It has significant engineering importance to evaluate the reliability of a system at its early design stage since any modification in design at a later time will be costly, and sometimes impossible. However, the early evaluation is challenging due to various factors, e.g. inaccurate expert judgements, insufficient test data and the incomplete knowledge of the system's structure. In this paper, we address the reliability of a complex system with unspecified structure. A Bayesian framework is developed for the reliability assessment as well as the further model uncertainty quantification. We consider a scenario that test data is drawn simultaneously from different components/subsystem levels, in which the overlapping nature has to be taken into consideration. A d-separation method is developed to construct the conditionally independent likelihoods. We then use a numerical case study to demonstrate our proposal.