Accountability in the workplace is critically important and remains a challenging problem, especially with respect to workplace safety management. In this paper, we introduce a novel notion, the Internet of Responsibilities, for accountability management. Our method sorts through the list of responsibilities with respect to hazardous positions. The positions are interconnected using directed acyclic graphs (DAGs) indicating the hierarchy of responsibilities in the organization. In addition, the system detects and collects responsibilities, and represents risk areas in terms of the positions of the responsibility nodes. Finally, an automatic reminder and assignment system is used to enforce a strict responsibility control without human intervention. Using blockchain technology, we further extend our system with the capability to store, recover and encrypt responsibility data. We show that through the application of the Internet of Responsibility network model driven by Big Data, enterprise and government agencies can attain a highly secured and safe workplace. Therefore, our model offers a combination of interconnected responsibilities, accountability, monitoring, and safety which is crucial for the protection of employees and the success of organizations.