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Research in the area of Autonomic Networks is on the rise. Autonomicity - realized through control loops, is an enabler for advanced self-manageability of network nodes and devices. Therefore, the specification and design of autonomic behaviors is required for each of the management functions defined by the well established FCAPS network management framework (Fault-, Configuration-, Accounting-, Performance- and Security-Management). In the context of Autonomic Fault-Management, mechanisms and algorithms are required that enable efficient and scalable interactions among the Fault-Management processes defined by the TMN (Telecommunications Management Network) standard. TMN defines Fault-Detection, Fault-Isolation, and Fault-Removal as the processes involved in Fault-Management. Therefore, in Autonomic Networks, some capabilities of Fault-Isolation must be in-built into a node and into the whole fundamental network architecture (apart from those aspects handled in the management plane), and its results must be fed into the embedded automatic Fault-Removal mechanisms. This imposes some scalability requirements on the employed algorithms. In this paper, we propose a novel scalable Markov Chain based algorithm for on-line Fault-Isolation. Furthermore, we analyze its computational and space complexity and evaluate its fault identification capabilities, as well as scaling properties on potential issues within an IPv6 network.