We will not recommended a single fixed meta-monitoring alerting rule set for your Prometheus and Alertmanager servers here, since there would be many variations of applicable rules and thresholds, depending on your environment. However, here are a few good publicly available meta-monitoring rulesets that you can use as a starting point:

• From the kube-prometheus project:
  • A Prometheus server ruleset
  • An Alertmanager ruleset
• From GitLab: A meta-monitoring ruleset.
• From the "Awesome Prometheus alerts" project: A set of Prometheus self-monitoring alerting rules.
• From the "Monitoring Mixins" project:
  • A Prometheus ruleset
  • An Alertmanager ruleset

The alerting rules should be wide-ranging, starting from testing the reachability of your Prometheus and Alertmanager servers by checking the up metric's value and its presence, and then checking whether the scraping, TSDB sample ingestion, and rule evaluation works fine, whether alerts are sent out to the Alertmanager without errors or delays, and so on.