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Failure detection is a significant challenge in most overlay network systems. And the choice of parameter configuration for a given failure detection scheme has a significant impact on the performance of the scheme. In the traditional coarse-grained parameter configuration (CGPC) model, the parameter configuration for each failure detecting process is uniform. In this paper, we analyze the disadvantages of CGPC model and then propose an alternate model, i.e. the fine-grained parameter configuration (FGPC) model, in which each detecting relationship is allocated with one independently configurable detecting process and the parameter configuration for each failure detecting process can be different. To make a tradeoff between detection time and probability of false positive for parameter configuration policies, we propose a new evaluation criterion, i.e. detection loss. Based on FGPC model, we discuss the two approaches, i.e. common approach and heuristic approach, to choose an optimal parameter configuration policy for failure detection scheme. Finally we show how to apply the FGPC model to a probe-based failure detection scheme in application-layer multicast systems as an example.