## 3 Data and Analysis
### Analysis of Special-Cause Variation
#### 3.3.1 Example of Control Chart
To heighten the reliability of detection results, significant special events are further determined by using two methods. With regard to the special causes triggering anomalous responses of the local track system, significant special events are determined by outliers of at least three control charts or rules in Table 4 at each measuring point. Usually, it is easy for a special event to cause the outliers in two control charts (individual control chart and moving range control chart), whereas the simultaneous triggers of outliers in the three control charts or rules are rarely found. In that case, the overlap of various control charts increases the credibility of special events. A total of sixteen significant special events are determined and listed in Table 5.  
As for the special causes triggering anomalous responses of the overall track system, significant special events are decided by outliers of the control charts at more than three measuring points. Detections of multiple sensors can effectively reduce the probability of outliers induced by sensor failure and increase the confidence of significant special events. A total of twenty-eight significant special events are determined and listed in Table 6. Among them, the durations of significant special events from 27 June 2015 to 29 June 2015 and from 12 May 2016 to 15 May 2016 are more than three days, which should be paid special attention. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Date**} & **Measuring Points with** **Outliers Detected** & **Number of Measuring Points** & **Date** & **Measuring Points with** **Outliers Detected** & **Number of Measuring Points** \\ \hline
2015.6.27–2015.6.29 & R-S-R-D14, S-G-R-D16, S-G-R-D21 & 4 & 2016.6.8 & R-S-R-D10, R-S-R-D15, S-G-R-D16, S-G-R-D18, G-D21 & 5 \\ \hline
2015.7.30–2015.7.31 & S-G-R-D16, S-G-R-D17, S-G-R-D18, G-D21 & 4 & 2016.6.19 & R-S-R-D15, S-G-R-D16, S-G-R-D18, G-D21 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Significant special events determined by outliers of the control charts at more than three measuring points. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Measuring Point**} & **Individual** & **Supplementary** & **Moving Range** & **EWMA Control Chart** & **Total** \\ \hline R-S-R-D10 & 6 & 1 & 21 & 10 & 38 \\ R-S-R-D13 & 16 & 18 & 22 & 8 & 64 \\ R-S-R-D14 & 11 & 10 & 16 & 10 & 47 \\ R-S-R-D15 & 16 & 64 & 31 & 10 & 121 \\ S-G-R-D16 & 13 & 7 & 21 & 15 & 56 \\ S-G-R-D17 & 29 & 67 & 37 & 43 & 176 \\ S-G-R-D18 & 16 & 17 & 23 & 15 & 71 \\ G-D21 & 14 & 31 & 24 & 10 & 79 \\ Total & 121 & 215 & 195 & 121 & 652 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of control chart outliers. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Measuring Point**} & **Date** & **Control Charts** & **Measuring Point** & **Date** & **Control Charts** \\ \hline R-S-R-D10 & 2018.4.3 & I, MR, EWMA & & 2017.11.19 & I, N2, N7 \\ R-S-R-D13 & 2015.9.19 & I, MR, EWMA & S-G-R-D17 & 2017.11.20 & I, N2, N7 \\ R-S-R-D14 & 2017.1.9 & I, MR, EWMA & & 2018.8.9 & I, MR, EWMA \\ R-S-R-D15 & 2016.1.5 & I, MR, EWMA & S-G-R-D18 & 2015.7.30 & I, MR, EWMA \\ S-G-R-D16 & 2015.7.30 & I, MR, EWMA & & 2015.11.6 & I, MR, EWMA \\ R-S-R-D10 & 2015.8.5 & I, MR, EWMA & & 2015.7.30 & I, MR, EWMA \\ R-S-R-D10 & 2015.7.30 & I, MR, EWMA & G-D21 & 2015.9.1 & I, N3, EWMA \\ R-S-R-D10 & 20159.6 & I, N8, MR & & 2015.11.6 & I, MR, EWMA \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Significant special events determined by outliers of at least three control charts or rules at each measuring point.