Equivalent machine method for approximate evaluation of buffered unreliable production lines

The addressed paper deals with a new analytical formulation called Equivalent Machine Method to evaluate the system throughput of a buffered serial production line. The machines are unreliable and both failure and repair times are assumed to be exponentially distributed. The proposed method is based on the analysis of the different states of each buffer using birth-death Markov processes. Then, each original machine is replaced by an equivalent one taking into account the probabilities of blockage and starvation. The throughput of the production line is defined as the bottleneck between the effective production rates of the equivalent machines. This method considers both homogeneous and non-homogeneous lines and reduces sensibly the state space cardinality of the Markov chain representation of the system and consequently the computational times. A comparative study based on different test instances existing in the literature is presented and discussed. The obtained results prove the effectiveness and the accuracy of the proposed method comparing with both simulation and existing approaches in the literature.