## 1 Introduction  
Industrial 6-DoF (degrees-of-freedom) robots are widely used for the automation of various manufacturing processes, such as welding, assembly, painting, inspection, etc. As the demand for industrial 6-DoF robots continues to increase, robot manufacturers are correspondingly researching the development and performance improvement of robots to meet the requirements of various applications. It is imperative to ensure the performance and reliability of robot drive components including servo motors and gearboxes in improving the accuracy and responsiveness of industrial robots. In particular, a high-precision gearbox with little backlash and high reduction ratio is a key component which determines the accuracy and performance of a robot, and since the weight of the gearbox is directly related to the payload of robots, a small size, light weight, and high torque density design is required. Therefore, high-precision gearboxes, such as harmonic drives [1] and planocentric type 2-stage precision gearboxes [2], are applied to many industrial robots requiring high accuracy and responsiveness. High-precision drive components occupy the highest proportion in the manufacturing cost of robots, and it is essential to ensure stable performance and reliability because they can cause downtime and accidents of the automated process in the event of a failure. In the field of reliability application, the most commonly used test methods for reliability qualification are zero-failure acceptance tests since they require fewer test samples and less test time compared to other test methods that guarantee the same reliability with a given confidence level [3]. To verify the reliability of drive components for industrial multi-joint robots, component-level life tests must be accompanied by a system-level life test in which the drive components are mounted on an actual robot, and predefined test modes are repeated to verify the durability. A zero-failure acceptance test concept can be applied to calculate the test time for the guaranteed life of each joint part in system-level life test, and an acceleration test is designed by comparing the test load with the load in guaranteed conditions. The load applied to the drive components of each joint of the robot will depend on the payload and the motion profile. This can also result in differences in the degree of damage to the drive components, which results in a difference in the required test time. As a consequence, the overall zero failure test time is determined by the longest test time among the required test times of each joint of the robot. If the variation of the required test time for each joint is large, the parts tested in excess of the required time have higher probability of failure, necessitating the repair or replacement of damaged components, and thus requiring more time and cost for the test. There is a method to stop the motion of the joint after the test time has been completed, but it can be cumbersome for the tester such as monitoring the time when the test time for each axis is completed and operating in a new test mode, etc. especially when the test scale is large. Therefore, one of the ideas to verify the durable life of a robot drive component through system-level accelerated life testing is to design a test mode with the same zero failure test time for all the joint drive components. At the same time, it is necessary to design the test with a high acceleration factor to reduce the test time required to verify the durable life. For this purpose, the industry has been using robot simulation software to design test modes based on experience and intuition of engineers and trial and error. Therefore, it took a lot of time to derive robot motions that match the test times for the components of the individual joints equally, and there was a limit in the accuracy. Motivated by the above observation, the goal of this study is to develop a numerical method for designing robot motions for system-level life test of drive components of robot.