Crash Experience Warrant for Traffic Signals (2014)

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C H A P T E R 4 : S A F E T Y E V A L U A T I O N P R O C E D U R E Safety Evaluation Procedure Introduction This chapter documents the research conducted to develop an intersection safety evaluation procedure. This procedure was developed to facilitate the evaluation of the safety effect of traffic control signal installation at a stop-controlled intersection. The first section describes the development of a procedure for intersection safety evaluation. The second section describes the research conducted to develop the tools needed to implement the procedure. Development of a Safety Evaluation Procedure This section describes the development a safety evaluation procedure. The elements of the procedure were determined from a review of the literature (documented in Chapter 2), the findings from a survey of practitioners (documented in Chapter 3), discussion with the National Committee on Uniform Traffic Control Devices (NCUTCD) Signals Technical Committee, and guidance from the project panel. The procedure is based on that developed by McGee et al. (2003), but it uses the predictive methods described in Part C of the HSM (AASHTO, 2010). The first subsection to follow outlines the approach and scope of the safety evaluation procedure. The second subsection provides an overview of the procedure in terms of its input data requirements and analysis steps. Approach and Scope of Safety Evaluation Procedure The safety evaluation procedure is intended to provide: (1) an estimate of the safety of an existing two- way stop-controlled intersection, and (2) an estimate of the safety of this intersection if a traffic control signal were installed. By comparing these two estimates, some insight is obtained about the effect of the signal installation on traffic safety. The estimates obtained from the procedure were used to determine appropriate criteria for the crash experience warrant. Safety Estimation The predictive methods in the HSM were used as the basis for the safety evaluation procedure. These methods can be used to estimate the average crash frequency of the intersection as one measure of traffic safety. Specific estimates can be obtained for a wide range of configurations, crash severity categories, and crash type categories. Each predictive method includes safety performance functions (SPFs) and crash modification factors (CMFs). The CMFs can be used to refine the estimate based on consideration of geometric elements and traffic control features that have a quantified effect on safety. A second measure of traffic safety is the road-user crash cost. This cost is computed by summing the product of average crash frequency and average cost per crash for each crash-type and severity category. In this regard, it is recognized that a location with several severe crashes is considered less safe than a location with an equal number of crashes but none of which are severe. 37

Crash Categories Several safety performance measures are obtained through application of the procedure. Specifically, estimates of average crash frequency are obtained for two crash severity categories and three crash type categories. The severity categories are defined to include fatal-and-injury (FI) and property-damage-only (PDO) crashes. Injury crashes include all crashes with an incapacitating injury, non-incapacitating injury, or possible injury. This sensitivity to crash severity recognizes that a traffic control signal installation can cause a shift in the crash severity distribution (i.e., an increase in the percentage of PDO crashes). The need for this sensitivity was identified in the survey of practitioners and in discussions with the NCUTCD Signals Technical Committee. It is difficult to develop statistically valid models for predicting fatal or incapacitating injury crash frequency because of the relative rarity of these crashes. However, reliable models have been developed to predict the combined frequency of FI crashes. In fact, Chapter 12 of the HSM includes separate models for predicting FI crash frequency and PDO crash frequency for urban intersections (AASHTO, 2010). The crash type categories typically influenced by signal installation include angle crashes and rear-end crashes. All other crash types are considered to be “other crashes.” This category includes all intersection- related crashes that are not angle or rear-end crashes. These crashes can be categorized as single-vehicle crashes or multiple-vehicle crashes. Single-vehicle crashes can involve a vehicle and a pedestrian, or a vehicle and a bicyclist. Angle crashes involve all crashes that occur at an angle and involve one or more vehicles on the major road and one or more vehicles on the minor road. These three crash type categories are recognized in Part C of the HSM. They are also the categories recommended by McGee et al. (2003) for evaluating the safety effect of signal installation. The procedure’s sensitivity to crash type category recognizes that a traffic control signal installation can cause a shift in the crash type distribution. This tendency is acknowledged in the MUTCD, which indicates that only some crash types are susceptible to correction by signal installation. The literature review indicated that angle crashes and rear-end crashes are the most common crash types to show a change in distribution proportions with the installation of a signal. The proportion of left-turn-opposed crashes may also change if a left-turn phase is included in the signal installation. However, left-turn-opposed crashes tend to be reported differently among agencies, and are difficult for enforcement officers to identify in the field (McGee et al., 2003). Also, the HSM predictive methods do not specifically address left-turn-opposed crashes. For these reasons, the procedure does not explicitly address left-turn-opposed crashes. Crash Severity Index The procedure described in NCHRP Report 491 includes consideration of crash cost. Crash cost is also included in the procedure was documented in Appendix B of NCHRP Report 617 (Harkey et al., 2008). The consideration of crash cost recognizes (1) that signal installation tends to influence the crash type and crash severity distributions, and (2) there are significant differences in severity associated with typical rear-end and angle crashes. The crash costs that Harkey et al. used in their analysis are summarized in the top half of Table 9 (i.e., in the rows associated with a rural area type). The crash costs shown in Table 9 were developed by Council et al. (2005). They represent “comprehensive” costs because they include human capital costs associated with a crash (i.e., medical cost, emergency services costs, property damage costs, and lost productivity costs) plus a monetary estimate of the reduced quality of life suffered by the victim and his or her family. If a crash cost is available for each K, A, B, C, and PDO severity category, then the costs associated with FI crashes can be computed as a weighted average of the cost for the K, A, B, and C categories, where the weight used is the proportion of crashes associated with each category. 38

