This paper presents an approximate decomposition method for the performance evaluation of non-homogeneous fabrication/assembly (F/A) systems with multiple failure modes, finite buffers, and a fixed assembly proportion. First, we introduce a mixed flow combined with fund flow and material flow to convert an F/A system to a virtual transfer line. Then, we decompose the virtual transfer line into several two-machine lines and establish a continuous decomposition model. To tackle the new emerging characteristics of the F/A system, we propose an F/A decomposition algorithm (FADA) for solving this model and obtain the throughput and buffer level of the F/A system to evaluate system performance. Also, we demonstrate the validity of the proposed model and algorithm by comparing with the results of simulation-based method and completion time approximation (CTA)-based method. Finally, we analyze the impact of several key parameters, including failure rates, repair rates, and buffer capacities, on the performance of the F/A system. The results show that our analytical method outperforms the existing methods and can help production managers to evaluate the system performance, analyze the possible modifications, and further find the best performance improvement of such F/A systems.@en