We have our alerts get sent out on a timeline that is highly configurable. You as the user can set the time you'd like to first know about an outage, and then build in escalations to other people or teams.
Once an outage is detected, you can choose how quickly after an outage you'd like to be notified, who gets the notifications, and on which channels. From there, if the outage isn't acknowledged or resolved by the next trigger event, the alerts will escalate as you configure them.
You can also see which servers and server groups this alert timeline is attached to, and edit from this view.