APPENDIX 10.2 – PROCEDURES AND EXAMPLES

CRASH FREQUENCY

Procedure	Example (see Tables 10.A2 and 10.A3)
Locate all crashes reported during the period of analysis
Define the different reference populations
For each reference population: Calculate the crash frequency at each site Calculate the average crash frequency in the reference population: where: f_rp = average crash frequency f_j = crash frequency at site j of a reference population n = number of sites Determine the minimum crash frequency that warrants a detailed safety analysis (I_T)	Two-lane rural roads Crash frequencies range from 0 to 14 crashes (Column 3 in Table A10.2.2) f_rp = 258 crashes / 55 sites = 4.69 crashes / site I_T = 2 x f_rp = 9.38 (9 crashes) Sections 1,10,12,45 and 52 are detected

CRASH RATE

Procedure	Example (see Tables 10.A2 and 10.A3)
Locate all crashes reported during the period of analysis
Define the different reference populations
For each reference population: Calculate the crash rate at each site: where: R_j = crash rate of site j (crashes/Mveh-km) R_rp = average crash rate (crashes/Mveh-km) f_j = crash frequency at site j P = period of analysis (years) L_j = section’s length of site j (km) Q_j = average annual daily traffic of site j (AADT) Calculate the average crash rate for the reference population: where: R_rp = average crash rate of (crash/Mveh-km) f_j = crash frequency at site j P = period of analysis (years) L_j = section’s length of site j (km) Q_w = weighted average annual daily traffic (AADT) Q_j = AADT of site j Determine the minimum crash rate that warrants a detailed safety analysis (I_T)	Two-lane rural roads For section #1: = 2.72 crashes/ Mveh-km Crash rates range from 0 to 4.73 crashes/Mveh-km (Column 4 in Table A10.2.2) = 1.94 crashes/Mveh-km I_T = 2 x R_rp = 2 x 1.94 = 3.88 crashes/Mveh-km Sections 10, 33, 35 and 39 are detected
Note: for intersections, L is not considered, and critical crash rates are expressed in terms of crashes/Mveh.

CALCULATOR: CRASH RATE

CRITICAL CRASH RATE

Procedure	Example (see Tables 10.A2 and 10.A3)
Locate all crashes reported during the period of analysis
Define the different reference populations
For each reference population: Calculate the crash rate at each site [EQ. 10.8] Calculate the average crash rate for the reference population [EQ. 10.9]	Two-lanes rural roads Column 4 in Table A10.2.2 For section #1: R₁ = 2.72 crashes/Mveh-km R_rp = 1.94 crashes/Mveh-km
Calculate the critical rate at each site: where: R_cj = critical crash rate at site j (crashes/Mveh-km) R_rp = average crash rate at similar sites (crashes/ Mveh-km) K = statistical constant: 1.036 for a level of confidence of 85% 1.282 for a level of confidence of 90% 1.645 for a level of confidence of 95% 2.326 for a level of confidence of 99% P = period of analysis (years) L_j = length of section j (km) Q_j = average annual daily traffic at site j (AADT)	For section #1, with a level of confidence of 85%: = 2.89 crashes/Mveh-km (Column 5 in Table A10.2.2) Critical crash rates range from 2.72 to 5.27 crashes/Mveh-km
Compare the crash rate and critical crash rate at each site. A detailed safety analysis is justified when the crash rate is higher than the critical rate	Sections 10, 35 and 45 are detected (85% level of confidence)
Note: for intersections, L is not considered, and critical crash rates are expressed in terms of crashes/Mveh.

CALCULATOR: CRITICAL CRASH RATE

EPDO

Procedure	Example (see Tables 10.A2 and 10.A3)
Locate all crashes reported during the period of analysis
Define the different reference populations
Select the weighting factors for each trauma category.	The weighting factors proposed by Agent (1973) are used in this example: 1.0 for property damage only crashes (PDO) 3.5 for minor injury crashes 9.5 for serious injury or fatal crashes
For each reference population: Calculate the EPDO index and the average EPDO index (at each site: EPDO_j = [EQ. 10.11] where: EPDO_j = equivalent property damage only index at site j w_i = weighting factor for a crash severity i f_ij = frequency of a severity i crash at site j = EPDO_j / f_j[EQ. 10.12] where: = average EPDO index at site j f_j = total crash frequency at site j Calculate the average in the reference population (EPDO_rp): = [EQ. 10.13] Determine the minimum EPDO value that warrants a detailed safety analysis (I_T)	Two-lane rural roads For section #1: EPDO₁ = 2 x 9.5 + 3 x 3.5 + 4 x 1 = 33.5 Column 6 in Table A10.2.2 EPDO range from 0 to 33.5 = 33.5 / 9 = 3.72 Column 7 in Table A10.2.2 range from 0 to 4.67 = 2.16 I_T = 2 x I_T= 2 x 2.16 = 4.32 Section 33 and 49 are detected

