# Anomaly Monitoring of Process Based on Recurrent Timeliness Rules (AMP-RTR)
## 4 Experimental Results
### Model Testing in Synthetic Datasets  
We generated synthetic datasets under different conditions to evaluate the performance of the periodic monitoring model. In order to verify the robustness of the model, we conducted two sets of simulation tests on the synthetic datasets. The first group of tests simulated the number of iterations required for the convergence of our monitoring model when the update time of cycle data in the manufacturing process is always later than the set cycle, as shown in Table 1. The number of iterations required for the convergence of the model when the data update time is always later than the set period (T = 7). Figure 4 shows the trend of the model converging to 0 when the update time is later than the set period to varying degrees. The second group of tests simulated the number of iterations required for the convergence of our monitoring model when the update time of cycle data fluctuates around the set cycle in the manufacturing process, as shown in Table 2. The number of iterations required for the convergence of the model when the data update time is always earlier than the set period (T = 7). Figure 4. Convergence trend of the model in the when the data are updated later. Figure 5 shows the convergence trend of the model in the case of updating times with different fluctuation amplitudes. When the data update time is always later than the set period, different parameter configurations correspond to different model convergence speeds, as shown in Table 1. When the update cycle is normalized to \(T=7\), we choose to show \(t=9\) and \(t=11\) for two main reasons. First, the time series of the input model are normalized to \([0-14]\), and \(t=9\) and \(t=11\) are more representative. Second, because the distribution of the time series is basically in line with the Gaussian distribution through statistical analysis, it is more reasonable to choose two values closer to cycle \(T=7\). Through the comparison of 01* and 02* experiments, we found that the same parameter configuration will also have different convergence speeds. The farther away the update time is from the period, the faster the model converges. Through the comparison of experiments 02* and 03*, we find that the same update time will also have different convergence speeds. The smaller the decay rate \(fall(A)\), the faster the model converges. Through the comparison of experiments 04* and 05*, we find that the larger the periodic update rate \(\alpha\), the faster the model converges. To sum up, the convergence speed of the \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameter Value**} & **The Last** & **Iteration Times of** \\  & \(f_{n}(t,\lambda 1A)\) & **Model Convergence** \\ \hline
01*\(\alpha=0.05\), \(fall=0.2\), \(t=09\) & \(-0.002\) & 167 \\
02*\(\alpha=0.05\), \(fall=0.2\), \(t=11\) & \(-0.006\) & 116 \\
03*\(\alpha=0.05\), \(fall=0.1\), \(t=11\) & \(-0.008\) & 64 \\
04*\(\alpha=0.10\), \(fall=0.1\), \(t=09\) & \(-0.018\) & 55 \\
05*\(\alpha=0.20\), \(fall=0.1\), \(t=09\) & \(-0.037\) & 28 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The number of iterations required for the convergence of the model when the data update time is always later than the set period (\(T=7\)). model is directly proportional to \(\alpha\) and inversely proportional to \(fall(A)\). The change trend of the timeliness score of the above five groups of experiments is shown in Figure 4.  
Figure 4 shows that the timeliness score changes linearly with the number of iterations under different parameters. The value of \(\alpha\) can be dynamically adjusted according to the sensitivity requirements of different production lines for abnormal monitoring. The update time of the data is earlier than the set period, and the attenuated value of the data timeliness score should be positive (i.e., \(Q_{decay}(t,\lambda|A)>0\)) within a period. When the timeliness score after data update is greater than 1, its value will be reset to 1.