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The Network-on-Chip (NoC) paradigm has been proposed as a favorable solution to handle the strict communication requirements between the increasingly large number of cores on a single chip. However, NoC systems are exposed to the aggressive scaling down of transistors, low operating voltages, and high integration and power densities, making them vulnerable to permanent (hard) faults and transient (soft) errors. A hard fault in a NoC can lead to external blocking, causing congestion across the whole network. A soft error is more challenging because of its silent data corruption, which leads to a large area of erroneous data due to error propagation, packet re-transmission, and deadlock. In this paper, we present the architecture and design of a comprehensive soft error and hard fault-tolerant 3D-NoC system, named 3D-Hard-Fault-Soft-Error-Tolerant-OASIS-NoC (3D-FETO). With the aid of efficient mechanisms and algorithms, 3D-FETO is capable of detecting and recovering from soft errors which occur in the routing pipeline stages and leverages reconfigurable components to handle permanent faults in links, input buffers, and crossbars. In-depth evaluation results show that the 3D-FETO system is able to work around different kinds of hard faults and soft errors, ensuring graceful performance degradation, while minimizing additional hardware complexity and remaining power efficient.