18.

(a) Figure 9.28 shows the RAID level 01 and RAID level 10 systems with eight physical disks. Draw the equivalent systems for level 01 and level 10 with four physical disks. (b)

Assume that two disks go bad. The sequence BBGG means that the first and second disks are bad and the third and fourth disks are good. With this scenario, the RAID level 01 disk is good because the two bad disks are in the same first striped disk, but the RAID level 10 disk is bad because the two bad disks are in the same first mirrored disk. How many permutations of four letters with two B’s and two G’s are there?

(c) Tabulate each permutation, and for each one determine whether the RAID disk is good or bad for levels 01 and 10.

(d) If two disks fail, use part

(c) to determine the probability that the RAID disk fails for levels 01 and 10. Which RAID system is more reliable?

(e) With 2n disks in general (so that n = 4 in Figure 9.28), how many permutations of 2n letters are there with 2 B’s and 2n – 2 G’s? (f)

How many of the permutations from part

(e) cause a RAID disk failure for level 01 and for level 10? (g) If two disks fail, use part

(f) to determine the probability that the RAID disk fails for levels 01 and 10. (h) Use part (g) to show that the probability that the RAID disk in Figure 9.28 fails is 4/7 for level 01 and 1/7 for level 10 if two disks fail.