## 5 Conclusions and Further Studies  
This paper identified three NN-based modeling approaches (FFNN, CFNN, and RBFN) that obviate the need for the assumptions required when LSM-based RSM is used to \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Estimation Model**} & \multicolumn{3}{c}{**Optimal Factor Settings**} & \multicolumn{1}{c}{\multirow{2}{*}{**Process Mean**}} & \multirow{2}{*}{**Process Bias**} & \multirow{2}{*}{**Process Variance**} & \multirow{2}{*}{**EQL**} \\ \cline{2-2} \cline{5-8}  & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & & & & & \\ \hline LSM & \(1.000\) & \(0.071\) & \(-0.2500\) & \(494.6720\) & \(5.3270\) & \(1977.5320\) & \(2005.9170\) \\ FFNN & \(0.999\) & \(0.999\) & \(-0.6230\) & \(499.8690\) & \(0.1310\) & \(7.7630\) & \(7.7800\) \\ CFNN & \(0.792\) & \(-0.752\) & \(0.9990\) & \(499.6870\) & \(0.3120\) & \(2.8540\) & \(2.9520\) \\ RBFN & \(0.999\) & \(0.999\) & \(-0.4300\) & \(500.0520\) & \(0.0520\) & \(23.2190\) & \(23.2210\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Comparative results of the case study. Figure 21: Criterion space of the estimated functions in the case study. (**a**) LSM-based RSM. (**b**) Proposed FFNN. (**c**) Proposed CFNN. (**d**) Proposed RBFN. approximate the mean and standard deviation functions. The feed-forward NN structure-based RD modeling methods are alternative options for identifying a functional relationship between input factors and process mean and standard deviation in RD. Compared with the conventional RD modeling method, the proposed approach has significant advantages with regard to accuracy and efficiency. The proposed RD modeling methods can easily be implemented using existing software such as MATLAB. The results of both the two types of simulation studies and case study show that the proposed RD modeling methods provide better optimal solutions than conventional LSM-based RSM. The main results are summarized, and the variability index, EQL, and \(R^{2}\) are central to the model validation criteria. (i) In simulation study 1, the proposed RD modeling methods showed, on average, 139 times lower process bias and 1.5 times lower process variance than LSM-based RSM in terms of variability, and about four times smaller in EQL. Moreover, among the three NN-Based modelings, FFNN showed the lowest value in terms of EQL. (ii) In simulation study 2, the proposed RD modeling methods showed 11 times lower process bias and one time lower process variance than LSM-based RSM on average in terms of variability and about 1.2 times smaller in EQL. Among the three NN-Based modelings, FFNN also showed the lowest value. (iii) In the case study, the proposed RD modeling methods showed significantly lower results than LSM-based RSM, with an average process bias of 102 times and process variance of 85 times in terms of variability, and about 86 times smaller in EQL. Among the three NN-Based modelings, CFNN and FFNN showed much lower values than RBFN. (iv) Specifically, in the printing machine case study, the \(R^{2}\) values for the estimated standard deviation functions are 45.452%, 73.51%, 69.47%, and 99.99%, when the conventional LSM-based RSM, FFNN-based modeling, CFNN-based modeling and RBFN-based modeling methods are applied respectively. In future work, the proposed NN structures-based RD methods could be used to estimate multiple responses (RD multi-objective optimization problem), time-series data, big data, and simulation data [60]. But the activation and transfer function in the hidden and output layers should be carefully investigated and selected separately when applied. In addition, in this study, a classical case study was performed to verify the proposed methodology, but in the future study, a field-based case study that suggests optimal process conditions for productivity improvement in a smart factory will be performed. Conceptualization, T.-H.L. and S.S.; Methodology, T.-H.L. and S.S.; Modeling, T.-H.L. ; Validation T.-H.L. and S.S.; Writing--Original Draft Preparation, T.-H.L.