A first-out alarm is an alarm

Alarm

An alarm device or system of alarm devices gives an audible or visual alarm signal about a problem or condition.Alarm devices include:* burglar alarms, designed to warn of burglaries; this is often a silent alarm: the police or guards are warned without indication to the burglar, which increases...

 that indicates in some manner that it was the first of a series. This is necessary in circumstances such as an automatic trip or shutdown of equipment, where many alarms will annunciate as a result of a shutdown. The first-out alarm will clearly identify the root cause

Root cause

A root cause is rarely an initiating cause of a causal chain which leads to an outcome or effect of interest. Commonly, root cause is misused to describe the depth in the causal chain where an intervention could reasonably be implemented to change performance and prevent an undesirable outcome.In...

of the trip or shutdown.