Worldwide competition and diverse demand of customers pose great challenges to manufacturing enterprises. How to organize production to achieve high productivity and low cost becomes their primary task. In the mean time, the rapid pace of technology innovation has contributed to the development of new types of flexible automation. Hence, increasing manufacturing enterprises convert to multi-product and small-batch production, a manufacturing strategy that brings increased output, reduced costs, and quick response to the market. A distinctive feature of small-batch production is that the system operates mainly in the transient states. Transient states may have a significant impact on manufacturing systems. It is therefore necessary to estimate the dynamic performance of systems. As the assembly system is a typical class of production systems, in this paper, we focus on the problem of dynamic performance prediction of the assembly systems that produce small batches of different types of products. And the system is assumed to be characterized with Bernoulli reliability machines, finite buffers, and changeovers. A mathematical model based on Markovian analysis is first derived and then, the analytical formulas for performance evaluation of three-machine assembly systems are given. Moreover, a novel approach based on decomposition and aggregation is proposed to predict dynamic performance of large-scale assembly systems that consist of multiple component lines and additional processing machines located downstream of the assemble machine. The proposed approach is validated to be highly accurate and computationally efficient when compared to Monte Carlo simulation.