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In this paper, we consider a model for the dynamic multiple-fault diagnosis (DMFD) problem arising in online monitoring of complex systems and present a solution. This problem involves real-time inference of the most likely set of faults and their time-evolution based on blocks of unreliable test outcomes over time. In the DMFD problem, there is a finite set of mutually independent fault states, and a finite set of sensors (tests) is used to monitor their status. We model the dependence of test outcomes on the fault states via the traditional D-matrix (fault dictionary). The tests are imperfect in the sense that they can have missed detections, false alarms, or may be available asynchronously. Based on the imperfect observations over time, the problem is to identify the most likely evolution of fault states over time. The DMFD problem is an intractable NP-hard combinatorial optimization problem. Consequently, we decompose the DMFD problem into a series of decoupled subproblems, one for each sample epoch. For a single-epoch MFD, we develop a fast and high-quality deterministic simulated annealing method. Based on the sequential inferences, a local search-and-update scheme is applied to further improve the solution. Finally, we discuss how the method can be extended to dependent faults.