Maximally Permissive Robustness Discovery in Automated Manufacturing Systems With an Unreliable Resource

This article studies the maximally permissive robustness analysis of states in Petri net (PN) modeling automated manufacturing systems with a single unreliable resource. Namely, we focus on determining the robustness of each state in the event of an unreliable resource failure. First, we represent a single unreliable resource failure by forbidding the firings of succeeding transitions of places using the unreliable resource. Then, we show that the reachability graph of a PN can be used to determine the robustness of all states; however, it may suffer from formidable computational difficulty. Finally, we present a linear programming-based necessary and sufficient condition to check the robustness of all states in terms of the solution of integer linear programming problems. We show that the proposed linear programming approach performs well in terms of computational complexity and effectiveness.