Nurses working in the hospital setting increasingly have become overburdened by managing alarms that, in many cases, provide low information value regarding patient health. The current trend, aided by disposable, wearable technologies, is to promote patient monitoring that does not require entering a patient's room. The development of telemetry alarms and middleware escalation devices adds to the continued growth of auditory, visual, and haptic alarms to the hospital environment but can fail to provide a more complete understanding of patient health. As we begin to innovate to both address alarm overload and improve patient management, perhaps using fundamentally different integration architectures, lessons from the aviation flight deck are worth considering. Commercial jet transport systems and their alarms have evolved slowly over many decades and have developed integration methods that account for operational context, provide multiple response protocol levels, and present a more integrated view of the airplane system state. We articulate three alarm system objectives: (1) supporting hazard management, (2) establishing context, and (3) supporting alarm prioritization. More generally, we present the case that alarm design in aviation can spur directions for innovation for telemetry monitoring systems in hospitals.