Do you have a pager rotation schedule or are you a sucker that is simply on-call forever?
An on-call rotation schedule documents who is "carrying the pager" (or responsible for alerts and emergencies) at which times.
You might literally "pass the pager", handing it to the next person periodically, or everyone might have their own pager and your monitoring system consults a schedule to determine who to page. It is best to have a generic email address that goes to the current person so that customers don't need to know the schedule.
A rotation schedule can be simple or complex. 1 week out of n (for a team of n people) makes sense if there are few alerts. For more complex situations splitting the day into three 8-hour shifts makes sense. "Follow the sun" support usually schedules those 8-hour shifts such that a global team always has a shift during daylight hours. You might take a week of 8-hour shifts each n weeks if your team has 3n people. The variations are endless.
This schedule serves many people: You, your customers, management and HR.
It serves you well because it lets you plan for a life outside of work. I put the highest priority on having a good work-life balance. If you don't have a good work-life balance, and you don't have a rotation schedule, physician heal thy self.
The rotation improves service to customers because it takes the "chaotic panic of trying to find a sysadmin" and makes it easy and predictable.
It serves management because it gives them confidence that the next emergency won't happen while everyone is "away".
It serves HR since, of course, your company gives compensation time or pay as required by law. If your schedule is in machine-readable format, a simple script can read it to generate reports for the payroll department.
If you think you don't have a schedule then it is "24x7x365" and you are a sucker. (But that doesn't mean you can answer "yes" for this question.)