Chaos in manufacturing systems: Study of different cases

Abstract

Since a few years, an abundant literature has been published in order to proof the existence of chaotic behaviors both in the field of science and in the field of technique. Until now very few articles studied the conduct of manufacturing production systems. Apparently some production systems let us think that their behavior might be chaotic. Nevertheless, in our opinion, the proof of existing chaos in the production systems has not been totally confirmed. The works presented in this article are aimed to make obvious and to prove the existence of chaotic behaviors in manufacturing production systems. After the presentation of the interest of this study in a manufacturing production environment, we present our analysis method of the dynamic of non-planned production systems. We then justify the choices which have been made regarding in particular: the sub-system in which our study is made, the variable of interest (temporal average of the number of parts in a waiting line), the determinism of the system parameters, and the imposed balance conditions (in the sense that the number of parts is finished regardless of the considered instant). In the second part are presented the results obtained with two manufacturing systems, both very simple and very similar, although they give very different results. We then compare the results with the rules of assignment and management of different waiting lines. In the last part, we show that an actual system, under certain management conditions, can also present a chaotic behavior. This study has been realized from the modeling of a flexible assembly cell.