# Time-Series Prediction of Failures in an Industrial Assembly Line Using Artificial Learning
## 4 Results and Discussion
### Discussion  
In this study, the prediction of the \"configuration\" parameter is performed using various artificial intelligence and statistical modelling approaches, and the performance of these models is evaluated based on statistical error metrics, namely RMSE, MAE, and MAPE. Initially, in a comparative study from the literature that investigated standalone and wavelet-based modelling approaches (Table 6), performance metrics for different models (MLP, ANFIS, and NARX) were reported. [PERSON] and [PERSON] (2017) collected time series of the climatological variable global horizontal radiation. They present a model with a lower error [33]. This is because their model includes both its delays and exogenous inputs such as humidity, temperature, wind speed, and sunshine duration. Thus, the model can easily catch the relations among all climatic variables. It is also important to note that some studies involved pre-processed data and employed different evaluation metrics. Another significant point is the diversity in the modelled parameter and its unit across studies. These differences hinder a direct one-to-one comparison. Nevertheless, the overall behaviour of the models appears to align with the expected outcomes. For instance, [PERSON] et al. (2025) reported that the GRU model performs faster than LSTM [35], which is consistent with the findings of the present study, where the training durations are recorded as 1826.525 s for LSTM and 1724.109 s for GRU. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Modelling Studies** & **Model** & \begin{tabular}{l} **Modelled** \\ **Parameter** \\ \end{tabular} & **RMSE (\({}^{\star}\))** & \(R^{2}\) & **Additional Metrics** \\ \hline \multirow{4}{*}{Proposed models} & NAR & & 1.107 & 0.987 & MAE = 2.592, MAPE = 0.895\% \\  & LSTM & Time-series data, & 4.159 & 0.917 & MAE = 5.081, MAPE = 5.081\% \\  & ANFIS & Time-series data, & 1.409 & 0.988 & MAE = 2.805, MAPE = 0.862\% \\  & GRU & configuration of & 2.871 & 0.966 & MAE = 4.124, MAPE = 2.848\% \\  & CNN-RNN & & 5.551 & 0.968 & MAE = 5.063, MAPE = 2.948\% \\  & MLP & & 1.418 & 0.986 & MAE = 2.122, MAPE = 0.876\% \\ \hline \multirow{4}{*}{[PERSON] and [PERSON] (2017)[33]} & MLP (wavelet) & & 0.0682 & 0.896 & MAPE = 5.15\% \\  & ANFIS & Global horizontal & 0.0389 & 0.965 & MAPE = 2.98\% \\  & ANFIS & irradiance & 0.0410 & 0.896 & MAPE = 3.37\% \\  & ANFIS (wavelet) & (Whm\({}^{-2}\) day\({}^{-1}\)) & 0.0662 & 0.961 & MAPE = 4.88\% \\  & NARX & (Wavelet) & & 0.0329 & 0.940 & MAPE = 2.32\% \\ \hline \multirow{2}{*}{\begin{tabular}{l} [PERSON] et. al. \\ (2007)[34] \\ \end{tabular} } & MLP & \begin{tabular}{l} Number of tourists \\ (count) \\ \end{tabular} & \begin{tabular}{l} 147,909 \\ 147,909 \\ \end{tabular} & NA & MAE = 127,838.8, MAPE = 14.96\% \\ \hline \multirow{4}{*}{\
\begin{tabular}{l} [PERSON] et. al. \\ (2025)[35] \\ \end{tabular} } & GRU & & 1.750 & NA & Train time(s) = 22.256, MAPE = 0.230\% \\  & LSTM & Temperature (\({}^{\circ}\)C) & 1.701 & NA & Train time(s) = 23.796, MAPE = 0.213\% \\  & BIGRU & & 1.889 & NA & Train time(s) = 27.095, MAPE = 0.273\% \\  & BILSTM & & 2.016 & NA & Train time(s) = 29.813, MAPE = 0.232\% \\ \hline \multirow{4}{*}{
\begin{tabular}{l} [PERSON] et. al. \\ (2025)[36] \\ \end{tabular} } & RNN & Main outlet slurry & 9.8188 & 0.853 & MAE = 7.2049, MAPE = 0.3025\% \\  & LSTM & flow rate, MOSFR & 9.9564 & 0.838 & MAE = 7.2458, MAPE = 0.3042\% \\  & SVR (**) & (m\({}^{3}\)h\({}^{-1}\)) & 19.578 & 0.695 & MAE = 14.5567, MAPE = 0.6099\% \\ \cline{1-1}  & ICEEMDAN-MPA- & GNNS (****) height & 2.49 & 0.98 & MAE = 2.12, MAPE = 2.85\%, \\ \cline{1-1}  & GRU (**) & coordinate (\({}^{\circ}\)) & & Weighted quality evaluation index = 0.463 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the proposed model with similar ones in the literature. Overall, the findings suggest that the modelling approaches proposed in this study outperform their counterparts in the literature in terms of both lower error and higher prediction accuracy.