In this paper, the natures of random and pseudo-random input sequences and their influence on permanent and intermittent fault detecting are analyzed. The aliasing fault coverage between the pseudo-random and random sequences is estimated. The activity probability features of the intermittent faults are considered. The self-test circuits of the intermittent faults are illustrated. The experimental results based on real circuits are obtained through simulation. The mathematical analysis and experimental results show that the quality of the pseudo-random testing is better than that of the random testing for the permanent and intermittent faults. The Markov chain models are used in obtaining the input sequence length needed for determining if a circuit fault is intermittent or permanent.