# Root Cause Tracing Using Equipment Process Accuracy Evaluation for Looper in Hot Rolling
## 3 Root-Cause-Tracing Algorithm
### Correlation Analysis between EPAE and Production Stability  
Taking the finishing rolling area as an example, the EPAE score in this area includes five aspects: side guides, loopers, AGC, bending rolls, and shifting rolls. Simultaneously, abnormal conditions in the finishing rolling area include the head of the finishing rolling area abnormalities, body abnormalities in the finishing rolling area, and tail abnormalities in the finishing rolling area.  
The strip production process is complex and involves many parameters, so the same anomaly in the finishing rolling area may occur multiple times. In this section, the total number of abnormalities in the finishing rolling area of each strip is used as an indicator of production stability, and the correlation between the total number of abnormalities and the EPAE score is analyzed.  
The Pearson correlation coefficient, also known as the Pearson product-moment correlation coefficient, is used to measure the linear correlation between two sets of data \(X\) and \(Y\), and its value ranges from \(-1\) to \(1\)[24]. The calculation formula is  
\[r=\frac{\sum_{i=1}^{n}(X_{i}-\bar{X})(Y_{i}-\bar{Y})}{\sqrt{\sum_{i=1}^{n}(X_{ i}-\bar{X})^{2}}\sqrt{\sum_{i=1}^{n}(Y_{i}-\bar{Y})^{2}}} \tag{18}\]  
where \(\bar{X}\) and \(\bar{Y}\) are the average values of data \(X\) and data \(Y\). The closer the absolute value of \(r\) is to \(1\), the stronger the correlation between the two sets of data. In this section, the two sets of data \(X\) and \(Y\) are, respectively, the EPAE score and the number of anomalies appearing in the finishing rolling area.  
In order to facilitate the data analysis, consider representing the score as follows:  
\[\begin{cases}[x],&|x-[x]|<0.5\\ [x]+1,&|x-[x]|\geq 0.5\end{cases} \tag{19}\]  
where \(x\) is the EPAE score and \([x]\) is the rounding function. This equation aims to classify data into different categories as much as possible, such as number \(1.1\), which are classified as \(1\), since \(|1.1-[1.1]|=|1.1-1|<0.5\), \(1.1\) is classified as number \(1\), and so on, \(1.6\), \(1.7\) are represented as \(2\). After the above operations, the same score may correspond to multiple abnormal times, so these abnormal times need to be averaged.  
The EPAE score and the number of abnormal occurrences of production stability in the finishing rolling area of a 2250 mm hot strip production line in a certain month are collected and used in Equation (19) to calculate the Pearson correlation between each EPAE score and the number of abnormal occurrences in the finishing rolling area.  
From Table 3, it is not difficult to see that the factors of the finishing rolling side guide plate, looper, automatic gauge control (AGC), finishing rolling bending roll, and shifting roll are negatively correlated with the number of abnormalities in the finishing rolling area. In particular, the absolute value of the correlation coefficient between the finishing rolling side guide plate and the finishing rolling bending roll is large, and the significance level \(p\)-value is also much less than 0.05. This shows that the higher the EPAE score, the fewer the number of abnormalities and the higher the production stability. Therefore, the EPAE score will be applied subsequently to reflect the production stability.