Similarity Transformation of Discrete Part Production Lines

In order to improve the computational efficiency of models of production lines with unreliable machines, we propose the similarity transformation method by adjusting the design parameters, such as times between machine failures, times to repair and buffer capacities, in an equal proportion. It is found that the system throughput remains almost unchanged under the similarity transformation. The typical manufacturing system, serial production line, is taken as an example to verify the proposed method. Theoretical analysis and numerical experiments have been performed to confirm the feasibility and effectiveness of the method. The results show that the throughput error is no more than 5% and the calculation time is much less than that of the original model. Therefore, it is helpful to apply the similarity transformation method to large production line models to reduce computational complexity.