Our team has a set of guidelines to determine the severity of a production issue. The severity drives the level of communication/escalation. Of course, the guidelines are only guidelines and don't replace human judgement.
The factors in the guidelines:
- How many customers are impacted? (few, many, most/all)
- Severity of the problem? (single feature unavailable, hard outage, potential data damage)
I can't put the full set of guidelines here, but you get the gist. With each level of severity, there is a timeline associated with it (SLA). If the SLA isn't met, the incident bumps a level.
You might want to search "incident management classification" for more examples.