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In performance modeling of parallel synchronous iterative applications, the longest individual execution time among parallel processors determines the iteration time and often must be estimated for performance analysis. This involves the mean maximum calculation which has been a challenge in computer modeling for a long time. For large systems, numerical methods are not suitable because of heavy computation requirements and inaccuracy caused by rounding. On the other hand, previous approximation methods face challenges of accuracy and generality, especially for heterogeneous computing environments. This paper presents an interesting property of extreme values to enable Effective Mean Maximum Approximation (EMMA). Compared to previous mean maximum execution time approximation methods, this method is more accurate and general to different computational environments.