Aaron Turcott, thank you for posting this question.
Based on my understanding, you would like to get alert only when the alerting condition has remained true for a while. Please correct me if I am wrong.
If you go via the "Alert creation" scenario as mentioned in the question, where Azure triggers an alert on a metric ONLY if the alert has firing for a specific amount of time - this creates additional alerts which are not actionable. Therefore, this is not a scenario which is readily available.
Instead, you could achieve the similar outcome using the combination of "Aggregation type" and "When to evaluate" condition in alert rule condition:
The setting above translates to - check for average for metric value every 15 minutes and if it is <10 for the last 15 minutes generate alert.
Another similar outcome could also be achieved if you are forwarding the metrics to Log Analytics workspace using the "Log based alert rule". There, an option is available to trigger after only X violations of alerting condition have happened. For example, consider the following:
In this case, the query is run every 5 minutes, but an alert is raised only if there are 2 violations, i.e., the alert will be generated after 10 minutes only.
You may choose to use either of the options to achieve the end goal.
Hope this helps.
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