Table 9. Unit crash costs. Area Type Control Type Severity Level Crash Cost by Crash Type1, dollars Angle Rear End Rural (speed limit of 50 mi/h or more) Signal Fatal or injury 126,878 52,276 Property damage only 8,544 5,901 Stop Fatal or injury 199,788 34,563 Property damage only 5,444 3,788 Urban (speed limit of 45 mi/h or less) Signal Fatal or injury 64,468 44,687 Property damage only 8,673 11,463 Stop Fatal or injury 80,956 56,093 Property damage only 7,910 12,295 Note: 1 – Source: Council et al. (2005). Costs are in 2001 dollars. The conversion of crash frequency to annual crash cost was viewed by Harkey et al. (2008) as a rational and effective method for comprehensively assessing the effect of signal installation on safety. With this approach, the estimated crash frequency associated with each crash type and severity category for the two-way stop-controlled intersection is converted into an annual crash cost. The estimated crash frequency for the proposed signalized intersection is converted in a similar manner. The difference in the annual crash costs for the existing and proposed intersections represents a single-valued indication of the change in safety associated with the signal installation. The conversion of crash frequency into cost has some negative perception issues because it monetizes the value of human life. Nevertheless, it has been a viable basis for making investment decisions, and it is often an important component of engineering alternative analysis. Moreover, when it is used solely to provide a single-valued indication of a change in safety, the computed cost can be converted into a severity index value by dividing the cost by a constant and dropping the units of dollars from the resultant quantity. This unit-less severity index provides the same relative information as crash cost but without conveying the value placed on life and limb. After conversion to signal control, an intersection can have an average crash frequency that is larger than that of the stop-controlled intersection prior to conversion, even with no change in traffic volume. This result can occur when the increase rear-end crashes exceeds the decrease in angle crashes associated with signal installation. However, the converted intersection may still be associated with a lower annual crash cost because rear-end crashes tend to have a lower severity and cost than angle crashes. In this regard, the conversion to signal control is still considered to have improved the safety of the intersection. Procedure Scope The safety evaluation procedure was developed to have a broad scope in terms of the types of intersection configurations that can be evaluated and the types of crashes considered. A broad scope was needed to ensure that the proposed crash experience warrant is applicable to most intersections. Table 10 identifies the scope elements. 39

Table 10. Scope elements for the safety evaluation procedure. Element Conditions Control types Two-way stop control converted to signal control Area type Urban, rural Major road through lanes 2, 4 Intersection legs (and travel directions) 3, 4 (each leg serves two-way traffic) Crash severity categories Fatal-and-injury (FI), property damage only (PDO) Crash type categories Angle, rear-end, other Several of the scope elements are dictated by the capabilities of the HSM predictive methods. Notably, the number of through lanes on the major road is currently limited to a maximum of four by the HSM. The geometry of the intersections considered is limited to three- and four-leg intersections where each intersection leg serves two-way traffic. This limitation is dictated by the HSM. It is primarily a concern for streets in downtown areas and at freeway interchanges. Intersections in these areas often include one or more legs that have one-way traffic flow. These configurations have a unique set of conflicting movements and conflict points that justify the development of separate SPFs (and possibly complete predictive methods). Application Overview This subsection provides an overview of the safety evaluation procedure’s application. Initially, data required to apply the procedure are summarized. Then, the six analysis steps associated with the procedure are outlined. Data Required to Apply Procedure The procedure will require several types of input data. These data are described in the following paragraphs. The data are categorized as “minimum” and “desirable.” The minimum input data represents the essential data elements needed to conduct the safety evaluation. The desirable input data will require additional effort to acquire but, if used, should provide a more reliable estimate of the expected change in crash frequency due to signal installation. Minimum Input Data • Number of intersection legs. • Number of through lanes on the major road. • Annual Average Daily Traffic (AADT) volume for the major street for a specified analysis year. • AADT volume for the minor street for same year as used to define the major-street AADT. • Number of approaches with a left-turn lane (or bay). • Number of approaches with a right-turn lane (or bay). • Presence of intersection lighting. • Presence of left-turn phasing (only for urban signalized intersection). • Use of right-turn-on-red signal operation (only for urban signalized intersection). • Use of red-light-camera enforcement (only for urban signalized intersection). Desirable Input Data The data described in the following list are needed along with that identified as Minimum Input Data. 40

