The growing complexity of software used in large-scale, safety critical cyber-physical systems makes it increasingly difficult to expose and hence correct all potential defects. There is a need to augment the existing fault tolerance methodologies with new approaches that address latent software defects exposed at runtime. This paper describes an approach that borrows and adapts traditional `System Health Management' techniques to improve software dependability through simple formal specification of runtime monitoring, diagnosis, and mitigation strategies. The two-level approach to health management at the component and system level is demonstrated on a simulated case study of an Air Data Inertial Reference Unit (ADIRU). An ADIRU was categorized as the primary failure source for the in-flight upset caused in the Malaysian Air flight 124 over Perth, Australia in 2005.