MISRs are widely used as signature circuits for VLSI built-in self tests. To improve the aliasing probability of MISRs, multiple MISRs and M-stage MISRs with m inputs are available, where M is grater than m. The aliasing probability as a function of the test length is analyzed for the compaction circuits for a binary symmetric channel. It is observed that the peak aliasing probability of the double MISRs is less than that of M-stage MISRs with m inputs. It is also shown that the final aliasing probability for a multiple MISR with d MISRs is 2dm and that for an M-stage MISR with m imputs is 2M if it is characterized by a primitive polynomial.