# Automatic Evaluation of the Robotic Production Process for an Aircraft Jet Engine Casing
## 3 Solution of the Problem
### Data Analysis and Determination of the Significant Parameter  
The welding parameter values listed in Table 2 were stored to files with a designed structure to facilitate downstream analysis. For each production part, the data for all 36 manufactured welds were collected.  
Figures 10 and 11 show example trends for a few of the selected and recorded parameters, which included welding current and voltage (Figure 10) and the welding speed (Figure 11).  
The data produced from the saved parameter trends were collated with the quality control data, which included the welding results for all welded joints. Table 4 is a matrix of defects for each weld of the considered sample of part numbers.  
The analysis of the collected quality control data from the welding process operation considered in this work revealed that the most prevalent weld defect in the operation was missing weld penetration along a certain part of, or along the entire weld.  
One of the assumptions of the project was to implement the solution in production conditions using the existing equipment. The main determining factor was the limited computing capacity of the robot IRC5 controller. To make a comparison of the collected signals of the defined welding process parameters that are listed in Table 2, indicators were calculated using statistical functions, which included the following:  
* standard deviation;
* variance;
* skewness;
* kurtosis;
* average value.  
\begin{table}
\begin{tabular}{c  
Analyzing the data, there were more then 900,000 records of data per one production part, which resulted in about 1500 indicator values for one part. The batch of 50 production parts generated 1800 values for only one indicator type. All the indicators calculated for the groups of the main welding parameters and the WeldGuide system parameters were analyzed. Examples of indicator values for welding voltage and speed are shown in Table 5.  
The calculated indicators were compared with the quality control data listed in Table 4. The analysis of the results provided a determination of the limit value of an indicator for which the welding result was conforming. The values of the skewness indicators, whose absolute values were higher than the limit value, indicated the presence of weld defects. Figure 12 shows a set of the absolute values of welding voltage trend skewness (WeldVolt) for three exemplary welds for twenty subsequent parts processed. The determined limit value for this indicator was 0.5 for a conforming welding result. Any indication above this value was directly correlated to incomplete weld penetration (Nb\({}_{20}\)) and foreign material inclusion (Nw). A value of the determined skewness above the determined limit value was also a characteristic of the rarer defects, such as missing weld penetration (Nb\({}_{70}\)) and material burn through (Np).  
The defects for which the parameter limit value was exceeded were approximately 50% of the total number of non-conformities in the welds of analyzed groups of production parts.  
Figure 12: Example values of the skewness for the welding voltage trends.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Weld**} & \multicolumn{2}{c}{**Standard Deviation**} & \multicolumn{2}{c}{**Variance**} & \multicolumn{2}{c}{**Skewness**} & \multicolumn{2}{c}{**Kurtosis**} & \multicolumn{2}{c}{**Average Value**} \\ \cline{2-10}  & **A** & **B** & **A** & **B** & **A** & **B** & **A** & **B** & **A** & **B** \\ \hline \(1\) & 0.476 & 0.002 & 0.227 & 0.0000031 & 0.246 & \(-