Different formulations have been proposed to estimate the reliability of engineering systems according to their design specification. However, the as-built state might differ from the design specification, and aging and deterioration are affecting the performance of the systems over time. Physics-based fragility estimates that are explicitly developed as functions of state variables defining the state of the system can be coupled with state-dependent models for the deterioration and results from Structural Health Monitoring (SHM). State-of-the-art state-dependent models for the deterioration of the state variables are able to incorporate the possible interaction between different deterioration processes and can be used as inputs in the physics-based fragilities to estimate the future reliability of the system. SHM can be used to assess the current state of the system as well as to calibrate the state-dependent deterioration models, which can then be used to better predict the performance of the system at future times. Current state-dependent models are defined in terms of the finite change in the state variables in the unit of time of a chosen discretization for the time domain. This makes the model parameters discretization-dependent and makes the simulation and calibration processes time-consuming and computationally expensive. In this paper, we propose a novel formulation that uses a system of Stochastic Differential Equations (SDE) for modeling the change in the state variables of the system. Using this formulation, the model parameters do not depend on the chosen discretization in the time domain.