Dependence Modeling for Multivariate System Reliability Prediction

Both the reliability-wise system structure and the multivariate component lifetime distributions are required for accurately predicting a complex system’s reliability. Most of existing research work either assumes these components’ lifetime distributions are statistically independent or they are subject to a well-defined multivariate joint distribution, such as a multivariate Gaussian distribution. However, oftentimes the independence assumption does not match engineering practice since components usually have interactions with each other due to common manufacturing defects and shared environmental conditions, etc. On the other hand, a multivariate joint Gaussian distribution may not be adequate, because it cannot describe distribution skewness or upper/lower tail dependency among multivariate lifetime data that are often observed in real data sets. As a result, the system reliability assessment may be biased.In this study, we present a data-centric multivariate distribution construction framework that is based on a sequence of copula functions. Under this framework, historical degradation data from different components within a system are utilized to derive the multivariate degradation model, and various types of dependency among these components are explicitly scrutinized and used for either component or system level performance prediction. Our contributions include that 1) we apply the pair copula construction (PCC) method on more than two degradation processes to explicitly model the association of these processes; 2) we connect the system structure and system failure prior information to the PCC structure to simplify the construction of multivariate distribution; and 3) we demonstrate the biasness in system reliability prediction if the dependencies existed in component failure processes are ignored. This study highlights the applicability and flexibility of the pair copula construction method for conducting multivariate reliability analysis for complex systems. A case study of degradation analysis of optical materials is used to demonstrate our proposed approach.