An improved decomposition method for the analysis of production lines with unreliable machines and finite buffers

We consider production lines consisting of a series of machines separated by finite buffers. The processing time of each machine is deterministic and all the machines have the same processing time. All machines are subject to failures. As is usually the case for production systems we assume that the failures are operation-dependent. Moreover, we assume that the times to failure and the times to repair are exponentially distributed. To analyze such systems, a decomposition method was proposed by Gershwin. The computational efficiency of this method was later significantly improved by the introduction of the so-called DDX algorithm. In general, this method provides fairly accurate results. There are however cases for which the accuracy of this decomposition method may not be so good. This is the case when the reliability parameters (mean times to failure and mean times to repair) of the different machines have different orders of magnitude. Such a situation may be encountered in real production lines. The purpose of this paper is to propose an improvement of Gershwin's original decomposition method that provides accurate results even in the above mentioned situation. The basic difference between the decomposition method presented in this paper with that of Gershwin is that the times to repair of the equivalent machines are modeled as generalized exponential distributions instead of exponential distributions. This allows us to use a two-moment approximation instead of a one-moment approximation of the repair time distributions of these equivalent machines.