# Anomaly Monitoring of Process Based on Recurrent Timeliness Rules (AMP-RTR)
## 4 Experimental Results
### Conduct Simulation Experiments on Semiconductor Manufacturing Datasets
#### 4.2.2 Process of Simulation Experiment  
We have carried out simulation experiments on the data set of the actual semiconductor manufacturing process to test how the model can effectively monitor the abnormalities of the production line. Obviously, the time of data acquisition must be regularized first, especially when the time interval between two data updates is too large. Due to confidentiality, all data labels are anonymous or modified. However, the main results are still valid. As a manufacturing enterprise, the manufacturer is committed to providing users with reliable products. Therefore, the abnormal monitoring ability of the production line plays an important role in the normal work of the manufacturing enterprise. The RTR model is based on the time stamp of each periodic data update, such as the time series of temperature, humidity, voltage and current generated periodically. The data are generated periodically, and the generated time series are transmitted to the model in real time. Then, the timeliness of periodic data is evaluated based on these time series. On this basis, the evaluation value of data timeliness is monitored for abnormalities. Monitor whether the timeliness score is less than 0 or more than 1 for many times. First, we convert all timestamps in the Secom dataset into UNIX timestamps. Then, we calculate the interval of every two adjacent timestamps and normalize the time interval. Finally, we input the processed time series into the RTR model. We conducted four groups of experiments. In these four groups of experiments, \(fall=0.2\) in group \(11^{\#}\) and group \(12^{\#}\), \(fall=0.1\) in group \(13^{\#}\) and group \(14^{\#}\). Among them, \(\alpha=0.05\) in group \(11^{\#}\) and group \(13^{\#}\) experiments, and \(\alpha=0.10\) in group \(12^{\#}\) and group \(14^{\#}\) experiments. In group \(11^{\#}\) and \begin{table}
\begin{tabular}{c c} \hline \hline
**Serial Number** & **Time Series** \\ \hline
1 & 19/07/2008 11:55:00 \\
2 & 19/07/2008 12:32:00 \\
3 & 19/07/2008 13:17:00 \\
4 & 19/07/2008 14:01:00 \\
5 & 19/07/2008 14:43:00 \\... &... \\
1550 & 16/10/2008 02:22:00 \\
1551 & 16/10/2008 02:55:00 \\
1552 & 16/10/2008 03:37:00 \\
1553 & 16/10/2008 04:11:00 \\
1554 & 16/10/2008 04:58:00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Datasets of semiconductor manufacturing process. group \(12^{\#}\) experiments, the condition for model convergence is when the timeliness score is less than 0, as shown in Figure 6. In group \(13^{\#}\) and group \(14^{\#}\) experiments, the condition for model convergence is that the number of times the timeliness score is greater than 1 meets the set threshold, as shown in Figure 7.  
Figure 6 shows the trend that the timeliness score converges to 0 when two different periodic update rates \(\alpha\) are used. Obviously, the larger the periodic update rate \(\alpha\), the faster the model converges. The timeliness score value of the periodic data at the beginning of the first cycle is set to 1. During the iterative change of the timeliness score of periodic data, we record the times when the timeliness score is greater than 1. Since the maximum timeliness score is 1, it will be reset to 1 when the value is greater than 1. In this case, the condition for model convergence is that the number of times the timeliness score is greater than 1 meets the threshold. According to Formula (10), the threshold value set by group \(13^{\#}\) is \(200\) (\(N(A)=100\times fall(A)\times\frac{1}{\alpha}\times\frac{1}{T-t}=100\times 0.1 \times 20\times 1=200\)), and the threshold value set by group \(14^{\#}\) is \(100\) (\(N(A)=100\times fall(A)\times\frac{1}{\alpha}\times\frac{1}{T-t}=100\times 0.1 \times 10\times 1=100\)). Figure 7 shows the change of timeliness score. From Figure 7, we can conclude that the smaller the value of \(\alpha\), the faster the model converges. In addition, the larger the value of \(\alpha\), the larger the change range of the timeliness score.