A stochastic approach to the security evaluation of a dynamic system is presented. The mean first passage time (MFPT) of a multi-dimensional system from its domain of attraction is defined as a security measure, and a closed form expression for the asymptotic estimate of the MFPT is derived. The proposed method encompasses various multi-dimensional dynamic systems, and the analysis of a power system model is used as a case study. The power system is represented by a multi-bus constant voltage, constant impedence model, and the assumption of low damping is waived to widen the application of the results. In this study, small perturbations in dynamic systems have been modelled as weak wideband gaussian coloured noises. Corresponding sensitivity results for a 19-bus power system are presented.