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Due to continuous technology downscaling modern embedded real-time systems become more and more susceptible to the occurrence of errors. The usage of appropriate countermeasures is necessary to prevent a system failure. In this paper we present a new reliability estimation technique for such systems. As a key novelty a formal analysis method will be introduced that approximates the probability of failure of a priority driven bus during a period of time, enabling fast and accurate reliability calculation. It removes the major drawbacks of existing approaches, e.g. random-based Monte-Carlo simulation that requires long runtimes. However Monte-Carlo simulation serves as reference method to demonstrate the accuracy of our approach by comparing analysis and simulation results. Finally we consider the design of mixed-criticality systems which combine different safety requirements on a single component.