## 3 Methodology
### BLCC Creation
#### 3.2.2 Bottom Level: Review-Based \(g\)-Chart for Performance Monitoring  
At the bottom level of the BLCC, the performance of an attribute is monitored; only reviews mentioning the attribute are considered at this level to exclude the effect of attribute importance. To avoid the issue of a small number of reviews, a \(g\)-chart is adopted in the review-based control chart for the first time. A \(g\)-chart can monitor the intervals between rare events without being affected by the amount of data. In the present study, a \(g\)-chart is created for each attribute to monitor the number of non-negative reviews between two negative reviews (complaints). A large average interval implies fewer complaints for an attribute in a given time period, indicating a better performance of the attribute. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rule** & **Description** & **Indicated Problem** \\ \hline Rule 1 & One point is more than 3 standard deviations from the mean. & The subgroup is out of control. \\ \hline Rule 2 & Nine points in a row are on the same side of the mean. & A long-term bias exists. \\ \hline Rule 3 & Six points in a row are continually increasing (or decreasing). & A trend exists. \\ \hline Rule 4 & Fourteen points in a row alternate in direction, increasing and then decreasing. & Oscillation exists. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Tests for special-cause variation for \(p\)-chart. A \(g\)-chart requires the structured data in Table 3 to be transformed into a new format, that is, the number of non-negative reviews between negative reviews. Thus, the construction of a \(g\)-chart begins with data transformation, as shown in Figure 4.  
Data transformation consists of three steps and is conducted for each attribute. First, only reviews that mention attribute \(i\) (\(x_{ij}=1\)) are extracted as a new dataset, and a new review sequence identifier, \(m\), is assigned to each review in chronological order, starting from 1 to \(M_{i}\). Second, only negative reviews (i.e., \(y_{ij}=1\)) are extracted as a new dataset, and another review sequence identifier, \(n\), is assigned to each negative review in chronological order from 1 to \(N_{i}\). Finally, for each negative review \(n\), the number of event opportunities, \(O_{i,n}\) (i.e., the number of reviews that mention attribute \(i\) until the \(n\)th negative review, or, the sequence identifier \(m\) corresponding to review \(n\)), and the complaint interval, \(C_{i,n}\) (i.e., the number of non-negative reviews between the \((n-1)\)th and \(n\)th negative reviews), are calculated using Equation (7). For instance, if negative comments appear in the first and eleventh reviews and the reviews between them are non-negative, then \(C_{i,s}\) and \(C_{i,2}\) are 0 and 10, respectively. If negative comments appear in a review and in the immediately succeeding review, then the interval is 0. It should be noted that \(O_{i,1}\) for the first negative review can be set differently if information on the previous reviews is available so that an accurate value of \(O_{i,1}\) can be obtained. \[C_{i,n}=\left\{ \begin{array}{cc}O_{i,n}-1&(n=1)\\ O_{i,n}-O_{i,n-1}-1&(n\geq 2)\end{array} \right.\qquad\text{where }O_{i,n}=m \text{ of review }n \tag{7}\]  
The \(g\)-chart is created using \(C_{i,n}\). Following the studies by [PERSON] [47; 51], the complaint probability, \(q_{i}\), is estimated based on the minimum-variance unbiased estimator, as expressed in Equation (8). \[q_{i}=\frac{N_{i}-1}{N_{i}\big{(}\overline{C}_{i,n}+1\big{)}}=\frac{N_{i}-1}{ \sum_{n=1}^{N_{i}}C_{i,n}+N_{i}} \tag{8}\]  
The CL, UCL, and LCL are then calculated using Equations (9)-(11), respectively. Considering that the geometric distribution is highly skewed, the probability limit method [47] is adopted here instead of the more familiar \(\pm 3\) standard deviation method.