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Real-time systems typically have to satisfy complex requirements, mapped to the task attributes, eventually guaranteed by the underlying scheduler. These systems consist of a mix of hard and soft tasks with varying criticality, as well as associated fault tolerance requirements. Additionally, the relative criticality of tasks could undergo changes during the system evolution. Time redundancy techniques are often preferred in embedded applications and, hence, it is extremely important to devise appropriate methodologies for scheduling real-time tasks under failure assumptions.In this paper, we propose a methodology to provide a priori guarantees in fixed priority scheduling (FPS) such that the system will be able to tolerate one error per every critical task instance. We do so by using integer linear programming (ILP) to derive task attributes that guarantee re-execution of every critical task instance before its deadline, while keeping the associated costs minimized. We illustrate the effectiveness of our approach, in comparison with fault tolerant (FT) adaptations of the well-known rate monotonic (RM) scheduling, by simulations.