The presented work is dedicated to the robustness of a milk manufacturing workshop including time interval constraints. In such systems, operation times are included between a minimum and a maximum value. Weighted Marked Graphs are used for modelling. Some results proposing to transform Weighted Marked Graphs into Marked Graphs are reviewed, which allow obtaining a model that can be used to apply some robustness results of the state of the art. The main contribution of this paper is a computing algorithm of the maximal time disturbances allowed at a given point. Finally, to demonstrate the effectiveness and accuracy of the proposed algorithm, an application to a milk production unit is outlined. The possession of this exact value allows checking the death of marks on the levels of synchronization transitions of a P-time Petri net model without generating any false alarm. . The results show that the difference between the exact value and the lower bound of the state of the art algorithm is quite important.