In compact signature analysis ( CSA ) using Linear Feedback Shift Registers ( LFSR ), one unit connected in a closed loop form with the Circuit Under Test ( CUT ) is used as a random test pattern generator and signature analyzer in the same time; thus, reducing the hardware of signature analysis testing technique by 50 % [10]. However, it was found that the Steady State Aliasing Error Probability ( SS-AEP) of CSA has values between 0 and 1 depending on the CUT and the structure of the CSA; which inhibits its use for digital circuits testing. In a previous work, the hardware condition for the SS-AEP of CSA to be equal to /2k is obtained, leading to what is called the Improved Compact Signature Analysis ( ICSA ) [11]. In this paper, the dynamic behavior of the CSA and the ICSA, which reflects the minimum required length of the test pattern necessary for the compression technique to reach SS-AEP condition is studied, using the absolute value of the Second Maximum Eigenvalues ( SME ) of transition probability matrix ( TPM ). The results are compared with those of Open Loop testing systems with PP-LFSR, and Cyclic Code Linear Feedback Shift Register ( CC-LFSR). The comparison indicates that when the probability of the system to be fault-free is equally likely, the ICSA has similar dynamic performance as the conventional testing systems, but in the general case, the ICSA needs shorter pattern than CC-LFSR and slightly longer pattern than PP-LFSR in conventional testing to reach steady state, and as k increases the difference between the dynamic behavior of the ICSA and PP-LFSR decreases