How this is exactly done is depending on the RAID adapter (more precisely: the adapters driver software), so i can give you only general directions.

If the failing disk is part of a RAID you will probably not be able to manage the disk device itself. A RAID works like this: there are several disks connected to an adapter. The driver software of the adapter makes one big virtual disk out of the several physical ones and presents this virtual construct as a physical disk to the machine. (This is what is done during the "RAID initialization" or however it is called with your software. The driver/adapter writes some bookkeeping information onto the physical disk to be able to use them the described way.)

Only this virtual disk is added to a VG as a "Physical Volume" and from there on normal LVM procedures apply.

Your first task is to make the PV free from OS access. You can do this by either breaking the mirror (if the VG is mirrored) or by varying off the VG as zaxxon suggested. Since the "disk" in the VG is only a virtual construct there is no strict relationship between disks and logical volumes. All the logical volumes on the virtual RAID disk are "smudged across" the physical disks comprising the RAID.

After this you need to use the adapters driver software (in case of the IBM SCSI RAID adapter this is plugged into SMITty and the diag utility) to remove the disk from the RAID, after which the RAID is in status "reduced". then physically change the disks and add the new disk to the RAID. This will probably take some time as the new disk has to be written with the data first to be useful in the RAID. Only then varyon again and start using the VG again.

Do you need to backup? In principle you don't, because in a RAID all the disks hold all the information with redundancy. The classical case is 5 disks holding the capacity of 4 - for this penalty it is possible to replace every single disk without losing data, because the data it holds is also available on the other 4. This does NOT mean that a backup would be a bad idea: not at all! It is better to have a backup you don't need than to need a backup you don't have.

I hope this helps.

bakunin