## 3 Methodology
### DIPA with Staged Charts  
In this step, DIPA is conducted based on the proposed review-based \(p\)- and \(g\)-charts. DIPA is a new visualization tool for representing the temporal changes in attributes' importance and performance. The proposed DIPA focuses on the fact that the CL of attribute \(i\)'s \(p\)-chart and \(g\)-chart (i.e., \(\text{CL}^{p}_{i}\) and \(\text{CL}^{g}_{i}\)) can be an indicator of the attribute's average importance and performance, respectively, as expressed in Equations (12) and (13). According to Equation (13), the performance index ranges from 0 to 1, given that \(\text{CL}^{g}_{i}\) can vary between zero and infinity. In this step, a dynamic IPA is conducted using DIPA, i.e., a new visualization tool for representing the time-varying changes of attributes' importance and performance. The DIPA focuses on the fact that the \(\text{CL}^{p}_{i}\) and \(\text{CL}^{g}_{i}\) can be indicators of an attribute's average importance and performance, respectively, as shown in Equations (12) and (13). Here, Equation (13) makes the performance index range from 0 to 1, given that the \(\text{CL}^{g}_{i}\) can vary between 0 and infinity.  
\[\text{importance index}_{i}=\text{CL}^{p}_{i} \tag{12}\]  
\[\text{performance index}_{i}=1-\frac{1}{1+\text{CL}^{g}_{i}} \tag{13}\]  
In Sections 3.1 and 3.2, the CL was calculated once for the entire dataset (or the entire time horizon), resulting in a single fixed value. The CL is useful to diagnose the overall status of the process in a retrospective manner, but it cannot grasp the trends over time or predict the future status. The DIPA overcomes this limitation using staged control charts.  
The DIPA first divides the entire time horizon into multiple stages and calculates the CL, UCL, and LCL of the individual stages; such a control chart with multiple stages is called a staged control chart. The DIPA then calculates the average importance and performance levels of attribute \(i\) in each stage, \(s\), using the CLs of staged BLCCs, as expressed in Equations (14) and (15). In these equations, \(\text{CL}^{p}{}_{i,s}\) and \(\text{CL}^{S}{}_{i,s}\) denote the CL of the staged \(p\)- and \(g\)-charts of attribute \(i\) in stage \(s\), respectively.  
\[\text{importance index}_{i,s}=\text{CL}^{p}_{i,s} \tag{14}\]  
\[\text{performance index}_{i,s}=1-\frac{1}{1+\text{CL}^{S}{}_{i,s}} \tag{15}\]  
The proposed DIPA is performed by tracking how the index values change over time. It is a two-dimensional graph with importance and performance on the \(y\)-axis and \(x\)-axis, respectively. According to Equations (14) and (15), the point (\(\text{CL}^{p}{}_{i,s}\), \(1-1/(1+\text{CL}^{S}{}_{i,s})\)) on the DIPA represents the average importance and performance of attribute \(i\) in stage \(s\). The DIPA connects the points of the same attribute with arrows in the increasing order of \(s\) or in chronological order, which allows us to grasp temporal changes in attributes' importance and performance.  
The DIPA also requires the setting of two boundary values by which relatively low and high levels of importance and performance are determined. Basically, such boundary values can be set by the user. The average levels of the attributes can be used as a reference, and if available, the competitors' status and market averages can be reflected by setting the boundary values.