A robust decomposition method for the analysis of production lines with unreliable machines and finite buffers |
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Authors: | Hervé Le Bihan Yves Dallery |
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Institution: | (1) Laboratoire d'Informatique de Paris 6, Université Pierre et Marie Curie, 4 Place Jussieu, F 75252 Paris cedex 05, France;(2) Laboratoire Productique Logistique, Ecole Centrale de Paris, Grande Voie des Vignes, F 92295 Chatenay Malabry cedex, France |
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Abstract: | 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 3,7]. Moreover, we assume that the times to failure and the repair times are exponentially distributed. To analyze such systems, a decomposition method was proposed by Gershwin 13]. The computational efficiency of this method was later significantly improved by the introduction of the so called DDX algorithm 5,6]. In general, this method provides fairly accurate results. There are, however, cases for which the accuracy of this decomposition method may not be acceptable. This is the case when the reliability parameters (average failure time and average repair time) of the different machines have different orders of magnitude. Such a situation may be encountered in real production lines. In 8], an improvement of Gershwin's original decomposition method has been proposed that in general provides more accurate results in the above mentioned situation. This other method is referred to as the Generalized Exponential (GE) method. The basic difference between the GE method and that of Gershwin is that it uses a two moment approximation instead of a single moment approximation of the repair time distributions of the equivalent machines. There are, however, still cases for which the accuracy of the GE method is not as good as expected. This is the case, for example, when the buffer sizes are too small in comparison with the average repair time. We present in this paper a new decomposition method that is based on a better approximation of the repair time distributions. This method uses a three moment approximation of the repair time distributions of the equivalent machines. Numerical results show that the new method is very robust in the sense that it seems to provide accurate results in all situations. |
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Keywords: | production lines unreliable machines finite buffers decomposition method hyper exponential distributions" target="_blank">gif" alt="dash" align="MIDDLE" BORDER="0">exponential distributions |
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