Works presented in this paper deal with the robustness of manufacturing job-shops with time constraints. A computing algorithm of a lower bound of the maximal time disturbances allowed in a given point is provided. To demonstrate the effectiveness and accuracy of this algorithm, two industrial examples are depicted. The possession of this bound allows checking the death of marks without the generation of too many false alarms. From a practical point of view, the death of a mark corresponds to an incorrect treatment of a given product. In food or pharmaceutics industries, this scenario is not acceptable because it jeopardizes health of humans. When a disturbance is lower than the bound value, the production remains correct and no quality alarm is generated.