## Materials and Methods
### Phase-I: Application of DEA for Risk Calculation and Ranking
Since the same weighting process is applied for all the DMUs, their evaluations can then be made on a comparison basis, with a higher cross-risk score indicating a higher risky DMU. For those DMUS, which have illogical weights in the basic DEA model, a relatively low or higher risk value will be calculated. Therefore, for ranking purpose, this method serves a type of sensitivity analysis by applying a method of a different set of weights to each DMU, with a back channel mechanism of self-generated weights rather than an externally imposed [20]. So the target value, which is a value of 1 to be considered for the best DMU, can now be changed, and after application of CEM it can vary, but the selection of best DMU (with the lowest Risk) will be easier.So after applying model (1) for calculating risk R\({}_{0}\) in road safety field, the lowest level has been considered as the frontier of safety. As explained above, for ranking purposes, a cross risk procedure [20] has been adopted to obtain the best ranking, as shown in Table 3.  
The major advantage of using DEA here is that it can handle multiple inputs and multiple outputs. Moreover, DEA has some benefits as it does not require an assumption of a functional form relating inputs to outputs; DMUs considered in DEA are directly compared against a peer or combination of peers; Inputs and outputs used in DEA can have different measurement units. In this study, number of crashes (NoC) and number of affected persons-injured or killed (NoAP) are considered as two outputs, while exposure variables--average volume to capacity on each segment (V/C), total daily vehicle miles \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Rating DMU** & & & **Rated DMU** & \\ \hline  & 1 & 2 & 3 &...... & \(n\) \\ \hline
1 & \(E_{11}\) & \(E_{12}\) & \(E_{13}\) &...... & \(E_{1n}\) \\
2 & \(E_{21}\) & \(E_{22}\) & \(E_{23}\) &...... & \(E_{2n}\) \. & & & & & & \\ \(n\) & \(E_{n1}\) & \(E_{n2}\) & \(E_{n3}\) &...... & \(E_{nm}\) \\ Mean & \(\overline{E_{1}}\) & \(\overline{E_{2}}\) & \(\overline{E_{3}}\) &...... & \(\overline{E_{n}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A Generalized Cross-Efficiency Matrix (CEM) [20]. travelled on each segment (VMT), and total daily vehicle hours travelled on each segment (VHT)were considered as three inputs. Although the segment length also varied, it was not included here because it was already been involved in the backup calculation of VMT. Based on Model (1), the range of risk value began at 1 and proceeded to a higher value, so a segment with a value of 1 was considered safest, while the road segment with the highest value was considered the most dangerous. Moreover, the cross risk method [20] was used to make all the DMUs comparable. Table 3 presents the results. As the ranking was done on a priority basis to evaluate the safety condition of that segment, the risk value of 91.07 was the highest value in the table and was ranked first (i.e., the most risky segment). The top 10 riskiest segments are shown in Table 3 to explain an idea of risky segment selection for improvement. Furthermore,