## 3 Results
### Rules for Explaining the Results
We will compare these results to the previous ones, taking into account how the fixed parameter influences the output._  
_Figure 5 (Yield Strength Predictions with Fixed Ram Speed):_  
_This graph, like the previous one, shows the isolines for yield strength. The solid lines show different yield strength values based on varying silicon content and casting speed, with data density shown through shading._  
_Compared to the earlier graph of yield strength without a fixed ram speed, the iso-lines here may show a different pattern. However, without seeing the previous graph simultaneously, we can't compare the exact differences. Generally, yield strength still seems to increase with higher silicon content and casting speed._  
_Figure 5 (Standard Deviation with Fixed Ram Speed):_  
_The graph (Figure 5b) displays the standard deviation of the yield strength predictions, shown by the dotted isolines. A quick comparison with the previous standard deviation graph (if they were side by side) would indicate whether fixing the ram speed has made the predictions more or less consistent at different silicon content and casting speeds._  
_Data Density Considerations:_  
Figure 5: Prediction of yield strength as a function of casting speed (horizontal axis) and Si content at fixed value of ram speed, which equals 15.405 mm/s: (**a**) mean value according to Equation (1) and (**b**) local standard deviation according to Equation (4). The shading that indicates data density has not changed. The darkest areas still imply the highest data density and therefore the most reliable predictions for yield strength. Fixed Parameter Impact:  
Fixing the ram speed means that it is no longer a variable in the prediction of yield strength. This control can help to isolate the effects of silicon content and casting speed on yield strength. It could potentially lead to more accurate predictions since one less variable might reduce the complexity of the material behavior being modeled. Combined Comparison:  
When comparing these graphs with the previous ones, you would look for any changes in the shape and spacing of the isolines, which would suggest how the fixed ram speed has affected the relationship between silicon content, casting speed, and yield strength. To compare effectively, you would need to overlay the graphs or switch between them to observe how the isolines for both yield strength and standard deviation shift. Any shifts could inform you about the sensitivity of yield strength to casting speed and silicon content when the ram speed is held constant. In practical terms, if the fixed ram speed has led to a reduced standard deviation in the yield strength at certain levels of silicon content and casting speed, this could mean more reliable and consistent production outcomes for those specific conditions. It would also mean that the process window for achieving desired yield strength with acceptable variability has become more well-defined. Figure 6 illustrates the outcome, with yield strength plotted as a function of casting speed and Si content at a constant ram speed which amounts to 15.471 mm/s and at a constant Mn content which amounts to 0.469. Note that only a smaller part of the explanation is presented here:  
Comparison with Previous Graphs (Variable and Fixed Ram Speeds):  
Comparing these graphs to the previous ones with variable and different fixed ram speeds, we can make several observations:  
1. **Sensitivity and Predictability:** With the additional fixed parameters (ram speed and Mn content), the sensitivity and predictability of yield strength to changes in Si con-tent and casting speed may differ. The shape and spacing of the isolines in the new graphs suggest that the relationships between these variables and yield strength have changed. 2. **Effect of Fixed Parameters:** By fixing ram speed and Mn content, we are looking at a more specific scenario in the casting process.