Due to the sheer size and complexity of modern chemical processes, single centralized monolithic monitoring strategies are not always well suited for detecting and identifying faults. In this paper, we propose a framework for distributed fault detection and identification (FDI), wherein the process is decomposed hierarchically into sections and subsections based on a process flow diagram. Multiple hierarchical FDI methods at varying levels of granularity are deployed to monitor the various sections and subsections of the process. The results from the individual FDI methods contain mutually nonexclusive fault classes at different levels of granularity. We propose an adaptation of the Dempster-Shafer evidence theory to combine these diagnostic results at different levels of abstraction. The key benefits of this scheme as demonstrated through two case studies a simulated CSTR-distillation column system and the Tennessee Eastman challenge process are improved diagnostic performance compared to individual FDI methods, robust localization of even novel faults, and a coherent explanation of the entire plant's state.