An alarm suspend system utilizes an alarm trigger responsive to physiological parameters and corresponding limits on those parameters. The parameters are associated with both fast and slow treatment times corresponding to length of time it takes for a person to respond to medical treatment for out-of-limit parameter measurements. Audible and visual alarms respond to the alarm trigger. An alarm silence button is pressed to silence the audible alarm for a predetermined suspend time. The audible alarm is activated after the suspend time has lapsed. Longer suspend times are associated with slow treatment parameters and shorter suspend times are associated with fast treatment parameters.