That's more something outside OBIEE as OBIEE itself will not really be able to tell you when it's down ...
So you have tons of options like monitoring tools or just some lines of shell script / python / perl / java or any other script language.
There are couple of ideas i would provide from the OBIEE side.
B.1.2 Determining if System Processes are Dying or Unresponsive
You can create a cron script to check this and send an notification alert to the team about the failure.
This focuses almost all the methodologies that we can try using.
Also refer : OBIEE 11g environment going down.
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Have a great day ahead
- madasamy M.