On multivariate copula modeling of dependent degradation processes

Multivariate degradation processes have been observed in many engineering systems. Most existing multivariate degradation modeling techniques, such as multivariate general path models or multivariate Wiener process models, assume an underlying Gaussian dependence structure. Unfortunately, in reality, the dependencies among degradation processes are often nonlinear, asymmetric and greatly tail-skewed, and thus limit the usefulness of the conventional modeling techniques in practice. To overcome these limitations, in this paper, we develop a copula-based multivariate modeling framework. Three fundamental copula classes are applied to model the complex dependence structure among correlated degradation processes. Statistical inference and model selection techniques, including two graphical diagnostic tools, a test of independence and a goodness-of-fit test, are employed to identify the best model. The advantages of the proposed modeling framework are demonstrated through simulation studies. And we also discuss the effect of ignoring tail dependence on system failure probability assessment. Finally, the applications of the copula-based multivariate degradation models on both system reliability evaluation and remaining useful life prediction are provided. The proposed methodology is illustrated using a numerical example.