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The key objectives of this paper are to analyze and implement a novel moving horizon model predictive estimation scheme based on constrained nonlinear optimization techniques for inferring the survival functions and residual useful life (RUL) of components in coupled systems. The approach employs a data-driven prognostics framework that combines failure time data, static and dynamic (time-series) parametric data, and the Multiple Model Moving Horizon Estimation (MM-MHE) algorithm for predicting the survival functions of components based on their usage profiles. Validation of the approach has been provided based on data from an electronic throttle control (ETC) system. The proposed prognostic approach is modular and has the potential to be applicable to a wide variety of systems, ranging from automobiles to aerospace.