Using Redundant Multithreading (RMT) for error detection and recovery is a prominent technique to mitigate soft-error effects in multi-core systems. Simultaneous Redundant Threading (SRT) on the same core or Chip-level Redundant Multithreading (CRT) on different cores can be adopted to implement RMT. However, only a few previously proposed approaches use adaptive CRT managements on the system level and none of them considers both SRT and CRT on the task level. In this paper, we propose to use a combination of SRT and CRT, called Mixed Redundant Threading (MRT), as an additional option on the task level. In our coarse-grained approach, we consider SRT, CRT, and MRT on the system level simultaneously, while the existing results only apply either SRT or CRT on the system level, but not simultaneously. In addition, we consider further fine-grained task level optimizations to improve the system reliability under hard real-time constraints. To optimize the system reliability, we develop several dynamic programming approaches to select the redundancy levels under Federated Scheduling. The simulation results illustrate that our approaches can significantly improve the system reliability compared to the state-of-the-art techniques.