• Crash history – count of crashes occurring at, or related to, the intersection during each year of the most recent two- to five-years. Categorized as FI or PDO, and as angle, rear-end, or other type. • AADT volume for the major street for each year represented in the crash history. • AADT volume for the minor street for each year represented in the crash history. • Estimate of AADT volume for the major street that would prevail immediately after signal installation. • Estimate of AADT volume for the minor street that would prevail immediately after signal installation. • Local calibration factor for each predictive method. • Intersection skew angle (if in a rural area; not needed if in an urban area). • Pedestrian volume data (only for urban signalized intersection). • Number of lanes crossed by a pedestrian (only for urban signalized intersections). • Number of bus stops near the intersection (only for urban signalized intersections). • Presence of a public school near the intersection (only for urban signalized intersections). • Number of alcohol sales establishments near the intersection (only for urban signalized intersections). Guidance The crash history data must represent crashes that occur at the intersection, or are considered to be related to the intersection’s presence. The crashes will need to be categorized as rear-end, angle, or “other.” Angle crashes were defined previously in the subsection titled Crash Categories. These crash type categories are dictated by the crash types recognized in Part C of the HSM. Crash data are considered to be “desirable,” and not a minimum requirement. If they are provided, then the EB method can be used in the predictive method to obtain a more reliable estimate of the average crash frequency. There should be no changes in the geometry of, or traffic control features at, the subject intersection during the time period represented by the input data. This period should extend backward in time from the most recent year to the last year for which it is known that no changes occurred. The time period should not exceed five years. If the AADT volume is available for one or more years, but it is not available for all years, then it can be estimated for the missing years using the available AADT and judgment regarding annual changes in traffic volume at nearby intersections. Part C of the HSM provides rules for estimating AADT for those years for which it is not available. After the signal is installed, the major-street and minor-street AADTs at the intersection may increase more rapidly than can be explained by historic increases in traffic volume, possibly due to the signal’s more attractive operation and safety benefits. Desirably, the analyst will estimate these two AADTs using (1) traffic forecasts or (2) available AADTs and adjustment factors obtained from the AADTs of other intersections at which a signal was installed. If the Minimum Input Data approach is used, then the estimate of AADT that would prevail after signal installation can be assumed to equal the AADT associated with the most recent year for which crash data are available. Local calibration factors are used with each predictive method to ensure that the predicted crash frequency is representative of intersections in the jurisdiction within which the subject intersection is located. A procedure for computing this factor is described in Appendix A to Part C of the HSM. If this factor is not used, then the implication is that the estimated crash frequencies are representative of the intersections in the jurisdiction without further re-calibration. The last six items in the list of Minimum Input Data represent data used to define various CMFs that are included in a predictive method. Their inclusion in this list is consistent with guidance in Appendix A to Part C of the HSM. The use of these CMFs will improve the accuracy of the predicted crash frequency. 41

Procedure Steps Step 1. Assemble Input Data and Models. Determine whether the desirable input data are available. If they are available, obtain them. Otherwise, obtain the minimum input data. Obtain the necessary SPF coefficients and CMF values from the appropriate HSM Part C chapter for the existing intersection, and for the proposed signalized intersection. Step 2. Estimate the Average Crash Frequency for the Existing Intersection. Use the SPFs and CMFs corresponding to the existing intersection to compute the predicted average crash frequency for the average stop-controlled intersection that is otherwise similar to the existing intersection. If crash data are provided, use the SPFs and CMFs with the EB Method (described in Part C of the HSM) to compute the expected average crash frequency for the existing intersection. One estimate of the average crash frequency (and its variance) is obtained for each of the following categories: FI angle crashes, FI rear-end crashes, FI other crashes, PDO angle crashes, PDO rear-end crashes, and PDO other crashes. Add all of these values to obtain an estimate of the total average crash frequency. Compute the crash severity index for the existing intersection using the average crash frequency estimates and their corresponding crash costs. One index estimate (and its variance) is obtained for each of the aforementioned six categories. Add all of these values to obtain an estimate of the total severity index. Step 3. Estimate the Average Crash Frequency for the Intersection if a Signal was Installed. Use the SPFs and CMFs corresponding to the signalized intersection to compute the predicted average crash frequency for the average signalized intersection that is otherwise similar to the existing intersection. One estimate of the average crash frequency (and its variance) is obtained for each of the following categories: FI angle crashes, FI rear-end crashes, FI other crashes, PDO angle crashes, PDO rear-end crashes, and PDO other crashes. Add all of these values to obtain an estimate of the total average crash frequency. Compute the crash severity index for the signalized intersection using the average crash frequency estimates and their corresponding crash costs. One index estimate (and its variance) is obtained for each of the aforementioned six categories. Add all of these values to obtain an estimate of the total severity index. Step 4. Determine if there is a Significant Change in Crash Frequency due to Signal Installation. Using the total average crash frequency estimates from Steps 2 and 3, compute the change in total average crash frequency (i.e., average crash frequency change = estimated crash frequency from Step 3 – estimated crash frequency from Step 2). Compute the variance of the change in total average crash frequency (i.e., variance of change = variance from Step 3 + variance from Step 2). Compare the change in total average crash frequency with the variance of this change to determine if the result is significantly significant. The statistical significance of the change in average crash frequency is determined by dividing it by the square root of the corresponding variance. The hypothesis in this test is that there is no change in safety. Hence, it is a two-tail test such that the absolute value of the computed ratio would need to exceed 1.64 (corresponding to a 0.10 significance level) to reject the hypothesis. If there is a statistically significant change in the total average crash frequency, then the signal installation is very likely to have an effect on traffic safety. If the computed change is negative, then the signal installation is likely to improve safety. If the computed change is positive, then the signal installation is likely to degrade safety. 42

