On the Equivalence Between Robustness and Liveness in Automated Manufacturing Systems

There are two foundational problems in automated manufacturing systems. One is to determine their robustness (i.e., checking whether a marking is robust or nonrobust) while the other is to determine their liveness (i.e., determining whether a marking is live, bad, deadlock, or livelock). However, existing methods deal with them separately. This renders the existing methods inefficient in practice. In this article, we investigate the relation between robustness and liveness. First, we show how to define robustness in different net systems, i.e., the live, bounded, and nonreversible or reversible net systems. Second, we present a reachability graph-based method to assess the robustness of markings. Third, we clarify the relation between robustness and liveness, and conclude that liveness is a special case of robustness, under which the set of unreliable transitions is null. As a result, the robustness determination method developed in this article proves to be much general and can be used to check the liveness of each marking.