Once the first new drive had been rebuilt, I shut the system down, popped the next old drive out, replaced it with a new 2 TB unit, and rebuilt the RAID again. Because I am using Level 5 RAID, one out of the four drives can fail without incurring any data loss, so the remaining three drives can always rebuild a fourth. Once they arrived, I popped the dead drive first, replaced it with a new 2 TB unit, powered the RAID up, and set it to rebuild the new drive.
Rather than keep replacing 1 TB drives, I decided that it was time to replace all four drives with new 2 TB units. Holding my Time Machine backup drive and configured as a Level 5 array, its 3 TB space had been steadily eaten away until less than 450 GB were remaining. My upgrade was rather forced on me, when the original four 1 TB hard drives started to fail after more than four years of continuous and quite heavy use. If you have a hardware RAID system like the Promise Pegasus R4, how easy is it to increase its drive capacity non-destructively?