Modern manufacturing enterprises have invested in a variety of sensors and IT infrastructure to increase plant floor information visibility. This offers an unprecedented opportunity to track performances of manufacturing systems from a dynamic, as opposed to static, sense. Conventional static models are inadequate to model manufacturing system performance variations in real-time from these large non-stationary data sources. This paper addresses a physics-based approach to model the performance outputs (e.g., throughputs, uptimes, and yield rates) from a multi-stage manufacturing system. Unlike previous methods, degradation and repair dynamics that influence downtime distributions in such manufacturing systems are explicitly considered. Sigmoid function theory is used to remove discontinuities in the models. The resulting model is validated using real-world datasets acquired from the General Motor's assembly lines, and it is found to capture dynamics of downtime better than traditional exponential distribution based simulation models. Index Terms-nonlinear stochastic differential equation (n-SDE) model, mean time between failure (MTBF), mean time to repair (MTTR), recurrence analysis, multi-stage manufacturing systems