Note that if additional years of crash data are used with the EB method in Step 2, then the variance of the expected average crash frequency may be reduced, and a statistically significant result may be obtained. Step 5. Determine if there is a Net Safety Benefit Associated with the Signal Installation. The total severity indices from Steps 2 and 3 are used in this step to determine if there is a net safety benefit associated with the signal indication. Using the total severity index estimates from Steps 2 and 3, compute the change in the total severity index (i.e., index change = index from Step 3 – index from Step 2). Compute the variance of the total severity index change (i.e., variance of change = variance from Step 3 + variance from Step 2). Compare the index change with the variance of this change to determine if the result is significantly significant. The statistical significance of the index change is determined by dividing it by the square root of the corresponding variance. The hypothesis in this test is that there is no change in safety. Hence, it is a two-tail test such that the absolute value of the computed ratio would need to exceed 1.64 (corresponding to a 0.10 significance level) to reject the hypothesis. If there is a statistically significant change in the total severity index, then the signal installation is very likely to have an effect on traffic safety. If the computed index change is negative, then the signal installation is likely to provide a net safety benefit. If the computed index is positive, then the signal installation is likely to cause a net safety dis-benefit. If neither the change in total average crash frequency nor the change in total severity index is statistically significant, then the safety effect of signalization is not known with sufficient degree of certainty to be the sole basis for the decision to install a signal. In this case, other factors and signal impacts (e.g., operations) will need to be evaluated to determine if signal installation is justified. Development of Selected Models and Parameters This section describes the research that was conducted to develop the necessary tools to support the safety evaluation procedure. Research was conducted on three topics to develop these tools. The findings for each research topic are documented in a separate subsection. The first subsection describes the development of a predictive model for selected crash type and severity categories. The second subsection describes the development of an overdispersion parameter for each predictive model. The third subsection describes the estimation of crash cost for selected crash type and severity categories. Development of Crash-Category-Specific SPFs The safety evaluation procedure is intended to provide an important sensitivity to angle and rear-end crash types. This sensitivity is needed to evaluate the effect of signalization because angle and rear-end crash frequency tends to be notably influenced by the presence (or absence) of a traffic control signal. For the same reason, the procedure is intended to provide an important sensitivity to crash severity. In addition, the procedure is intended to support the use of the EB Method for the existing stop-controlled intersection. For the aforementioned reasons, a predictive model is needed for each combination of area type, number of legs, control type, crash type category, and crash severity category of interest. The crash type and severity categories of interest include: FI angle crashes, FI rear-end crashes, PDO angle crashes, and PDO rear-end crashes. However, none of the predictive models in the HSM are specific to the desired combinations of crash type or severity categories (AASHTO, 2010). To meet the aforementioned need, the HSM predictive models were disaggregated into separate “equivalent” predictive models for each combination of crash type category (angle or rear end) and crash severity category (FI or PDO). The disaggregated methods are shown as Equation 1 to Equation 6. 43

