This paper quantifies the approximation error in Clark?s approach [1] to computing the maximum (max) of Gaussian random variables; a fundamental operation in statistical timing. We show that a finite Look Up Table can be used to store these errors. Based on the error computations, approaches to different orderings for pair-wise max operations on a set of Gaussians are proposed. Experiments show accuracy improvements in the computation of the max of multiple Gaussians by up to 50% in comparison to the traditional approach. To the best of our knowledge, this is the first work addressing the mentioned issues.