CALCULATOR: EPDO INDEX

RSI

Procedure	Example (see Tables 10.A2 and 10.A3)
Locate all crashes reported during the period of analysis
Define the different reference populations
For each reference population: Calculate the average cost of each crash type in the reference population Calculate the RSI and the average at each site [EQ. 10.14] where: RSI_j = relative severity index at site j f_ij = frequency of a type i crash at site j C_i= average cost of a type i crash [EQ. 10.15] where: f_j = total crash frequency of site j	Two-lane rural roads A cost grid must be developed, based on nationwide data. Values of Table 10.3 are used in this example. For section #1: RSI₁ = (2 x $104,600) + (2 x $173,200) + (1 x $175,900) + (2 x $109,700) + (2 x $341,600) = $1,634,100 = $1,634,100 / 9 = $181,567 Columns 8 and 9 in Table A10.2.2 RSI range from $0 to $2,707,500 range from $0 to $237,200
Calculate the population average RSI () [EQ. 10.16]
Determine the minimum value of RSI that warrants a detailed safety analysis (I_T)	I_T = 2 x = 2 x $162,817 = $325,634 No section is detected by this criterion

COMBINATION OF FREQUENCY AND RATE

Procedure	Example (see Tables 10.A2 and 10.A3)
Locate all crashes reported during the period of analysis
Define the different reference populations
For each reference population: Calculate the crash frequency and crash rate at each site [EQ. 10.8] Calculate the average crash frequency and the average crash rate in the reference population [EQ. 10.7] and [EQ. 10.9] Determine the minimum crash frequency and the minimum crash rate that warrant a detailed safety analysis Rank the sites according to these detection criteria	Two-lane rural roads Columns 3 and 4 in Table A10.2.2 f_rp= 4.69 crashes per site R_rp= 1.94 crashes/Mveh-km Minimum investigation thresholds: 2 x f_rp and 2 x R_rp I_T = 2 x f_rp = 2 x 4.69 = 9.38 crashes I_T = 2 x R_rp = 2 x 1.94 = 3.88 crashes/Mveh-km According to this combination of criteria, section 10 warrants a detailed analysis

BINOMIAL PROPORTION

Procedure	Example
Locate all crashes reported during the period of analysis
Define the different reference populations
For each reference population: Calculate the total crash frequency and the frequency of each type of crash considered, at each site Calculate the proportion of each type of crash considered in the reference population	Two-lane rural roads Surface conditions (reference population and section #45): Of the 12 crashes reported on section #45, 7 have occurred under wet-surface conditions (58%). The equivalent proportion in the reference population is 27%.
Calculate P(Fij ³ fij) based on [EQ. 10.4]	For wet-surface conditions: The probability of observing 0, 1, ...6 wet surface crashes on section #45 and the corresponding cumulative distributions are shown in the table below. The probability of observing 6 or fewer wet-surface crashes is 98%. Consequently, the probability of observing 7 or more crashes is only 2% (i.e. the frequency of wet-surface crashes at the site is abnormally high).

CALCULATOR: BINOMIAL TEST

CRASH PREDICTION MODELS

Procedure	Example (see Tables 10.A2 and 10.A3)
Locate all crashes reported during the period of analysis
Define the different reference populations
For each reference population: Determine the crash frequency and traffic volume at each site. Develop the crash prediction model for the reference population.	Two-lane rural roads Columns 2 and 3 in Table A10.2.2 The following model has been fitted to the 55 sections of this example: f_p = 0.0084 Q^0,76 where: f_p = predicted crash frequency / 3 years Q = average annual daily traffic (AADT)
Calculate the estimated crash frequency at each site using the crash prediction model (f_pj)	For section 1: f_p1 = 0.0084 × 6050^0,76= 6.07 crashes/3 years Column 10 in Table A10.2.2 f_p range from 1.31 to 7.84 crashes/3 years
Calculate the potential for improvement (P.I.) at each site. P.I._j = f_j- f_pj	For section 1: P.I.₁ = 9-6.07 = 2.93 crash/3 years Column 11 in Table A10.2.2 P.I. range from 4.56 to 8.43 crash/3 years
Rank the sites according to their potential for improvement	Sections 10, 45, 1, 36 and 52 have the highest potential for improvement

The following table presents a summary of the results obtained with the numerical example.

It shows that:

Section 10 has been detected by 6 of these 8 identification criteria. Clearly, this section has a safety problem. When the problem is obvious, the choice of the identification criteria has less impact on the selection of sites.
The crash frequency criterion detected mostly those sections with high traffic volumes (with the exception of section 10, every section detected has a daily traffic volume of more than 6,000 vehicles, while the average AADT is 4,400 vehicles). On the other hand, the crash rate criterion detected mostly sections with low traffic volumes (with the exception of section 10, every section detected has a daily traffic volume of fewer than 2,000 vehicles). This is a typical result for these criteria.
Three criteria make direct use of the concept of potential for improvement to rank sections or its derivative: crash frequency, crash prediction model and empirical Bayesian (EB) methods. However, there are differences in the sections identified. Results obtained with the crash prediction model are deemed to be more reliable than those obtained with the crash frequency criterion as the estimate of the average crash frequency (reference population) is more accurate. Similarly, the result obtained using EB methods is seen to be more reliable than those obtained with the prediction model since it also improves the accuracy of the crash frequency at a site.

While definitive conclusions cannot be derived from an example, it nevertheless illustrates how the detection of sites may differ depending on the detection criterion used. For this reason, it is strongly recommended to make use of more than one identification criterion and to compare the obtained results.