## 3 Methods
### Service Quality Risk Evaluation
The following equation can represent this:  
\[\text{CII}=\text{a}_{\text{i}}\times\text{CSI} \tag{5}\]  
The contributory improvement index (CII) is a synthetic index that combines both the standardized weight and customer satisfaction index (CSI) to provide a comprehensive understanding of their relative importance. The CII was calculated by multiplying the standardized weight derived from [PERSON]'s model by the CSI quality attribute rating. The attributes with a higher CII were more aligned with customer requirements and contributed to greater satisfaction. The CII ranged from 0 to 1 (both the standardized weight and CSI were normalized). * Step 3: Combination of the CII and the FMEA  
The risk priority order of failure modes can be determined by utilizing the RPN in an FMEA. According to [PERSON] and [PERSON] (2018), this study defined \"risk priority number of service quality risk management (RPN\({}^{\text{SQR}}\))\" as the product of \"worth improving the level of an attribute, occurrence of quality failure and detection of quality failure\". Therefore, CII could be used to replace the severity (S) in the original RPN equation (RPN = S \(\times\) O \(\times\) D), and we amended the equation as \(\text{RPN}^{\text{SQR}}=\text{CII}\times\text{Oc}\times\text{D}\). Then, we put it into the \"correctionratio (Cr)\" proposed by [PERSON] [61]. The modified Cr can be expressed by the following equation:  
\[\text{Cr}=1-\frac{\text{RPN}_{\text{Tg}}^{\text{SQR}}}{\text{RPN}_{0}^{\text{ SQR}}}=1-\frac{\text{CII}_{\text{Tg}}\times\text{Oc}_{\text{Tg}}\times\text{D}_{ \text{Tg}}}{\text{CII}_{0}\times\text{Oc}_{0}\times\text{D}_{0}} \tag{6}\]  
where:  
\(\text{RPN}_{0}^{\text{SQR}}\): current risk priority number of service quality risk management;  
\(\text{RPN}_{\text{Tg}}^{\text{SQR}}\): goal risk priority number of service quality risk management;  
\(\text{CII}_{0}\): current contributory improvement;  
\(\text{CII}_{\text{Tg}}\): goal contributory improvement;  
\(\text{Oc}_{0}\): current failure occurrence;  
\(\text{Oc}_{\text{Tg}}\): goal failure occurrence;  
\(\text{D}_{0}\): current failure detection;  
\(\text{D}_{\text{Tg}}\): goal failure detection. Assuming that the detection (D) was constant, this meant \(\text{D}_{\text{Tg}}=\text{D}_{0}\), then the equation of Cr value could be simplified as the following equation:  
\[\text{Cr}=1-\frac{\text{CII}_{\text{Tg}}\times\text{Oc}_{\text{Tg}}}{\text{ CII}_{0}\times\text{Oc}_{0}} \tag{7}\]  
An attribute with a higher CII was more in line with customer needs and contributed to greater satisfaction. In other words, attributes with a low CII represent a lower quality of service risk and are not worth improving. [PERSON] and [PERSON] [15] took the lowest current contributory improvement (CII\({}_{0}\)) as the goal contributory improvement (CII\({}_{\text{Tg}}\)); that is, \(\text{CII}_{\text{Tg}}=\min\{\text{CII}_{i}\},i=1,\ldots,\text{N}\). In addition, the lowest current failure occurrence (Oc\({}_{0}\)) was taken as the goal failure occurrence (Oc\({}_{\text{Tg}}\)); that is, \(\text{Oc}_{\text{Tg}}=\min\{\text{Oc}_{0}\},i=1,\ldots,\text{N}\) (N represents the number of service attributes).