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This paper proposes a reliability-driven task scheduling scheme for multiprocessor real-time embedded systems that optimizes system energy consumption under stochastic fault occurrences. The task scheduling problem is formulated as an integer linear program where a novel fault adaptation variable is introduced to model the uncertainties of fault occurrences. The proposed scheme, which considers both the dynamic power and the leakage power, is able to handle the scheduling of independent tasks and tasks with precedence constraints, and is capable of scheduling tasks with varying deadlines. Experimental results have demonstrated that the proposed reliability-driven parallel scheduling scheme achieves energy savings of more than 15% when compared to the approach of designing for the corner case of fault occurrences.