An improved decomposition method for evaluating the performance of transfer lines with unreliable machines and finite buffers

In this paper, we consider transfer lines consisting of a series of machines separated by finite buffers. The processing time of each machine is deterministic and may be not identical. All machines are prone to operation-dependent failures, and the times between failures and the times to repair are assumed to be exponentially distributed. Many analytical methods have been developed to evaluate the performance of such lines. In general, these methods provide fairly accurate results. However, in some real cases where the orders of magnitude of machines’ reliability parameters (mean times between failures and mean times to repair) are not at the same level, the accuracy of these existing methods may not be good enough. The purpose of this paper is to propose an improved decomposition method that performs well even in the situation above. We use generalised exponential distributions instead of exponential distributions to approximate the repair-time distributions of the fictitious machines, and a new ADDX algorithm is developed to calculate the performance parameters such as the production rate and the average buffer levels. Numerical results indicate that the improved decomposition method provides more accurate results and converges in most cases. It is feasible and valid to evaluate the performance of transfer lines with unreliable machines and finite buffers.