## 4 Experiments and Results
### Real World Dataset  
This paper used event log data from real world process data. The datasets of the factory that the paper is analyzing can be accessed at [32]. This real world factory produces metal parts such as ball nuts and wheel shafts. With this production process, we have 28 machines for milling, wire cutting, laser marking, round grinding, flat grinding, turning, turning and milling, and lapping. Table 5 shows some of the event logs.  
Table 5 shows 106 sets of cases from the data sets. The activity name in the table simply expresses the name of the actual process included in the log data [32]. Each case includes the type of machine used, the start and end times of activities, and the number of manufactured products. The quantity of products to be manufactured is also used as an important factor, and this variable distinguishes cases where the same product is produced by the same set of machines but with a different number of productions. In the absence of these data, bias may occur. These data describe the process of producing 31 products. We use the transition based embedding method proposed earlier to map the event log data into a vector format, and then proceed with modeling through artificial intelligence. After manufacturing residual cycle prediction modeling is completed, the model of the training dataset and the model of the testing dataset are compared to demonstrate the model being appropriate, where we implemented the MAE:  
\[\text{MAE}=\frac{1}{n}\sum_{t=1}^{n}\lvert A_{t}-F_{t}\rvert \tag{7}\]  
Figure 10 visually expresses the flow of the process at the manufacturing site, as well as how the activities in Table 5 proceed. This figure visually expresses the trace of case 106 described in the previous table, where this process starts from Machine 8 and proceeds along the blue dotted line. Each process is finally terminated with QC2. The following process is a relatively simple process, but since a smart factory process is very complex, it may be difficult to train an artificial intelligence neural network [19]. This is because it can interfere with the creation of a valid digital twin with repeated activities that interfere, making it difficult to understand. In this paper, to create a more meaningful digital twin model, in the case of a repeated process, the process was abstracted and considered as one activity.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Case ID** & **Activity\({}_{\text{Machine}}\)** & **Start Time** & **Complete Time** & **Qty** \\ \hline Case 106 & Turning/Milling–Machine 8 & 15 March 2012: 10:14 & 15 March 2012: 15:44 & 39 \\ Case 106 & Turning/Milling–Machine 8 & 15 March 2012: 16:55 & 15 March 2012: 20:38 & 39 \\ Case 106 & Turning/Milling Q.C. & 19 March 2012: 7:00 & 19 March 2012: 7:28 & 39 \\ Case 106 & Laser Marking–Machine 7 & 19 March 2012: 9:38 & 19 March 2012: 10:51 & 39 \\ Case 106 & Flat Grinding–Machine 11 & 19 March 2012: 14:42 & 19 March 2012: 15:20 & 39 \\ Case 106 & Final Inspection Q.C. & 21 March 2012: 15:27 & 21 March 2012: 17:57 & 39 \\ Case 106 & Packing & 22 March 2012: 0:00 & 22 March 2012: 1:00 & 39 \\ Case 106 & Final Inspection Q.C. & 22 March 2012: 11:50 & 22 March 2012: 13:05 & 39 \\ \hline \end{tabular}
\end{table}
Table 5: Industrial event log of Case 106.