We describe the Generic Smart Alarm, an architectural framework for the development of decision support modules for a variety of clinical applications. The need to quickly process patient vital signs and detect patient health events arises in many clinical scenarios, from clinical decision support to tele-health systems to home-care applications. The events detected during monitoring can be used as caregiver alarms, as triggers for further downstream processing or logging, or as discrete inputs to decision support systems or physiological closed-loop applications. We believe that all of these scenarios are similar, and share a common framework of design. In attempting to solve a particular instance of the problem, that of device alarm fatigue due to numerous false alarms, we devised a modular system based around this framework. This modular design allows us to easily customize the framework to address the specific needs of the various applications, and at the same time enables us to perform checking of consistency of the system. In the paper we discuss potential specific clinical applications of a generic smart alarm framework, present the proposed architecture of such a framework, and motivate the benefits of a generic framework for the development of new smart alarm or clinical decision support systems.