The aim of this chapter is to introduce a new model for mission network analysis, where the operability of any node can vary with time. There are several existing frameworks for analyzing dependency representations such as FDNA and SODA, which were introduced and used throughout this book. These frameworks have been studied and can be used to identify critical nodes in the mission network, but such analysis is typically performed in a static fashion. In many applications, immediate system failure is not the only concern to a mission, and analyses should also account for the time it takes to detect the failure and recover the system operability.