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This paper describes an approximate analytical method for evaluating the average values of throughput and buffer levels of closed three-machine production systems with finite buffers. The method includes a new set of decomposition equations and a new building block model. The machines have deterministic processing times and geometrically distributed probabilities of failure and repair. The numerical results of the method are close to those from simulation. The method performs well because it takes into account the correlation among the numbers of parts in the buffers. Extensions to larger systems are discussed. [Supplementary materials are available for this article. Go to the publisher's online edition of HE Transactions for the following free supplemental resource: Appendix of additional numerical results] Keywords: Transfer line, loop, decomposition, Markov chain, 1. Introduction 1.1. Closed-loop systems A loop is a material flow system that consists of work centers or machines separated by storage areas (buffers) in which material travels from machine [...]

More and more machines are increasing their flexibility so as to be able to produce different products with the same tooling. In this context, it is necessary to have fast and accurate methods to evaluate the system performance. This paper presents an approximate analytical method for the performance evaluation of production systems in which Z different types of products are produced. The proposed method is based on the decomposition of the complex system into a set of simpler building blocks, each one formed by two machines and Z homogeneous buffers. The set of building blocks models the whole behavior of the original system. The performance of each building block is evaluated by using the aggregation technique applied to two-machine lines in which the behavior of several products is modeled by an aggregate product, thus simplifying the complexity of the analysis. The numerical results reported in this paper prove the method provides accurate results. Keywords: Flow lines, multi-product, aggregation, decomposition, 1. Introduction A frequent solution to the problem of increasing shop floor productivity is to use flexible machines. These are machines that are equipped with general purpose tooling allowing different [...]