In the statistical static timing analysis (S-STA), the timing information, such as a gate delay, a signal arrival time, and a slack, is treated as a random variable, and the statistical maximum operation is an important basic operation. Since the maximum of two Gaussian random variables is not Gaussian, various techniques for representing a non-Gaussian distribution have been proposed. Among them, the Gaussian mixture model is distinguished from the others in that it can handle various correlations, non-Gaussian distributions, and slew distributions easily, which are important in S-STA. In this paper, we propose a new statistical maximum operation for Gaussian mixture models, which takes the cumulative distribution function curve into account, and show some experimental results to evaluate its performance.