The criticality index IC_j is computed for each rural road segment j here considered (i.e., for motorways, national, regional and provincial road in every municipality) and it is a measure of criticality that considers both the absolute width of the danger of the road segment (number of accidents happened in the last available year) and the stability over time of this data (number of accidents happened in the whole period for which accident data is available). It can be described as:

IC_j = I_j(l) * R_j(k), where I_j(l) is the number of accidents happened outside urban areas in the last available year l, R_j(k) is the autocorrelation of the time series of the number of road accidents (in the period from 1991 to l, that is to say 2004 or 2006).

R_j(k) allows evaluating road segments depending upon the persistence over time of road accidents there happened. From the statistic point of view, R_j(k) is defined, for each road segment j, by the ratio between covariance of the time series (in the period 1991-2004, 1991-2006) and the lagged one and the variance.

In formula, R_j(k) = cov(X_j,i, X_j,i+k) / var(X_j) where the lag k is equal to 1, and the variable X_j,i presents the number of accidents happened in the road segment j at time i.

In conclusion, the criticality index, IC_j points out the level of accidents happened in the road segment in the last year, weighted by the persistence over time of such a level.

It is important to underline that the index is not normalised and is bounded to:

• a minimum value equal to 0, in the case of lack of accidents in the last year, or in the case of lack of autocorrelation of the accident time series;

• and a maximum value at a regional level, equal to the highest value of accidents happened in the last year in all road segments of the road network in Piedmont (in the hypothesis of an autocorrelation value of 1).

The index IC_j, allows building a ranking of criticality of road segments in the region, pointing out the cases for which the attention must be focussed on the condition of the network (practicability and signs) and traffic.