# Analysis and Application of Selected Control Charts Suitable for Smart Manufacturing Processes
## 5 Suggestion of Methodology for NPCC Practical Utilization  
Based on previous simulations, obtained outcomes and general principles of statistical process control, a methodology for practical utilization of NPCCs was created. The steps of this methodology are depicted using the following scheme in Figure 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **SSCC** & **NP-CUSUM** \\ \hline \(\bullet\) & Distribution with bigger kurtosis than for normal distribution & \(\bullet\) & Distribution with bigger kurtosis than for normal distribution \\ \(\bullet\) & Distribution with smaller kurtosis than for normal distribution & \(\bullet\) & Distribution with smaller kurtosis than for normal distribution \\ \(\bullet\) & Asymmetric distribution & \(\bullet\) & Nonconstant variance (for larger samples and \(n=5\)) \\ \(\bullet\) & \multicolumn{1}{c}{} & \\ \end{tabular}
\end{table}
Table 2: Summary of analysis of NPCCs for location monitoring. Source: own research.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **MAD** & **Mood** \\ \hline \(\bullet\) & Distribution with smaller kurtosis than for normal distribution & \(\bullet\) & Distribution with bigger kurtosis than for normal distribution \\ \(\bullet\) & Distribution with bigger kurtosis than for normal distribution & \(\bullet\) & Asymmetrical distribution \\ \(\bullet\) & Distribution with bigger kurtosis than for normal distribution & \(\bullet\) & Nonconstant variance (for smaller samples) \\ \(\bullet\) & Nonconstant variance (for larger samples) & \(\bullet\) & Nonconstant mean \\ \(\bullet\) & \multicolumn{1}{c}{} & \\ \(\bullet\) & Autocorrelated data & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of analysis of NPCCs for variability monitoring. Source: own research.  
Phases 1 and 4 contain similar activities, as they are well-known for the standard methodology of statistical process control applications. For that reason, only Phases 2 and 3, which represent the innovative core of the designed methodology, will be described in more detail. The collection of data and their analysis are very significant activities in the frame of statistical monitoring because especially verification of data assumptions forms the base for the objective decision of whether to apply the classic Shewhart CC or some NPCC. The effective verification of data assumptions calls for combining multiple statistical tests with graphical methods.  
Significant attention must be paid to the analysis of potential outliers or suspicious values. When causes of them cannot be identified, these values must not be removed from the data set and must remain part of the following data analysis.  
The phase of the selection of a suitable CC is wholly based on the previous results of performed simulations, and it creates the heart of this methodology design. When all data prerequisites are met, the classic Shewhart CC can be used, but when some of the data prerequisites are violated, applying the classic Shewhart CC could result in incorrect conclusions. Thus, the utilization of a suitable NPCC is a reasonable alternative in these cases. Phase 3 is clearly described using flowcharts (see Figures 2 and 3).  
Figure 1: Scheme of the designed methodology. Source: own research.  
Figure 2: Flowchart for practical utilization of NPCCs for location monitoring. Source: Adapted from [55]. Legend: LS—large samples.  
Figure 3: Flowchart for utilization of NPCCs for variability monitoring. Source: Own research. Legend: LS—large samples, SmS—small samples.