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 DP, however, was originally made for comparison between different test standards and is not an optimized formula for the synthesis of vibration environments.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.

In order to verify the reliability of drive components for industrial robots, component-level life tests must be accompanied by a system-level life test using actual robots in which predefined robot motions are repeated throughout the test. To properly verify the durability of drive components through a system-level life test, it is important to design test modes so that the required test time is the same for all joint drive components of the robot, and it is necessary to design test modes with a high acceleration factor so as to shorten the required test time as much as possible. To solve this problem, the present research proposes a method for designing robot motions that makes the accelerated life test time for all the drive components of the robot equal. In particular, we solve a dynamic based motion optimization problem for an industrial 6-DoF (degrees-of-freedom) robot that minimizes the AM-GM (arithmetic mean to geometric mean) ratio of the acceleration factors of each joint. The results show that $C^2$-continuous test modes with the same acceleration factor, which is inversely proportional to the cycle time of the robot motion, can be derived.