( ) CCMFCMFCMFNN nangfispfangfip ×××××= 21,,,, ( ) CCMFCMFCMFNN nrefispfrefip ×××××= 21,,,, ( ) CCMFCMFCMFNN notherfispfotherfip ×××××= 21,,,, ( ) CCMFCMFCMFNN nangpdospfangpdop ×××××= 21,,,, ( ) CCMFCMFCMFNN nrepdospfrepdop ×××××= 21,,,, ( ) CCMFCMFCMFNN notherpdospfotherpdop ×××××= 21,,,, otherpdoprepdopangpdopotherfiprefipangfiptp NNNNNNN ,,,,,,,,,,,,, +++++= ( )angfiangfi paA ,, ln+= ( ) ( )[ ]min,,, lnlnexp AADTcAADTbAN majangfiangfispf ×+×+= Equation 1 Equation 2 Equation 3 Equation 4 Equation 5 Equation 6 where, Np,fi,ang = predicted average FI angle crash frequency, crashes/yr; Np,fi,re = predicted average FI rear-end crash frequency, crashes/yr; Np,fi,other = predicted average FI other crash frequency, crashes/yr; Np,pdo,ang = predicted average PDO angle crash frequency, crashes/yr; Np,pdo,re = predicted average PDO rear-end crash frequency, crashes/yr; Np,pdo,other = predicted average PDO other crash frequency, crashes/yr; Nspf,fi,ang = predicted average FI angle crash frequency for base conditions, crashes/yr; Nspf,fi,re = predicted average FI rear-end crash frequency for base conditions, crashes/yr; Nspf,fi,other = predicted average FI other crash frequency for base conditions, crashes/yr; Nspf,pdo,ang = predicted average PDO angle crash frequency for base conditions, crashes/yr; Nspf,pdo,re = predicted average PDO rear-end crash frequency for base conditions, crashes/yr; Nspf,pdo,other = predicted average PDO other crash frequency for base conditions, crashes/yr; CMFi = crash modification factor i; and C = calibration factor. The aggregation of the individual methods (to predict total average crash frequency) is described by the following equation: Equation 7 where, Np,t = total predicted average crash frequency, crashes/yr. The safety performance function (SPF) in Equation 1 is computed using Equation 8. Its coefficient “A” is computed from the regression coefficient a and the appropriate proportion p using Equation 9. Equation 8 with Equation 9 where, a, b, c = regression coefficients (provided in the HSM); AADTmaj = average daily traffic volume for the major road, veh/day; AADTmin = average daily traffic volume for the minor road, veh/day; pfi,ang = proportion of FI angle crashes; Afi,ang = equivalent regression coefficient for the FI angle crash SPF. 44

The coefficient a and the proportion p are obtained from the HSM. A variation of Equation 8 and Equation 9 can be used to obtain the SPFs used in Equation 2 to Equation 6; however, these SPFs are not shown herein. The regression coefficients for each SPF are listed in Table 11, Table 12, and Table 13 for the FI SPFs for rural three-leg intersections, rural four-leg intersections, and urban intersections, respectively. The values for coefficient A are computed using Equation 9 when appropriate. Where the calculation of A is not shown in the table, then the HSM SPF is directly applicable and the coefficient a from the HSM can be substituted for A in the SPF. In all cases, the coefficients b and c are taken directly from the HSM. Table 11. Coefficients for SPFs that predict FI crash frequency at rural three-leg intersections. Area Type Number of Legs Control Type Major- Road Lanes Crash Type Coefficient Values1 Rural 3 Stop control on minor road 2 All types A = -9.86 + ln(Pfi) = -10.739; Pfi = 0.415 b = 0.790 c = 0.490 Angle A = -9.86 + ln(Pfi) + ln(Pang) = -12.030; Pfi = 0.415; Pang = 0.275 b = 0.790 c = 0.490 Rear-end A = -9.86 + ln(Pfi) + ln(Pre) = -12.087; Pfi = 0.415; Pre = 0.260 b = 0.790 c = 0.490 4 All types a = -12.664 b = 1.107 c = 0.272 Angle A = -12.664 + ln(Pang) = -13.661; Pang = 0.369 b = 1.107 c = 0.272 Rear-end A = -12.664 + ln(Pre) = -14.062; Pre = 0.247 b = 1.107 c = 0.272 Signal 2 not available 4 not available Note: 1 – Variable definitions: Pfi = proportion FI crashes; Pang = proportion angle FI crashes; Pre = proportion rear-end FI crashes. Proportions obtained from HSM Tables 10-5, 10-6, and 11-9. The SPFs provided in the HSM Chapter 12 for urban intersections are specific to either multiple- vehicle crashes or to single-vehicle crashes. SPFs for predicting total (all types) crashes are not available in Chapter 12. The HSM advises that total crashes are computed by adding the predicted multiple-vehicle crash frequency and single-vehicle crash frequency. 45

