Software fault tolerance is an important issue when using software systems in safety-critical applications. In such systems, software robustness is an essential requirement for improving software fault tolerance. Since an operating system (OS) is a major part of a safety-critical system, its robustness has considerable influence on the system's overall robustness. In recent years, researchers have emphasized the importance of considering the OS state in robustness testing. OS state is determined by analysis of the interactions between OS components. In this paper, an approach, named TIMEOUT, is proposed for robustness testing of embedded real-time OSs. This approach reveals the impact of time delays, i.e. inputs with invalid timing delay, on the OS kernel functionality. TIMEOUT takes the OS state into account and improves the existing robustness testing methods. The proposed approach has been implemented and the experiments have been performed on Linux PREEMPT-RT, which is an embedded real-time implementation of Linux operating system. The results show that OS state can influence the OS behavior with respect to fault tolerance, in the presence of time delays. Based on the results of this approach, system developers can identify criticality of OS states and improve robustness of OS in those states.