## Appendix C The ST Method
### Vector \(z(j,D)\) of Inputs  
Now, going along with Equation (57), the vector \(z(j,D)\) of grading inputs \((z(j)_{L},z(j)_{P},\)\(z(j)_{A})\) becomes\[z(j,D)=(z(j)_{L},z(j)_{P},z(j)_{A})=(7,9,10). \tag{104}\]  
**Appendix C.8**: _Assigning the \(est(j,z,D)\) Grade_  
Then, using Equation (58), the \(est(j,z,D)\) grade directly assigned by the teacher to the \(j\)-th student by relying in the direct ST scheme is  
\[est(j,z,D)=\frac{z(j)_{L}+z(j)_{P}+z(j)_{A}}{TI}=\frac{7+9+10}{45}=\frac{26}{45 }=0.57. \tag{105}\]  
**Appendix C.9**: _Estimating the Absolute Deviation \(\Delta est(j,z,zo,D)\)_  
As stated by Equation (62), we consider an objective performance rate \(est(j,zo,D)\) of \(4/5\). It turns out that, agreeing with Equation (103), we have \(TI=45\); then, to achieve \(est(j,zo,D)=4/5\), a configuration of the vector \(zo(j,D)\) (cf. Equation (61)) that yields \(zo(j)_{L}+zo(j)_{P}+zo(j)_{A}=36\) will suffice. Thus, we could set  
\[zo(j,D)=(11,10,15). \tag{106}\]  
Then, the grade \(est(j,zo,D)\) will indeed be  
\[est(j,zo,D)=\frac{11+10+15}{45}=\frac{36}{45}=0.80 \tag{107}\]  
Therefore, agreeing with Equation (63) and using the values obtained by Equations (105) and (107), the absolute deviation \(\Delta est(j,z,zo)\) becomes  
\[\Delta est(j,z,zo,D)=|est(j,zo,D)-est(j,z,D)|=|0.80-0.57|=0.23 \tag{108}\]  
**Appendix C.10**: _Estimating the Mean Absolute Deviation \(\Delta\overline{est}\left(j,z_{q},zo,D\right)\)_  
We now set a labeling index \(q=2,1,\ldots,\theta(m)\), with \(\theta(m)=100\) aimed to label simulated replicates \(z(q,j)_{L}z(q,j)_{P}\) and \(z(q,j)_{A}\), (cf. Equation (64)). In this way, we obtained the vector \(z_{q}(j,D)\) defined by Equation (65), and we also obtained the simulated grades \(est(j,z_{q},D)\) defined by Equation (66). Additionally, we considered a value for \(\overline{est}(j,zo,D)\) of \(1/2\) to stand for the average value of the \(est(j,zo,D)\) grades assigned through the ST method. This in turn produced absolute deviations \(\Delta est\left(j,z_{q},zo,D\right)\) as specified by Equation (67). Then, the Mean Absolute Deviation \(\Delta\overline{est}\left(j,z_{q},zo,D\right)\) of Equation (68) resulted in  
\[\Delta\overline{est}\left(j,z_{q},zo,D\right)=\frac{\sum_{q=1}^{100}\left|1/2 -est\left(j,z_{q},D\right)\right|}{100}=0.07 \tag{109}\]  
**Appendix C.11**: _Obtaining the Complexity \(CP_{ST}\), Consistency \(CI_{ST}\) and Eficience \(\beta_{ST}\) Indexes Values_  
For this example, we set the numbers of components \(N_{ST}=8\), elements \(E_{ST}=112\) and operations \(Q_{ST}=48\) that the ST method involves (cf. Table 104). The minimum and maximum values for \(N_{M}\), \(E_{M}\) and \(Q_{M}\) entries across the addressed methods in this study are given in Table 2. Then Agreeing to Equations (89) through (91) for the ST method we take Pondered-Normalized indicator values of \(PN(N_{ST})=0.61\), \(PE(E_{ST})=1.0\), and \(PQ(Q_{ST})=0.80\) (cf. Table 3). Also, according to Equation (96) we assign values \(a=0.4\), \(b=0.3\) and \(c=0.3\) (cf. Table 4). reflecting the relative importance of each one of the afore given Pondered-Normalized factors in the determination of \(CP_{ST}\). Then, as stated by Equation (95), we have,