Table 12. Coefficients for SPFs that predict FI crash frequency at rural four-leg intersections. Area Type Number of Legs Control Type Major- Road Lanes Crash Type Coefficient Values1 4 Stop control on minor road 2 All types A = -8.56 + ln(Pfi) = -9.402; Pfi = 0.431 b = 0.600 c = 0.610 Angle A = -8.56 + ln(Pfi) + ln(Pang) = -10.033; Pfi = 0.431; Pang = 0.532 b = 0.600 c = 0.610 Rear-end A = -8.56 + ln(Pfi) + ln(Pre) = -10.962; Pfi = 0.431; Pre = 0.210 b = 0.600 c = 0.610 4 All types a = -11.554 b = 0.888 c = 0.525 Angle A = -11.554 + ln(Pang) = -12.181; Pang = 0.534 b = 0.888 c = 0.525 Rear-end A = -11.554 + ln(Pre) = -13.100; Pre = 0.213 b = 0.888 c = 0.525 Signal 2 All types A = -5.13 + ln(Pfi) = -6.209; Pfi = 0.340 b = 0.600 c = 0.200 Angle A = -5.13 + ln(Pfi) + ln(Pang) = -7.299; Pfi = 0.340; Pang = 0.336 b = 0.600 c = 0.200 Rear-end A = -5.13 + ln(Pfi) + ln(Pre) = -7.118; Pfi = 0.340; Pre = 0.403 b = 0.600 c = 0.200 4 All types a = -6.393 b = 0.638 c = 0.232 Angle A = -6.393 + ln(Pang) = -7.548; Pang = 0.315 b = 0.638 c = 0.232 Rear-end A = -6.393 + ln(Pre) = -7.144; Pre = 0.472 b = 0.638 c = 0.232 Notes: 1 – Variable definitions: Pfi = proportion FI crashes; Pang = proportion angle FI crashes; Pre = proportion rear-end FI crashes. Proportions obtained from HSM Tables 10-5, 10-6, and 11-9. 46

Table 13. Coefficients for SPFs that predict FI crash frequency at urban intersections. Area Type Number of Legs Control Type Major- Road Lanes Crash Type Coefficient Values1 Urban 3 Stop control on minor street 2 or 4 All types a = -14.010; b = 1.160; c = 0.300; w = 1.000 x = -6.81 + ln(Pfi) + 14.010 = 6.064; Pfi = 0.321 y = 0.160 – 1.160 = -1.000 z = 0.510 – 0.300 = 0.210 Angle A = -14.010 + ln(Pang) = -15.080; Pang = 0.343 b = 1.160 c = 0.300 Rear-end A = -14.010 + ln(Pre) = -14.875; Pre = 0.421 b = 1.160 c = 0.300 Signal 2 or 4 All types a = -11.580; b = 1.020; c = 0.170; w = 1.000 x = -9.750 + 11.580 = 1.830 y = 0.270 – 1.020 = -0.750 z = 0.510 – 0.170 = 0.340 Angle A = -11.580 + ln(Pang) = -12.853; Pang = 0.280 b = 1.020 c = 0.170 Rear-end A = -11.580 + ln(Pre) = -12.180; Pre = 0.549 b = 1.020 c = 0.170 4 Stop control on minor street 2 or 4 All types a = -11.130; b = 0.930; c = 0.280; w = 1.000 x = -5.33 + ln(Pfi) + 11.130 = 4.866; Pfi = 0.393 y = 0.330 – 0.930 = -0.600 z = 0.120 – 0.280 = -0.160 Angle A = -11.130 + ln(Pang) = -11.951; Pang = 0.440 b = 0.930 c = 0.280 Rear-end A = -11.130 + ln(Pre) = -12.215; Pre = 0.338 b = 0.930 c = 0.280 Signal 2 or 4 All types a = -13.140; b = 1.180; c = 0.220; w = 1.000 x = -9.25 + 13.140 = 3.890 y = 0.430 – 1.180 = -0.750 z = 0.290 – 0.220 = 0.070 Angle A = -13.140 + ln(Pang) = -14.198; Pang = 0.347 b = 1.18 c = 0.220 Rear-end A = -13.140 + ln(Pre) = -13.939; Pang = 0.450 b = 1.18 c = 0.220 Notes: 1 – Variable definitions: Pfi = proportion FI crashes; Pang = proportion angle FI crashes; Pre = proportion rear-end FI crashes. Proportions for angle and rear-end crashes obtained from HSM Table 12-11. 47

