After logging in as root type the following command
watch -n .1 cat /proc/mdstat
This will show you if your raid is up. Ideally you want to see [UU] next to your active blocks. If you see [ _U] then that disk is down. As far as the system continuing to run after failure As long as you are running RAID 1, 5 , or 10 and only one disk fails. You should be fine because there is redundancy. RAID 0 however does not. If this is being used in a business environment it is a good idea to have a spare installed in case of disk failure, a RAID will begin reconstructing the mirror immediately after detecting the fault in the drive.