## 6 Discussion  
### Discussion of the Skewness-Kurtosis Comparison  
In general, the comparison of skewness and kurtosis of the measured samples with theoretical distributions showed that it is difficult to determine suitable distribution functions for the investigated weld geometry parameters and SCFs. This might be related to non-stationary processes that result in variations along weld seams but also measurement inaccuracies; however, trends can be discovered and related to other published data.  
In the literature [38; 39; 40; 42; 43], weld toe radii and angles are sometimes stated to be normally distributed. Here, the weld toe radii seem to be better described by a lognormal distribution. This agrees with a number of recent studies [20; 36; 37]. As the sample distributions of the measured weld toe angles are symmetrical, it is possible that this parameter is indeed well-described by a normal distribution; however, more data should be assessed to verify this result.  
Figure 10: Skewness–kurtosis plot presenting the determined sample parameters and a number of common two-parameter distribution functions.  
Undercuts can be considered a type of weld defect; thus, gamma distributions might be a suitable choice to describe the depth of undercuts. Gamma distributions are frequently used for such tasks; however, more research is required. [PERSON] et al. [20] and [PERSON] et al. [36; 37] used a lognormal distribution to fit their data, which also accommodates very large numbers of small undercut depths; however, a lognormal distribution is not suited to describe distributions for which the maximum of data is equal to zero. In general, data for undercut depths are seldom presented nor considered in the literature. It is therefore not yet possible to come to a conclusion.  
Based on Figure 10, weld reinforcement heights could either be normally distributed or described by a lognormal, gamma, or inverse gamma distribution. In the literature, the height of welds is often described by a normal distribution [20; 36; 37; 43].  
Finding suitable distributions for the weld width and SCFs is difficult. Interestingly, the data for the automatically welded joints made by SAW, laser- and laser-hybrid welding is heavily skewed and outside the range presented in Figure 10. This could be related to the fact that the welder is able to manually adjust the welding process, while the automatic process is not able to do so. The constant heat-input with the inhomogeneous heat distribution in the plates might lead to a change in weld gap and thereby to a drift in weld width. The drift in weld width was confirmed by assessing the change of parameters along the weld seam for several segments.  
The reason for the scatter of the sample parameters of the SCFs might be related to the fact that the SCF calculation is based on the input of a number of geometrical features. Thus, the variability and any possible inaccuracy in the input parameters is transferred to the SCFs. As the MSE of the DNN is almost zero, inaccuracies of the DNN can be ruled out as long as the measured parameter are within the parameter range used to train the DNN. This was ensured by filtering measured parameters outside the training range; however, only a small amount of measured data was removed this way.  
Finally, the combination of various parameters might also be the reason why typical two-parameter distribution functions are not suitable to describe a complex parameter such as a SCF. Clearly, more data and research on the variability of this parameter are required to establish a better understanding of the variability of SCFs along weld seams.