( ) ( )[ ]min, lnlnexp0.1 AADTzAADTyxwF fimajfififific ×+×+×+= mvfisvfifi aax ,, −= mvfisvfifi bby ,, −= mvfisvfifi ccz ,, −= mvfi svfi fi C C w , ,= ( ) ( )[ ] mvfificmvfimajmvfimvfifispf CFAADTcAADTbaN ,,min,,,, lnlnexp ×××+×+= A generalized version of Equation 8 was developed to describe a single SPF for urban intersections that predicts same total crash frequency as would be obtained by adding the results from the multiple-vehicle and single-vehicle SPFs. The form of this generalized equation is shown in Equation 10. Equation 10 with Equation 11 Equation 12 Equation 13 Equation 14 Equation 15 where, afi,mv, bfi,mv, cfi,mv = regression coefficients for FI multiple-vehicle crashes; afi,sv, bfi,sv, cfi,sv = regression coefficients for FI single-vehicle crashes; wfi, xfi, yfi, zfi = computed coefficients for FI crashes; Fc, fi = correction factor for FI crashes; Cfi,mv = calibration factor FI multiple-vehicle crashes; and Cfi,sv = calibration factor FI single-vehicle crashes. The SPFs provided in HSM Chapter 11 for multilane rural highway intersections are specific to total (all severities) and to FI crashes. SPFs for predicting PDO crashes are not available in Chapter 11. The HSM advises that PDO crashes are computed by subtracting the predicted FI crash frequency from the predicted total (all severities) crash frequency. This guidance was used to derive an equivalent SPF for PDO crashes using Equation 10, with the reported FI and total-crash SPF coefficients in Equation 11 to Equation 15. Chapter 12 of the HSM does not provide SPF coefficients for FI single-vehicle crashes at three-leg and at four-leg stop controlled intersections. The HSM offers Equation 12-27 as an alternative means for estimating the average crash frequency for these two intersection types. Equation 12-27 is equivalent to Equation 8. The HSM indicates the proportion used for predicting FI single-vehicle crashes at three-leg and four-leg intersections is 0.31 and 0.28, respectively. These proportions are not in agreement with the corresponding proportions published in the final report for Project 17-26 (Harwood et al. 2007; Table 57). As a result, the SPFs for PDO and total single-vehicle crashes published in Chapter 12 of the HSM were used, with the average AADT values published by Harwood et al. (2007; Table 23), to estimate the desired proportions. The computed proportions for FI single-vehicle crashes at three-leg and four-leg intersections are 0.321 and 0.393, which are similar to those published by Harwood et al. (2007; Table 57). These proportions are used in Table 13 to estimate the desired coefficients for the total crash SPFs. The process used to develop the coefficients in the previous three tables was used to estimate the PDO coefficients. These coefficients are listed in Table 14. 48

Table 14. Coefficients for SPFs that predict PDO crash frequency. Area Type Number of Legs Control Type Major -Road Lanes Crash Type Coefficients A b c w x y z Rural 3 Stop control on minor road 2 All types -10.396 0.790 0.490 Angle -11.957 0.790 0.490 Rear-end -11.627 0.790 0.490 4 All types -12.526 1.204 0.236 -1.0 -0.138 -0.097 0.036 Angle -14.692 1.204 0.236 Rear-end -14.228 1.204 0.236 Signal 2 not available 4 not available 4 Stop control on minor road 2 All types -9.124 0.600 0.610 Angle -10.162 0.600 0.610 Rear-end -10.448 0.600 0.610 4 All types -10.008 0.848 0.448 -1.0 -1.546 0.040 0.077 Angle -11.930 0.848 0.448 Rear-end -12.126 0.848 0.448 Signal 2 All types -5.546 0.600 0.200 Angle -6.964 0.600 0.200 Rear-end -6.371 0.600 0.200 4 All types -7.182 0.722 0.337 -1.0 0.789 -0.084 -0.105 Angle -9.212 0.722 0.337 Rear-end -8.358 0.722 0.337 Urban 3 Stop control on minor street 2 or 4 All types -15.380 1.200 0.510 1.00 7.020 -0.950 0.040 Angle -16.719 1.200 0.510 Rear-end -16.201 1.200 0.510 Signal 2 or 4 All types -13.240 1.140 0.300 1.00 4.160 -0.690 0.030 Angle -14.830 1.140 0.300 Rear-end -13.845 1.140 0.300 4 Stop control on minor street 2 or 4 All types -8.740 0.770 0.230 1.00 1.700 -0.410 0.020 Angle -9.834 0.770 0.230 Rear-end -9.723 0.770 0.230 Signal 2 or 4 All types -11.020 1.020 0.240 1.00 -0.320 -0.240 0.010 Angle -12.431 1.020 0.240 Rear-end -11.748 1.020 0.240 Development of Estimated Overdispersion Parameters The safety evaluation procedure is intended to support the use of the EB Method for estimating the expected average crash frequency for the existing stop-controlled intersection. For these reasons, an overdispersion parameter is needed for each of the SPFs identified in Table 11 to Table 14. Unfortunately, the parameter is not available for the SPFs in these tables with derived coefficients. This section describes the techniques used to estimate the overdispersion parameter for each SPF with derived coefficients. The first subsection describes an analysis of the overdispersion parameters associated with FI, PDO and total (all severities) crash SPFs. The second subsection describes an analysis of the overdispersion parameters associated with angle, rear-end, and total (all types) crash SPFs. The third section describes the recommended overdispersion parameters that are derived using the findings documented in the previous two subsections. 49

