Reliability analysis of a complex system with hybrid structures and multi-level dependent life metrics

In practical engineering, the presence of dependent evidence is not rare due to various imperfections. Misuse of such information in reliability analysis will lead to conflicting or even erroneous results. In this paper, we propose a Bayesian reliability approach for complex systems with dependent life metrics. Notions such as explicit evidence and implicit evidence are established based on an identification of different roles of multiple dependent evidence in the likelihood construction. A likelihood decomposition method is developed to convert the overall likelihood into a product of Explicit Evidence-based Likelihood (EEL) function and Implicit Evidence-based Likelihood (IEL) function. An inferential diagram is developed to intuitively generate the required implicit evidence taking both outer-source information and the system configuration into consideration. An algorithm is then presented for implementation. The contribution of our work is a systematic investigation of the role of dependent evidence in system reliability evaluation and a full Bayesian approach that is applied to various system reliability models. Extensive numerical cases and a practical engineering case are demonstrated for validation and to illustrate the benefits of our approach.