-w 5000.0,100% -c 5000.0,100% -p 1
These thresholds would return BAD state (call it Critical or Unreachable, it doesn’t matter) and are suitable for a host-check. I have wrote this already. Host-check is performed only to see if the host is reachable or not. For it, Nagios doesn’t need Warning or Critical thresholds. If you ask, why the threshold is defined then? Well, the answer is, that Nagios could know if the packet loss is 100%, then set the host state to down and send a notification that the host is down.
If you define additional service, as I’ve said, you will get more precise output of the ping command and the thresholds in service check would then have more sense. In service check they should be like this:
-w 3000.0,80% -c 5000.0,100% -p 1
so Nagios could distinguish the warning from critical.
When Nagios notice that services start getting Critical states, then it checks the host to see if it is up or down. Probably in such scenario you will get notification for the services first, and then for the host (of course if it IS in down state).
Why does check_ping plugin don’t have down or unreachable thresholds? Because it doesn’t need them. With warning and critical thresholds everything is settled the way Nagios understands. Check-host-alive, when once set-up, it doesn’t have to be edited anymore, 'cause it is only a check to determine if the host is reachable. It isn’t meant to be the ping analyzing tool. For that you can create service with check_ping plugin.
As for the Centreon, personally, I don’t like it and it isn’t an official Nagios product. It is an add-on if you ask me.
Maybe you should read the Nagios documentation to understand how it works.