## 2 Method  
### Contact Transmission Model for Oil Contamination  
Workers' processing, handling, and assembling of workpieces cause the spread of oil contamination. The transfer process of oil contamination occurs in three states, namely, by means of workers' gloves, workbench surfaces, and workpiece surfaces. The transfer process follows the principle of mass conservation. Here, the Markovian process was introduced to analyze the transfer of oil contamination on various surfaces in a workshop. The workbench surfaces were numbered continuously from 1 to \(m\). Then, the gloves were numbered continuously from \(m+1\) to \(m+q\), where \(q\) represents the number of workers. A state space \(S\) was formulated according to Equation (1). Oil contamination carried by the workpieces can be regarded as a process parameter in which oil contamination is transferred between the glove and the workbench. Thus, in this study, the state space \(S\) did not consider the state of oil contamination carried by the workpieces.  
\[S=\{1,\ 2,\ \ldots,\ m,\ m+1,\ m+2,\ \ldots,\ m+q\} \tag{1}\]  
The modeling process of the contact transmission model can be described as follows.  
According to the actual layout of the SDS workshop, the workshop is divided into two main areas: the production area and the assembly area. The production area is composed of \(I\) production units. Assume that each production unit has \(a\) machines and \(b\) workbenches, and each machine can produce \(c\) workpiece per minute. Each workpiece carries \(d\) mgof liquid oil contamination after a cutting is completed. Meanwhile, the assembly area is composed of \(J\) assembly units. In general, an assembly worker oversees each assembly unit to complete the subsequent manipulation. For the production area, although each production unit is adjacent to each other, the workers only move to their own production unit. In other words, oil contamination is not transferred between the adjacent production units. For a single production unit, the worker puts the unprocessed workpiece into a machine. After waiting for the production to be completed, the worker takes out the workpiece and puts it on a workbench. Then, the worker puts in a new workpiece and repeats the process. Workers place the workpiece on the workbench to mark and lubricate it. When the number of workpieces loaded on each workbench reaches \(e\), they are transported to the assembly area. Usually, automatic transport vehicles are used in the workshop to transport workpieces from the production area to the assembly area, forming a connection between the two areas. However, the automatic vehicles transport the workpieces from the workbench in the production area to the assembly unit in the assembly area in a random manner. After the workers in the assembly unit perform secondary processing, such as assembling and wiping, the workpieces are put into a new transport vehicle and sent to the warehouse. The surface of the warehouse represents the terminated state of the oil contamination, and the transfer process inside the workshop is unaffected; thus, this state is also not included in the state space \(S\).  
On the basis of the assumed scenario, the oil contamination concentrations of workpieces, workbenches (or assembly tables), and workers' gloves at a certain time interval \(t\) were calculated. The workpiece was regarded as the medium through which oil contamination spreads across regions, and its concentration was considered to be the main factor affecting the distribution of oil contamination in the assembly area. The calculation of oil contamination concentration is described in the next subsections.