Hybrid dynamical systems (HDS) models are backbone of modeling a myriad of systems found in systems engineering, buildings, manufacturing, auto-pilot control, and chemical processes domains among others. Uncertainty quantification (UQ) techniques to ascertain output variability in HDS with parametric uncertainty is relatively understudied topic. In this paper, we present a novel method to enable UQ of HDSs. Specifically, we outline a computational pipeline to solve different types of Stochastic Hybrid Systems (SHS) with uncertainty in initial conditions. The developed method is based on a numerical integration technique Conjugate Unscented Transform (CUT) and discrete UQ technique. The developed method has been applied to different range of problems including theoretical problems and real life mechanical systems modeled in Simulink environment. Performance of the proposed method has been compared against Monte Carlo and Unscented Transform methods. Results indicate superior performance of the proposed technique over the existing methods.

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