It’s not possible to specify a minimum of consecutive occurrences before alerting starts in in Enterprise Manager, it will always scream out at first time touching the line. But you can do so in command line. Just execute DBMS_SERVER_ALERT.SET_THRESHOLD with parameter consecutive_occurrences set to a value >1. It’s a very nice way to stop annoying one-time-alerts!
Just another hint, how I found out: Sometimes you want to display the package header informations, mostly for packages shipped by Oracle. 🙂 One example is the above-mentioned DBMS_SERVER_ALERT, that specifies metric values. It’s not easy to find out which meatric means what or generally what (undocumented?) feature a package provides, but
select text from dba_source where NAME='DBMS_SERVER_ALERT' and type='PACKAGE' order by line;
may help a bit.