## 3 Results
### Illustrative Example of Model 4208 to Determine Hardenability Curves  
To evaluate the performance of the model, the hardenability curves of the 41 Cr4 and 42 CrMo4 steel (according standard [49]) grades are compared by examining the experimental and predicted results. In this particular example, the performance of the model is evaluated by comparing the predicted hardness values with the observed (experimental) values for the 41 Cr4 and 42 CrMo4 steel grades. As evident from Table 8 and Figure 7, the results show close agreement between the experimental and predicted values. The close agreement between the experimental and predicted hardness values indicates a high degree of accuracy and reliability in the model's ability to predict the hardenability of the steels. This robust predictive capability indicates the model's potential for optimizing heat treatment processes, assisting in material selection, and improving overall efficiency in the design and manufacture of steel components. Figure 6: Performance evaluation of Model 4208 on an unseen new test dataset. Illustrative Example of Model 4208 to Determine Restricted Hardenability Band of 42 CrMo4 Steel Grade  
In this section, the use case of the model in determining the hardenability band is discussed. Determining the H-band offers numerous advantages, including optimized material selection, enhanced component performance, cost-effective manufacturing, prevention of defects and failures, improved consistency and quality control, tailored material properties, and customization to specific customer requirements. Moreover, it aids in restricting the chemical composition ranges for applications and ensures the desired performance characteristics. Due to variations in chemical composition among different heats of the same steel grade, hardenability bands are defined using the Jominy end-quench test. The upper curve indicates maximum hardness values corresponding to the upper composition limits, while the lower curve represents minimum hardness values for the lower composition limits. Hardenability bands are valuable for both suppliers and customers, with most steels now purchased based on these bands. Suppliers ensure that a significant percentage, typically 93 or 95%, of mill heats meeting chemical specifications fall within the specified hardenability band [50]. The model can be used either manually or can be combined with Bayesian optimization or a genetic algorithm [14] to determine the limiting chemical compositions values within the required hardness stated by the customer. The integration of artificial neural networks with various modeling techniques, such as mathematical modeling, computational intelligence, and artificial intelligence is a common practice. The amalgamation of different methods within a single model enables the exploration of a larger problem space and leads \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Steel Grade**} & \multicolumn{10}{c}{**Distance in mm from Quenched End**} \\ \cline{2-13}  & \multicolumn{10}{c}{**Hardness in HRC**} \\ \cline{2-13}  & **1.5** & **3** & **5** & **7** & **9** & **11** & **13** & **15** & **20** & **25** & **30** & **40** & **50** \\ \hline \multirow{3}{*}{41 Cr4} & Exp. & 58.50 & 57.50 & 56.75 & 55.25 & 54.00 & 51.75 & 49.25 & 45.50 & 40.50 & 38.00 & 37.75 & 29.00 & 24.00 \\ \cline{2-13}  & Pred. & 58.38 & 57.71 & 56.57 & 55.49 & 54.05 & 51.69 & 48.70 & 45.61 & 40.64 & 38.34 & 36.39 & 29.39 & 23.90 \\ \hline \multirow{3}{*}{42 CrMo4} & Exp. & 56.33 & 55.33 & 54.17 & 53.50 & 52.00 & 49.00 & 45.17 & 42.00 & 37.67 & 35.17 & 34.00 & 31.83 & 28.67 \\ \cline{2-13}  & Pred. & 56.17 & 55.55 & 54.55 & 53.57 & 51.94 & 48.91 & 45.41 & 42.33 & 37.57 & 35.42 & 33.96 & 31.24 & 29.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Experimental and predicted hardness for 41 Cr4 and 42 CrMo4 steel grades. Figure 7: The target and predicted hardenability curves of 41 Cr4 and 42 CrMo4 steel grades.