An alarm system for a computer-based monitoring system such as a patient medical monitoring system is provided. The system comprises a main processor connected to a first speaker, a second processor communicatively connected to the main processor for exchange of messages; and a second speaker controlled by the second processor. A sensor is communicatively connected to the main processor of the monitoring system for receiving input such as physiologic input from a patient. The second speaker acts as a back-up in the event that the main processor fails to annunciate an alarm or an operator fails to respond to the first alarm within a predetermined time interval. An audible alarm is sounded when the main processor or second processor are not functioning normally.