A methodology has been developed for estimating the time variant reliability of a randomly vibrating series system, when the component response processes constitute a vector of mutually correlated log-normal random processes. A key feature in the development of the proposed method lies in the assumption, that for high thresholds, the number of level crossings of a non-Gaussian process can be modeled as a Poisson point process. The assumption of the outcrossings being Poisson distributed have been proved to be mathematically valid for Gaussian processes when the threshold approaches infinity (Cramer, 1966). However, it has been pointed out that for threshold levels of practical interest, this assumption results in errors whose size and effect depend on the bandwidth of the processes (Vanmarcke, 1972). While it can be heuristically argued that for high thresholds, the outcrossings of non-Gaussian processes can be viewed to be statistically independent and hence can be modeled as a Poisson point process, to the best of the authors’ knowledge, studies on the validity of this assumption for non-Gaussian processes, do not exist in structural engineering literature. The multivariate extreme value distributions obtained by the proposed method, is thus expected to inherit the associated inaccuracies and limitations due to this assumption.