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A system-level design process of reliable systems demands efficient reliability evaluation of the explored design alternatives. This paper presents a new approach to accelerate the reliability evaluation and, thus, the design space exploration for reliable systems. A new data structure denoted as system error decision diagram (SEDD) is proposed, which is based on both binary decision diagrams to model permanent errors and zero-suppressed decision diagrams to model transient errors. Both constructing the SEDD diagram and evaluating reliability based on it are detailed in an algorithmic way. The proposed approach is demonstrated for a control system taken from the automotive domain.