Mutivariate Correlated Degradation Modeling And Reliability Assessment For Engineering Systems

The degradation-based reliability modeling has been widely recognized as an efficient approach to solve the reliability issues, such as limited data, long lifetime, and no failure data, and so forth. With the continuous development of science and technology, advanced engineering products or systems oftentimes have multiple functions and required performances which can be associated by multiple performance degradation indicators. Due to deterioration, these performance degradation indicators degrade over time. On the other hand, as all of these performance degradation indicators reflect the status/health condition of a product/system, they are usually correlated with one another in a complex manner. There is, therefore, an urgent need for developing a suite of tools to model the dependency among multiple performance degradations. With such purpose, this thesis devotes to propose a set of models and approaches to model multivariate correlated degradation processes and evaluate the corresponding reliability measures. The major research contributions and innovative outcomes are summarized as follows:(1) Proposing of a bivariate random degradation model based on the Copula functions. In this work, by treating the parameters of Copula functions as stochastic quantities which vary from a piece of system to another, a bivariate degradation model is proposed. A two-stage Bayesian inference method is developed to estimate the unknown parameters. The Monte Carlo simulation method is used to compute the reliability function with a given confidence level. The results from the illustrative examples show that the proposed method is capable of characterizing the heterogeneity of each individual system in the same population.(2) Developing of a time-varying bivariate degradation model based on time-vary Copula functions. In this work, the feature of time-varying dependency among two performance degradation indicators is taken into account via a set of time-varying Copula functions. The illustrative examples demonstrate the advantages of the proposed method over the traditional time-constant bivariate degradation models. On the other hand, even if the time-varying dependency may not exist, the proposed method can also yield competitive results with that of the traditional time-constant models.(3) Investigating a multivariate correlated degradation model based on the D-Vine Copula. The multivariate degradation models reported in earlier literature assume that either multiple performance degradation indicators of a system are statistically independent or all of the performance degradation indicators have the same correlation structures. In this work, a new multivariate correlated degradation model is developed by introducing the D-Vine copula which allows for modeling multivariate correlation in a more flexible way. The accuracy of the proposed method in terms of characterizing the complex correlations among multiple degradation indicators is examined via a set of illustrative examples.