The presented approach for a top-down description of production lines is based on the concept of 'modules', corresponding to segments of the production line, and 'connections' between these modules. The flow of items through the line is modelled by stochastic variables describing the ability to deliver an item to the next module and the ability to accept an item from the preceeding module. Under an independence assumption, the behaviour of each module in a line can be described by the two probabilities pi and qj which depend on the boundary condition of the module, i.e. the values of the delivery probability pi-1 of the preceeding module, and the acceptance probability qj+1 of the following module. Under stationary conditions, this leads to a characteristic function for each module qj(pi-1,qj+1) which decribes the behaviour of the module in an integral way. Thus, instead of using a complex mathematical or simulation model, one may use the characteristic function. Microscopically relevant features of the production line correspond to properties of the characteristic function. The flow of items through a production line can then be calculated by solving a system of coupled equations which connect the characteristic functions of the different modules within the line. It has been demonstrated that characteristic functions of a part of a production line can be calculated ab initio based on the characteristic functions of the basic elements 'buffer' and 'station'. By solving the equation system describing the coupling between the single elements of the line, the production rate can be calculated without the need of simulation. For realistic failure rates in the order of magnitude of few percent or lower, the calculated production rates have a very low error compared with the full simulation model. It must be stressed that the work in this field is still in progress. All results are preliminary and must be verified by further experiments. However, it seems that the proposed macro-level model for modules in a production line is able to explain relevant properties of the line like, for example, the production rate.
Approximative modelling of manufacturing systems
Approximative Modellierung von Fertigungssystemen
2003
6 Seiten, 6 Bilder, 3 Quellen
Conference paper
English
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