A Maximally Permissive Robustness Analysis for Automated Manufacturing Systems Allowing Multiple Server Failures

As one of the essential issues when designing optimal control policies for automated manufacturing systems (AMSs) with unreliable resources, maximally permissive behavior should be ensured for the controlled system. This paper is devoted to the maximally permissive robustness analysis for AMSs allowing multiple server failures. First, all subnet systems are categorized by their usage of unreliable resources so as to provide more general definitions of the robust, strongly robust, and weakly robust markings. Second, we provide algorithms to compute reduced reachability graphs (R2Gs) and strongly connected components (SC2s), respectively. Then, the necessary and sufficient conditions to verify the robustness of markings are obtained by analyzing the transitions involved in each component in an SC2 and the relation between markings in the disconnected marking subset and SC2. Finally, the effectiveness and efficiency of the theoretical results are validated via examples. Note to Practitioners—Maximally permissive robustness analysis is an essential criterion for evaluating the control performance of robustness for AMSs with failure-prone resources. Ineffective handling of resource failures can lead to unexpected disruptions, decreased throughput, and diminished product quality. While much research has focused on developing robust control policies to ensure system resilience, there remain certain states that do not comply with these policies, even when they are designed to be robust. We present significant findings that assess the robustness of all system states when unreliable resources experience various failure scenarios. These results allow the researchers to design optimal robust controllers, thereby significantly enhancing the flexibility and efficiency of manufacturing processes. By applying the results of our robustness analysis, manufacturers can better prepare for and respond to resource failures, ultimately improving overall production performance.