Performance evaluation of linear and non-linear multi-product multi-stage lines with unreliable machines and finite homogeneous buffers

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.