Over the last two decades binary decision diagrams have been applied successfully to improve Boolean reliability models. Conversely to the classical approach based on the computation of the MCS, the BDD approach involves no approximation in the quantification of the model and is able to handle correctly negative logic. However, when models are sufficiently large and complex, as for example the ones coming from the PSA studies of the nuclear industry, it begins to be unfeasible to compute the BDD within a reasonable amount of time and computer memory. Therefore, simplification or reduction of the full model has to be considered in some way to adapt the application of the BDD technology to the assessment of such models in practice. This paper proposes a reduction process based on using information provided by the set of the most relevant minimal cutsets of the model in order to perform the reduction directly on it. This allows controlling the degree of reduction and therefore the impact of such simplification on the final quantification results. This reduction is integrated in an incremental procedure that is compatible with the dynamic generation of the event trees and therefore adaptable to the recent dynamic developments and extensions of the PSA studies. The proposed method has been applied to a real case study, and the results obtained confirm that the reduction enables the BDD computation while maintaining accuracy.