We introduce a new exact method combining the aggregation approach for Stochastic Well-Formed Petri Net (SWN) model with the decomposition approach initiated by Plateau to compute performance indices of parallel systems. We derive necessary conditions on the modelled systems that allow for the two methods to be combined. For parallel systems satisfying these necessary conditions, we develop two models with corresponding algorithms. The first model, which forbids colour synchronization between components of the system, yields to a strict generalization of each of the two methods. The second model, which covers a large range of real life systems, needs theoretical study that we undertake here. An example shows the intuitive ideas behind these developments.