlativity. Considering that the model is so complicated and analytically intractable, MCMC method is used to estimate the unknown parameters. A numerical example of LED lamp is given to demonstrate the usefulness and validity of the proposed model and method.(5) Reliability modeling approaches of products with dependent competing failure process is investigated. For the products subject to degradation and random shocks, the dependent competing failure model is established, where degradation process is described by Wiener process and shock process is described by Poisson process. In model, hard failure is caused by shock process and the shock loads can speed up the degradation process. Furthermore, the situation of shifting-threshold is also considered, where the threshold value of hard failure and soft failure decrease to a lower level after the arrival of a certain number of shocks.