This paper examines the performance analysis of a transfer line with unreliable machines and finite buffers. All machines have the same processing times. We propose a new decomposition method which decomposes a line into a set of two-machine lines. A sufficient set of equations is established to find performance measures such as production rate and average buffer levels. A simple iterative algorithm is then proposed to solve these equations. We also prove that the set of decomposition equations has a unique solution and that the proposed algorithm converges to that unique solution. Experimental results show that the proposed algorithm leads to a good solution.