Software or System Requirements often change during their operational lifetime. These changes take place due to misconceived requirements perceived during the requirement and design stages. Any changes in requirements are mostly evident during the run time of the system and are known as emergent faults. These emergent faults are unforeseen by the requirement engineers and so there is no built-in fault tolerance solution for the components in this system. In this paper we consider a real-time multi-network system of Alegent Health, where their application servers are used for critical Electronic Medical Record (EMR) application. These application servers frequently blow up due to memory leakages thus resulting in kicking off the users (doctor and nurses) of the system, elevating concerns on patient safety and also causing loss of revenue. We attribute this problem to be a misconceived requirement and as an emergent runtime fault. We propose a health monitoring system which will keep track of the health conditions of the servers with the objective of increasing overall system throughput, decreasing system downtime, and minimizing loss of data. We have proposed the use of the concept of Duration Calculus to specify the requirements of the system in terms of continuous state variables and discrete state variables.