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The application cross section "σAP" is a parameter used to characterize the systems single event upset (SEU) vulnerability, but does not give, in a direct way, the system's reliability. Reliability prediction of a system exposed to SEU can be improved with the knowledge of the system's time to failure (TTF) probability distribution function. This work presents two new methods suitable to provide this information. The first one is based on the construction of a function named the failure map function (FMF). FMF contains the information needed to calculate all the TTF statistical properties by means of numerical procedures. For the cases where the FMF function is difficult to obtain, a second method is presented which consist of injecting SEUs at a rate several orders of magnitude higher than the real rate. A histogram of the TTF random variable for the accelerated process is obtained. The system's reliability can then be derived by means of statistical and numerical procedures.