This paper presents a model of manufacturing system with two parallel workstations. The machines in the system are non-identical unreliable machines, and the processing times, failure times and repair times of the machines are assumed to be exponentially distributed. We show that such model can be considered a quasi-birth-death process (QBD) with a tri-diagonal block structure generator matrix. The solution method for the QBD process is a matrix-analytic method chosen based on the characteristic of the parallel system. At last a two station one buffer case with three parallel machines at each station is given to show the accuracy and efficiency of the proposed method.