Why are the nested RAID levels 1+5 or 1+6 almost unheard of? The nested RAID levels Wikipedia article is currently missing their sections. I don't understand why they are not more common than RAID 1+0, especially when compared to RAID 1+0 triple mirroring.
It is apparent that rebuilding time is becoming increasingly problematic as drive capacities are increasing faster than their performance or reliability. I'm told that RAID 1 rebuilds quicker and that a RAID 0 array of RAID 1 pairs avoids the issue, but surely so would a RAID 5 or 6 array of RAID 1 pairs. I'd at least expect them to be a common alternative to RAID 1+0.
For 16 of 1TB drives, here are my calculations of the naïve probability of resorting to backup, i.e. with the simplifying assumption that the drives are independent with even probability:
RAID | storage | cumulative probabilities of resorting to backup /m 1+0 | 8TB | 0, 67, 200, 385, 590, 776, 910, 980, 1000, 1000, 1000 1+5 | 7TB | 0, 0, 0, 15, 77, 217, 441, 702, 910, 1000, 1000 1+6 | 6TB | 0, 0, 0, 0, 0, 7, 49, 179, 441, 776, 1000 (m = 0.001, i.e. milli.)
If this is correct then it's quite clear that RAID 1+6 is exceptionally more reliable than RAID 1+0 for only a 25% reduction in storage capacity. As is the case in general, the theoretical write throughput (not counting seek times) is storage capacity / array size × number of drives × write throughput of the slowest drive in the array (RAID levels with redundancy have a higher write amplification for writes that don't fill a stripe but this depends on chunk size), and the theoretical read throughput is the sum of the read throughputs of the drives in the array (except that RAID 0, RAID 5, and RAID 6 can still be theoretically limited by the slowest, 2nd slowest, and 3rd slowest drive read throughputs respectively). I.e., assuming identical drives, that would be respectively 8×, 7×, or 6× maximum write throughput and 16× maximum read throughput.
Furthermore, consider a RAID 0 quadruple of RAID 1 triples, i.e. RAID 1+0 triple mirroring of 12 drives, and a RAID 6 sextuple of RAID 1 pairs, i.e. RAID 1+6 of 12 drives. Again, these are identical 1TB drives. Both layouts have the same number of drives (12), the same amount of storage capacity (4TB), the same proportion of redundancy (2/3), the same maximum write throughput (4×), and the same maximum read throughput (12×). Here are my calculations (so far):
RAID | cumulative probabilities of resorting to backup /m 1+0 (4×3) | 0, 0, 18, ?, ?, ?, ?, ?, 1000 1+6 (6×2) | 0, 0, 0, 0, 0, 22, 152, 515, 1000
Yes, this may look like overkill, but where triple mirroring is used to split-off a clone for backup, RAID 1+6 can just as well be used, simply by freezing and removing 1 of each drive of all but 2 of the RAID 1 pairs, and while doing so, it still has far better reliability when degraded than the degraded RAID 1+0 array. Here are my calculations for 12 drives degraded by 4 in this manner:
RAID | cumulative probabilities of resorting to backup /m 1+0 (4×3) | (0, 0, 0, 0), 0, 143, 429, 771, 1000 1+6 (6×2) | (0, 0, 0, 0), 0, 0, 71, 414, 1000
Read throughput, however, could be degraded down to 6× during this time for RAID 1+6, whereas RAID 1+0 is only reduced to 8×. Nevertheless, if a drive fails while the array is in this degraded state, the RAID 1+6 array would have a 50–50 chance of staying at about 6× or being limited further to 5×, whereas the RAID 1+0 array would be limited down to a 4× bottleneck. Write throughput should be pretty unaffected (it may even increase if the drives taken for backup were the limiting slowest drives).
In fact, both can be seen of as ‘triple mirroring’ because the degraded RAID 1+6 array is capable of splitting-off an additional RAID 6 group of 4 drives. In other words, this 12-drive RAID 1+6 layout can be divided into 3 degraded (but functional) RAID 6 arrays!
So is it just that most people haven't gone into the maths in detail? Will we be seeing more RAID 1+6 in the future?