We propose to build a fail-operational computing system from a primary self-checking controller and a secondary limp-home controller to guarantee an emergency operation in the case of hardware failure of the primary controller. A self-checking controller commonly builds on hardware-implemented fault detection, e.g. lock-stepping to reach a high diagnostic coverage of hardware faults. Such techniques come into contradiction with new features of modern CPUs such as inherent non-determinism of execution. Thus an interesting alternative to hardware-based self-checking in the primary controller is to implement software-based fault detection and recovery on the primary controller to detect and mask its hardware failures. We prove by means of stochastic model checking and prototype fault detection technique that the proposed approach not only reduces costs, but also guarantees higher availability of the computing system at the same safety level as common replicated execution on redundant hardware.