# Novel Service Efficiency Evaluation and Management Model
## 4 A Case Study  
As mentioned earlier, the set service operation must go through the service process of 5 workstations (w = 5) to complete. Assume there are \(n\) service operations and let \(Y_{h,j}=y_{h,j}\) for \(h=1\), 2, 3, 4, 5 and \(j=1\),2,..., \(n\), then the random variable matrix of \(\left[Y_{h,j}\right]\) and the observed value matrix \(\left[Y_{h,j}\right]\) can be displayed as follows:  
\[\left(\begin{array}{c}Y_{1,1},\ldots,Y_{1,j},\ldots,Y_{1,100}\\ Y_{2,1},\ldots,Y_{2,j},\ldots,Y_{2,100}\\ Y_{3,1},\ldots,Y_{3,j},\ldots,Y_{3,100}\\ Y_{4,1},\ldots,Y_{4,j},\ldots,Y_{4,100}\\ Y_{5,1},\ldots,Y_{5,j},\ldots,Y_{5,100}\end{array}\right)=\left(\begin{array} []{c}y_{1,1},\ldots,y_{1,j},\ldots,y_{1,100}\\ y_{2,1},\ldots,y_{2,j},\ldots,y_{2,100}\\ y_{3,1},\ldots,y_{3,j},\ldots,y_{3,100}\\ y_{4,1},\ldots,y_{4,j},\ldots,y_{4,100}\\ y_{5,1},\ldots,y_{5,j},\ldots,y_{5,100}\end{array}\right)=\left(\begin{array} []{c}0.34,\ 0.33,\ 0.36,\ \ldots,\ 0.33\\ 0.30,\ 0.31,\ 0.29,\ \ldots,\ 0.31\\ 0.33,\ 0.32,\ 0.30,\ \ldots,\ 0.32\\ 0.39,\ 0.35,\ 0.37,\ \ldots,\ 0.40\\ 0.27,\ 0.30,\ 0.29,\ \ldots,\ 0.28\end{array}\right)\]  
Therefore, the observed values of \(S_{Ith}^{*}\) for \(h=1\), 2, 3, 4, 5 with sample size \(n=100\) and \(\alpha=0.05\) are expressed as follows:  
\[S_{I10}^{*}=\frac{1-\delta_{10}^{*}}{\gamma_{10}^{*}}=\frac{1-0.35}{0.128}=5. 08,\]  
\[S_{I20}^{*}=\frac{1-\delta_{20}^{*}}{\gamma_{20}^{*}}=\frac{1-0.31}{0.139}=4. 96,\]  
\[S_{I30}^{*}=\frac{1-\delta_{30}^{*}}{\gamma_{30}^{*}}=\frac{1-0.32}{0.135}=5. 04,\]  
Figure 2: Flowchart of the service efficiency evaluation and management model.  
\[S_{I50}^{*}=\frac{1-\delta_{50}^{*}}{\gamma_{50}^{*}}=\frac{1-0.29}{0.139}=5.11.\]  
Then, calculate the \(MV\) as follows:  
\[MV=\sqrt{\frac{100}{\chi_{0.975,99}^{2}}}\times 5-\frac{t_{0.025,99}}{\sqrt{100}}= \sqrt{\frac{100}{128.422}}\times 5-\frac{1.984}{10}=4.214.\]  
Therefore, the statistical hypothesis testing rules are defined as follows:  
1. If \(S_{Ith}^{*}\geq MV\), then do not reject \(H_{0}\) and conclude that \(S_{Ith}\geq k\).
2. If \(S_{Ith}^{*}<MV\), then reject \(H_{0}\) and conclude that \(S_{Ith}<k\).  
As mentioned earlier, this paper will then use the five-axis radar chart with five 72-degree equal angles to evaluate the service operation efficiency of five workstations. First, mark the points located at 4.214 units (\(MV=4.214\)) away from the center of five axes and connect these five points to form a regular pentagon. This paper calls this regular pentagon an evaluation block. Next, the estimated values of the service efficiency indicators for the above-mentioned five workstations are labeled on the five axes, as shown in Figure 3 below:  
According to the above statistical testing rules, the service efficiency of Workstations 1, 2, 3, and 5 all meets the requirement, whereas the service efficiency of Workstation 4 does not meet the requirement, so its improvement is needed. When the service operation efficiency of all workstations meets the requirements, it means that the multi-workstation service operation efficiency has reached the required performance level. Obviously, this method can evaluate the performance of five workstations in the case study at the same time, which is equivalent to grasping the total performance of all workstation systems. Moreover, this method can immediately discover that the performance of Workstation 4 is poor, so it needs to be improved. If only the total performance of the process is evaluated, it is possible that the performance of the other four workstations is relatively good and the poor performance of the Workstation 4 is unnoticed. Thus, the opportunity for improvement will be missed.