The checkpointing scheme is a well-known technique to cope with transient faults in digital systems. This paper proposes an adaptive checkpointing scheme for the reliability improvement of real-time control systems with concurrent fault detection capability. With concurrent fault detection capability the effect of transient faults are assumed to be detected with no latency. The proposed adaptive checkpointing scheme is based on the reliability analysis of an equidistant checkpointing scheme. Numerical data show the proposed adaptive scheme outperforms the equidistant scheme from a reliability point of view.