## 3 Results and Discussion  
### Judgment Results, Instability Index Method  
The main objectives of this study's analyses were (1) to assess variability in each debris-flow risk factor, (2) calculate the values of prediction for each of the potential debris flows, (3) assign impact weightings in accordance with the magnitude of the variation value, and (4) assign a score value and weights to each risk factor. In addition, the slope instability index \(D_{t}\) (Equation (7)) was presented as a highly flexible mathematical model for statistical measurement. It was computed as follows:  
\[D_{t}=E_{a}^{0.038}\times E_{s}^{0.025}\times E_{sbs}^{0.023}\times E_{sf}^{0.0 03}\times F^{0.013}\times D^{0.009}\times R_{d}^{0.799}\times R_{h}^{0.092}, \tag{8}\]  
where \(E_{sf}\) is the shape coefficient, \(F\) is the distance from a fault, \(E_{a}\) is the total area of the catchment, D is the strata type, \(E_{s}\) is the average slope of the catchment area, \(R_{d}\) is the maximum daily rainfall, \(E_{sbs}\) is the average slope of the stream bed, and \(R_{h}\) is the maximum hourly rainfall.  
The upper- and lower-interval statistical methods were used to classify this study's observations as a means of verifying its debris-flow prediction model's probability of yielding misjudgments. The grading and scoring results of each factor were used as an independent variable matrix and were included in the slope-instability index of Equation (7). The results are displayed in Table 11. Stability index analysis of the model's training sample showed to have an interpretation accuracy rate of 67.8%, and the parallel figure for its validation sample was 78.7%, equating to an overall interpretation accuracy rate of 70.9%.  
By analyzing the landslide potential factor of the Ching-Shuei River using the instability index method, it was found that the advantage of the instability index method was that it could understand the landslide susceptibility zones of the landslide potential factor in detail and assign corresponding scoring values to understand the degree of impact on the catchment area of each grade distance of the collapse potential factor, and its disadvantage lied in that its weighting value was easily affected by the grade distance of the assessment process. The weights of the instability index method were obtained by dividing the standard deviation of each potential factor by the coefficient of variation of the mean. The process of finding the appropriate level of spacing of a potential factor will affect the standard deviation of the factor and the degree of importance of the factor in the subsequent evaluation, and the instability index method utilizes the linear superposition method of calculation [40; 47; 48]. The calculation process amplifies the influence of potential factors with high weighting values and reduces the influence of potential factors with low weighting values [49]. The results are similar to those of past scholars [49; 50; 51; 52].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Classification Result**} \\  & **Category** & **0** & **1** & **Total** \\ \hline Training sample & 0 & 67 (87.0\%) & 10 (13.0\%) & 77 (100\%) \\ (118 rows) & 1 & 28 (68.3\%) & 13 (31.7\%) & 41 (100\%) \\ Accurate discrimination rate = [(67 + 13)/(77 + 41)] \(\times\) 100\% \(\approx\) 67.8\% & \\ Validation & 0 & 34 (87.2\%) & 5 (12.8\%) & 39 (100\%) \\ sample (47 rows) & 1 & 5 (62.5\%) & 3 (37.5\%) & 8 (100\%) \\ Accurate discrimination rate = [(34 + 3)/(39 + 8)] \(\times\) 100\% = 78.7\% & \\ Overall sample & 0 & 101 (87.1\%) & 15 (12.9\%) & 116 (100\%) \\ (165 rows) & 1 & 33 (67.3\%) & 16 (32.7\%) & 49 (100\%) \\ Accurate discrimination rate = [(101 + 16)/(116 + 49)] \(\times\) 100\% = 70.9\% & \\ \hline \hline \end{tabular}
\end{table}
Table 11: Instability index analysis and judgment results.