We extend the decomposition approaches for flow lines with unreliable machines and limited buffer capacity as proposed by Gershwin and refined by Dallery et al. and by Burman by incorporating a new building block in the decomposition. This new building block is a three-machine, one buffer system which models a merging flow of material. While previous decomposition approaches led to a decomposition of the original network into virtual two-machine lines, we now use both virtual two- and three-machine lines. This requires a new set of decomposition equations for the virtual machines of the two-machine lines that surround the new building block modelling the merge. We present these equations, show how to solve them in an algorithm and present numerical results for non-cyclic networks in order to determine production rate and inventory level estimates.
