In many assembly systems, components may exhibit different quality behaviors. By selecting the mating part whose characteristics match with those of the main part, high precision assemblies can be achieved. Such a process is referred to as selective assembly. Most of the studies on selective assembly only consider the case where machines are reliable and the buffer capacity is infinite. However, unreliable machines and finite buffers are commonly observed in many assembly systems. This paper studies a two-component assembly system with unreliable Bernoulli machines and finite buffers. Analytical methods based on a two-level decomposition procedure are developed to analyze the system performance. The convergence of the procedure is justified analytically. Numerical study shows that such a method provides a high accuracy in performance evaluation.