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This paper deals with a new reliability model for nonrepairable systems, the Hyperbolic. A decreasing hazard rate approaching a value greater than zero is its distinctive characteristic. Potentially, many mechanisms of failure can produce mortality laws of Hyperbolic type. The "Deterioration", "Stress-Strength", and "Shocks" failure models discussed here are such models. To make the use of the Hyperbolic model easier, the maximum likelihood estimators of its parameters are given. They can be calculated without any difficulty, and appear to be acceptable for practical technological applications. Finally, two applicative examples are given. These examples exhibit that when the mechanism of failure is one of the types discussed, the Hyperbolic model shows a better fit compared with other alternative reliability models, like Gamma, and Weibull.