The aim of this work is to analyze the nondeterministic global dynamics of an electrically actuated microbeam under harmonic excitation with added noise, via a phase-space operator approach allowing a unified description for both deterministic and nondeterministic cases. In this context, the stochastic basins of attraction and attractors’ distributions replace the usual basin and attractor concepts. For the numerical analysis, an adaptative phase-space discretization strategy based on the classical Ulam method is adopted. The results highlight the importance of randomness and time-dependency of stochastic response on the global dynamics of systems with competing attractors. A dynamic integrity measure based on the obtained probability distributions is employed to confidently quantify the safety of the dynamical system. Finally, sample results on the influence of a parameter uncertainty on global dynamics are presented.