I have formatted my hard disks so that /home sits in one separate disk. Now that disk has become faulty. I am wondering whether it is possible to replace only that disk and make a new /home partion on a new disk, so that I can avoid a complete reinstall of the OS? (I know that almost all my user data will be lost)
Answer is yes, you don't need to re-install OS. You can create a new partition (block device like /dev/sdb2) and use it for /home. You can also copy the data in old /home over if you have a good backup or the old home is still readable.
In your case, it seems that the old /home (disk) became faulty. You want to use a new partition or new disk for /home. It is fine and you don't need to re-install the OS.
Steps in brief (recommend doing this using a LIVE CD, you don't HAVE TO though):
Reboot and you should be good.