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In MIL-STD-810, the environmental engineering consideration and laboratory tests by US military, the DP (damage potential) formula is used to calculate the fatigue damage by vibration environments which is a simplified version of a FDS (fatigue damage spectrum) formula. DP, however, was originally made for comparison between different test standards and is not an optimized formula for the synthesis of vibration environments. This paper presents the GRS (Gaussian Random Synthesis) formula for only vibration test synthesis featuring simplified DP formula and produce the same result as DP. Although the GRS provides insight into the synthesis of vibration tests, it must be used with care because it inherits the constraints of the original FDS formula.