This article introduces the concept of a bad square in a redundant arr
ay of inexpensive disks (RAID). Bad squares are used to prove upper li
mits on the reliability of the 2d-parity arrangement when there is the
possibility that a string of disks may fail simultaneously. Bad-squar
e analysis motivates several optimal string layouts which achieve thes
e limits. Bad squares also provide a means to calculate the mean time
to data loss for a RAID layout, without the use of Monte Carlo simulat
ion.