## 2 System Description  
### Tele-Abrasive Operation  
A tele-abrasive system is a shared-control system where an operator and an automated machine operate the system together [14; 15]. It is a teleoperation system that mainly consists of two main components, a human operator and a tele-abrasive machine, as shown in Figure 1. The operator interacts with the machine via the master controller to create a command for the slave device. Generally, the master controller is a passive manipulator--i.e., the operator controls the movement of the master controller. Then, its movement will be encoded as a movement command for the slave device.  
The slave device is a manipulator that is sent into an environment that is changing, dangerous, and/or difficult for humans to reach. This device moves in accord with the command shared from the master controller. An abrasive nozzle is mounted at the end-effector to clean a surface. A camera is installed in the working area to capture the movement of the slave device for the operator.  
Typically, the surface area of the complex structure that is to be cleaned can be thought of as sub (flat, rectangular) are as connected. During the operation, the operator navigates the abrasive nozzle on a two-dimensional plane parallel to the surface. Thus, the tele-abrasive task motion in this study is considered in reference only to a two-dimensional movement on the surface (X-Y plane).  
The purpose of this task is to clean the entire surface as quickly as possible. To minimize the time taken, the traveling distance to complete this task, and the costs associated with it, the width of the blasting path is set as equivalent to or slightly narrower than the blasted spot size [16], as shown in Figure 2. With this setup, an operator who navigates the nozzle inaccurately and imprecisely will produce poor surface quality. Therefore, in a conventional system, the path width is frequently set to be much narrower than the blasted spot size to cover variation caused by human arm movement error, which helps maintain surface quality. However, a narrower path results in a longer traveling distance, and then more time is required to complete the task. Consequently, the operator must be  
Figure 1: Tele-abrasive system.  
intensively trained to ensure that he or she is capable of performing the task competently and efficiently.  
Among the sources of variation mentioned earlier, recent research has proposed many approaches in an effort to reduce variation by improving visual perception [9], stabilizing time delay [10], and maximizing robot accuracy [17; 18; 19]. However, in teleoperation tasks, although human arm movement is a main part of a shared-control system, human movement error has received very little research attention. In this general area, [14] proposed an adaptive network-based fuzzy inference system (ANFIS) model to control human arm movement velocity in a gas tungsten arc welding task. Furthermore, [20] considered the problem of the physical interface between a human and a computer, which requires an approach to help the human operator perform a hand movement task in a more comfortable and, hence, more reliable way.  
In our tele-abrasive system, the variation in the tele-abrasive machine stage has been improved [19]. However, no research has considered the variation in the human operator stage (the position variation of the master controller caused by human error).  
To consider only the variation caused by human error, the system output is not a good measure because it includes the variation caused by many sources. Therefore, a multi-stage variation stream was employed to categorize variation from each source and see how it propagates throughout the process.