Homogenisation Techniques for the Analysis of Production Lines with Unreliable Machines Having Different Speeds

This paper deals with production lines consisting of a series of machines separated by finite buffers. The processing time of each machine is deterministic, i.e., a fixed amount of time is required to perform the operation. The machines are subject to failures. We assume that the times to failure and the times to repair are exponentially distributed. In the case of homogeneous lines, i.e. production lines in which all machines have the same processing time, the use of decomposition methods is now well established. One approach for extending the applicability of these decomposition techniques to non-homogeneous lines consists in first transforming the original line into an approximately equivalent homogeneous line. The purpose of this paper is to investigate the behaviour of the methods based on this approach and compare them. We also propose a way of combining different methods.