In a distributed real-time system, if node n has not heard from node i for T~((i))_(out) since its receipt of the latest broadcast from node i, it will be considered that node i failed; then the preferred list is modified in such a way that each node will be selected as the k~(th) preferred node of one and only one other node. This paper determines the 'best' timeout period T~((i))_(out) to diagnose the failure of a node by the other nodes and proposes an algorithm to modify the pr...