## 5 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**Traditional \(\overline{\text{X}}\)-R Control Chart ARL**} \\ \hline \(\boldsymbol{\lambda}\) & & & & & \multicolumn{3}{c}{**\(\boldsymbol{\delta}\) (Shift)**} & & & \\ \# & \(\boldsymbol{0.0}\) & \(\boldsymbol{0.2}\) & \(\boldsymbol{0.4}\) & \(\boldsymbol{0.6}\) & \(\boldsymbol{0.8}\) & \(\boldsymbol{1.0}\) & \(\boldsymbol{1.2}\) & \(\boldsymbol{1.4}\) & \(\boldsymbol{1.6}\) \\ \hline
**1.0** & 370.5 & 228.0 & 84.9 & 30.8 & 12.6 & 6.0 & 3.3 & 2.1 & 1.5 \\
**1.1** & 119.2 & 88.2 & 44.1 & 20.1 & 9.7 & 5.2 & 3.1 & 2.1 & 1.6 \\
**1.2** & 48.8 & 40.3 & 25.0 & 13.8 & 7.7 & 4.5 & 2.9 & 2.1 & 1.6 \\
**1.3** & 24.2 & 21.3 & 15.3 & 9.8 & 6.2 & 4.0 & 2.8 & 2.0 & 1.6 \\
**1.4** & 13.9 & 12.8 & 10.1 & 7.2 & 5.0 & 3.5 & 2.6 & 2.0 & 1.6 \\
**1.5** & 8.9 & 8.4 & 7.1 & 5.5 & 4.2 & 3.1 & 2.4 & 1.9 & 1.6 \\
**2.0** & 2.6 & 2.5 & 2.4 & 2.3 & 2.1 & 1.9 & 1.7 & 1.5 & 1.4 \\
**2.5** & 1.6 & 1.6 & 1.5 & 1.5 & 1.5 & 1.4 & 1.4 & 1.3 & 1.2 \\ \hline \hline \multicolumn{10}{c}{**Traditional \(\overline{\text{X}}\)-R Control Chart SDRL**} \\ \hline \(\boldsymbol{\lambda}\) & & & & \multicolumn{3}{c}{**\(\boldsymbol{\delta}\) (Shift)**} & & \\ \# & \(\boldsymbol{0.0}\) & \(\boldsymbol{0.2}\) & \(\boldsymbol{0.4}\) & \(\boldsymbol{0.6}\) & \(\boldsymbol{0.8}\) & \(\boldsymbol{1.0}\) & \(\boldsymbol{1.2}\) & \(\boldsymbol{1.4}\) & \(\boldsymbol{1.6}\) \\ \hline
**1.0** & 370.0 & 227.5 & 84.4 & 30.2 & 12.1 & 5.5 & 2.8 & 1.5 & 0.9 \\  
Figure 10: Standard deviation of the run length, highlighting the scenario in which the process is in control (\(\delta\) = 0.0 and \(\lambda\) = 1.0). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & \multicolumn{3}{c}{**8 (Shift)**} & & \\
**\#** & **0.0** & **0.2** & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & **1.4** & **1.6** \\ \hline
**1.0** & 372.45 & 228.54 & 85.32 & 30.43 & 12.55 & 5.93 & 3.35 & 2.11 & 1.56 \\
**1.1** & 118.56 & 87.10 & 44.23 & 20.32 & 9.56 & 5.17 & 3.11 & 2.10 & 1.59 \\
**1.2** & 48.54 & 39.54 & 24.89 & 13.77 & 7.67 & 4.54 & 2.95 & 2.08 & 1.58 \\
**1.3** & 24.10 & 21.09 & 15.45 & 9.71 & 6.14 & 4.03 & 2.76 & 2.00 & 1.60 \\
**1.4** & 13.91 & 12.61 & 9.77 & 7.27 & 4.99 & 3.50 & 2.56 & 1.97 & 1.60 \\
**1.5** & 8.70 & 8.83 & 7.06 & 5.52 & 4.10 & 3.08 & 2.41 & 1.92 & 1.59 \\
**2.0** & 2.56 & 2.50 & 2.42 & 2.29 & 2.05 & 1.87 & 1.70 & 1.54 & 1.42 \\
**2.5** & 1.57 & 1.55 & 1.54 & 1.50 & 1.45 & 1.40 & 1.36 & 1.29 & 1.26 \\ \hline \multicolumn{8}{c}{**IT2 TFN X-R Control Chart SDRL**} & \\ \hline \(\lambda\) & & & & & \multicolumn{3}{c}{**8 (Shift)**} & & \\
**\#** & **0.0** & **0.2** & **0.4** & **0.6** & **0.8** & **1.0** & **1.2** & **1.4** & **1.6** \\ \hline
**1.0** & 371.141 & 226.537 & 84.860 & 29.844 & 12.081 & 5.298 & 2.807 & 1.515 & 0.942 \\
**1.1** & 119.090 & 85.087 & 43.340 & 19.960 & 9.167 & 4.605 & 2.551 & 1.528 & 0.972 \\
**1.2** & 47.318 & 39.034 & 24.456 & 13.138 & 7.122 & 3.997 & 2.400 & 1.491 & 0.964 \\
**1.3** & 23.366 & 20.641 & 14.992 & 9.222 & 5.628 & 3.549 & 2.208 & 1.407 & 0.968 \\
**1.4** & 13.220 & 12.266 & 9.299 & 6.628 & 4.510 & 3.012 & 1.981 & 1.397 & 0.987 \\
**1.5** & 8.180 & 7.808 & 6.506 & 4.924 & 3.534 & 2.526 & 1.880 & 1.346 & 0.964 \\
**2.0** & 2.042 & 1.975 & 1.879 & 1.735 & 1.482 & 1.296 & 1.094 & 0.910 & 0.774 \\
**2.5** & 0.938 & 0.938 & 0.918 & 0.869 & 0.827 & 0.742 & 0.697 & 0.614 & 0.576 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulated values of ARL and SDRL found for IT2 TFN \(\overline{\text{X}}\) and R control charts. Figure 9: Average run length, highlighting the scenario in which the process is in control (\(\delta\) = 0.0 and \(\lambda\) = 1.0).