# Determining the Safety Level of State Roads: An Italian Case Study
## 5 Case Study
### Safety Indicator Evaluation
#### 5.4.3 Safety Performance Indicators  
Once the road layout is divided into elementary sections of 1 km, a set of safety performance indicators is associated with each of them. In particular, the following safety performance indicators are considered:  
* Observed crash frequency [observed crashes/km/year] is calculated as the number of crashes that occurred in one year in each 1-km elementary section. In particular, the annual crashes are calculated as the average of the crashes that occurred during the period under study (from 2015 to 2017). * Observed crash rate [observed crashes/km/year/(_AADT_ 365)-106], calculated by dividing the observed crash frequency for annual traffic and multiplying by 106 to obtain the number of observed crashes per one million vehicle passages. This indicator allows the exposure rate to be considered in terms of traffic volume. * Safety Potential (SAPO) [k/km-year], which quantifies the potential economic benefit that could be achieved in the specific road section due to the reduction of road fatalities and injuries. It is determined according to the Italian guidelines [5], as expressed in Equation (7). \[SAPO=\frac{N_{m}\cdot C_{m}+N_{f}\cdot C_{f}}{L}-(BTCI\cdot 365\cdot AADT)/10 6 \tag{7}\]  
where \(N_{m}\) and \(N_{f}\) are the number of fatalities and injuries, respectively, that occurred in the considered road section, \(L\) is the length of the road section, and \(C_{m}\) and \(C_{f}\) are the average costs associated with each road fatality and road injury, respectively. According to the Italian guidelines [62], the average cost of a road fatality is equal to \(\xi\)1,503,990.00, while the average cost of a single road injury is equal to \(\xi\)42,219.00. Finally, the \(BTCI\) is the base value of accident cost density, equal to \(24\ \xi/(1000\text{-veic}\cdot\text{km})\)[5] suggested for the overall Italian rural roads. It should be noted that this value is determined by the Italian guidelines developed in 2012. In fact, the reference value is quite high and could be updated according to the local context and the decreasing accident trend (as proposed in the following). * Expected crash frequency [expected crashes/km/year] is calculated as the number of expected crashes for one year per 1 km elementary section. * Expected crash rate [expected crashes/km/year/(_AADT_ 365)-106], calculated by dividing the expected crash frequency for annual traffic and multiplying by 106. * Excess of expected crashes over predicted crashes [crashes/year/km], calculated as the difference between the annual expected crashes and the annual predicted crashes, as detailed in Equation (8). \[Excess\ of\ crashes=N_{exp,\ 1\ km}-N_{pred,\ 1\ km} \tag{8}\]  
This indicator allows us to evaluate the safety level of each specific 1-km section with respect to the average safety of similar elementary sections (expressed in terms of predicted crashes). Positive values of this indicator represent a more dangerous section compared to the \"average\", while negative values are associated with less dangerous locations. Basically, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Elementary Sections** & **Length** & \(N_{obs,1\ km}\) & \(N_{pred,1\ km}\) & \(N_{exp,1\ km}\) \\ \cline{2-5}
**(1 km) 1** & **[km]** & **[Crashes/3 Years]** & **[Crashes/3 Years]** & **[Crashes/3 Years]** \\ \hline Minimum & 1 & 0.00 & 0.62 & 0.38 \\ Maximum & 1 & 12.00 & 3.47 & 8.78 \\ Average & 1 & 1.83 & 1.63 & 1.72 \\ Standard deviation & 0 & 2.28 & 0.64 & 1.57 \\ Total & 132 & 241.00 & 214.52 & 226.67 \\ \hline \hline \end{tabular}  
* Minimum, maximum, average, standard deviation, and total values were calculated for 132 elementary sections of 1 km length.  
\end{table} 
Table 7: Summary of empirical-Bayesian analysis results for 1 km elementary sections. the predicted crashes represent the average conditions for the considered road section, taking into account the geometric and traffic conditions. The excess represents the inherent hazard of the site with respect to the average of similar sites.