# Analysis and Application of Selected Control Charts Suitable for Smart Manufacturing Processes
## 6 Practical Application  
Verification of the designed methodology was performed using real data from a supplier for the automotive industry. The organization specializes in coating interior components with natural and synthetic leather. The weight of the adhesive that is automatically applied by a robot was set as a controlled characteristic. The weight of the adhesive after drying is calculated as the difference in the weight of the plastic part before application of the adhesive and the weight of the part after application of the adhesive and its drying. The weight of each piece is determined. The measured values were divided into 30 subgroups with a range of 5 units.  
Subsequently, a data analysis was performed to determine whether the basic data assumptions had been met. The Anderson-Darling test was used to verify normality. Its results showed that the data are not normally distributed. Based on Figure 4, it can be concluded that the data are slightly skewed and contain some potential outliers or suspicious values.  
Verification of data independence was performed using the Box-Pierce test. The resulting P-value of the test was 0.676, so it is greater than 0.05, and we can say that the data are independent. However, the most strongly violated data prerequisite seems to be kurtosis, as is clear from Figure 5 and from the value of the coefficient of kurtosis, which is equal to 17, 88.  
The potential outliers and suspicious values were analyzed, but the reasons for their occurrence were not identified. For this reason, it was inappropriate to remove these values from the data set. However, using classical control charts, several points should be outside control limits UCL or LCL (see Figure 6), leading to useless searching for the nonexistent causes and time losses for the operators or forcing them to make unnecessary process adjustments (this is called tampering).  
Figure 4: Box plot. Source: own research using SW Minitab.  
For these reasons, a suitable NPCC was selected using the suggested algorithm depicted in Figures 2 and 3, i.e., an NPCC based on the Mood statistic (for monitoring process variability) and an NP-CUSUM chart (for monitoring process position) were applied.  
Figure 5: Histogram. Source: own research using SW Minitab.  
Figure 6: Parametric Shewhart control charts for mean and range. Source: own research using SW Minitab.  
The values of the calculated statistics necessary for the construction of the selected control charts can be found in Table A1 (Appendix D). Figure 7 shows the NPCC based on the Mood statistic. As can be seen, all points are located inside the control limits. In terms of variability, the process is statistically stable.  
Regarding the evaluation of the process's statistical stability in terms of location, an NP-CUSUM chart was constructed. The values of the required statistics are given again in Table A1 in Appendix D. The resulting CC is shown in Figure 8. This control chart does not contain any points beyond the control limits, so it can be said that the process is statistically stable.  
The results of this case study support Hypothesis 4 that NPCCs are resistant against potential outliers, which is suitable in situations when it is not possible to find causes of their occurrence.  
Figure 8: Nonparametric CUSUM control chart. Source: own research.  
Figure 7: Nonparametric control chart based on the Mood statistic. Source: own research.