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This paper presents a factorial hidden Markov model (FHMM)-based diagnostic reasoner to handle multiple intermittent faults. The dynamic multiple fault diagnosis (DMFD) problem is to determine the most likely evolution of fault states, the one that best explains the observed test outcomes over time. In our previous research work, we have shown that the problem of diagnosing dynamic multiple faults in the presence of imperfect test outcomes, is an NP-hard problem. Here, we combine a Gauss-Seidel coordinate ascent optimization method with a Soft Viterbi decoding algorithm for solving the DMFD problem. We demonstrated the algorithm on small-scale and medium-scale systems and the simulation results shows that this approach improves primal function value (1.4%~8.3%) and correct isolation rate (1.7%~11.4%) as compared to a Lagrangian relaxation method discussed in our previous work.