[ ] ( )2,, tpttp NkNV ×= Analysis of Parameters Describing FI and PDO Crash Frequency This subsection describes an analysis of the parameters associated with a series of SPFs calibrated by Harwood et al., 2007. They calibrated one set of SPFs for intersections in Minnesota, and a second set for intersections in North Carolina. For multiple-vehicle crash SPFs, they reported dispersion parameters for FI, PDO, and total (all severities) crashes as well as the proportion of FI and PDO crashes. They reported the same statistics for single-vehicle crash SPFs. These values are shown in Table 15. Table 15. Overdispersion parameters for FI, PDO, and total crash SPFs. State Crash Type Variable Crash Severity Variable Value by Control Type and Legs Stop on Minor Road Signal 3 Legs 4 Legs 3 Legs 4 Legs Minnesota Multiple- vehicle Overdispersi on parameter All 1.10 0.20 0.41 0.51 FI 0.85 0.17 0.26 0.36 PDO 1.26 0.29 0.46 0.55 Proportion of all crashes FI 0.350 0.352 0.372 0.329 PDO 0.650 0.648 0.628 0.671 Single- vehicle Overdispersi on parameter All n.a. 0.31 0.18 0.30 FI n.a. 0.15 n.a. 0.09 PDO n.a. 0.14 0.42 0.28 Proportion of all crashes FI 0.368 0.420 0.391 0.248 PDO 0.632 0.580 0.609 0.752 North Carolina Multiple- vehicle Overdispersi on parameter All 0.51 0.66 0.87 0.69 FI 0.55 0.79 0.67 0.46 PDO 0.47 0.51 0.77 0.60 Proportion of all crashes FI 0.369 0.415 0.342 0.336 PDO 0.631 0.585 0.658 0.664 Single- vehicle Overdispersi on parameter All 1.11 n.a. 0.53 0.11 FI n.a. n.a. 0.64 0.03 PDO 0.93 0.49 0.57 0.21 Proportion of all crashes FI 0.304 0.365 0.227 0.241 PDO 0.696 0.635 0.773 0.759 Note: n.a. – not available. The overdispersion parameter is used to quantify the variation among intersections in terms of their average crash frequency. This variation is quantified using the following equation. Equation 16 where, V[Np,t] = variance of total predicted average crash frequency among intersections, (crashes/yr)2; and kt = overdispersion parameter for total crash frequency. Consider a group of similar intersections for which the crash history is known. An SPF can be developed to predict total average crash frequency for this group. Similarly, an SPF can be developed to predict FI average crash frequency, and an SPF can be developed to predict PDO average crash 50

[ ] [ ] [ ] [ ] [ ]( ) 5.0,,,,, 2 pdopfippdopfiptp NVNVNVNVNV ρ++= frequency. The following relationship will hold between the variance of the predicted average crash frequencies. Equation 17 where, V[Np,fi] = variance of predicted FI average crash frequency among intersections, (crashes/yr)2; V[Np,pdo] = variance of predicted PDO average crash frequency among intersections, (crashes/yr)2; and ρ = correlation coefficient. Substitution of Equation 16 into Equation 17 yields the following relationship between the overdispersion parameters. Equation 18 where, kfi = overdispersion parameter for FI crash frequency; and kpdo = overdispersion parameter for PDO crash frequency. A similar equation can be produced for the crash type categories of interest (i.e., angle, rear-end, other). These equations can be used with the overdispersion parameters in the HSM to estimate the overdispersion parameters for the desired crash-category-specific SPFs. Equation 18 reduces to Equation 19 when the correlation coefficient ρ equals 0.0. Equation 19 where, pfi = proportion FI crashes; and ppdo = proportion PDO crashes (= 1.0 − pfi). The following variation of Equation 19 was used to develop an equation for predicting the reported overdispersion parameter for total crash frequency. The coefficient b1 is included in the equation to compensate for the assumption that the correlation coefficient equals 0.0. Equation 20 where, b1 = regression coefficient. A regression analysis using the data in Table 15 indicated that the best-fit model has a coefficient b1 equal to 1.84. It is associated with a coefficient of determination R2 of 0.87. The fit of the model to the data is shown in Figure 8. A supplemental analysis examined the correlation between the overdispersion parameters for FI and PDO crashes. The results of this analysis are described using the following equation. Equation 21 where, c1 = regression coefficient. A regression analysis indicated that the best-fit model has a coefficient c1 equal to 1.11. It is associated with an R2 of 0.58. The fit of the model to the data is shown in Figure 9. ( ) ( )[ ]221 pdopdofifit pkpkbk += fipdo kck 1= ( ) ( )22 pdopdofifit pkpkk += ( ) ( ) ( ) ( ) ( )[ ] 5.02,2,2,2,2, 2 pdoppdofipfipdoppdofipfitpt NkNkNkNkNk ρ++= 51

Figure 8. Comparison of predicted and measured overdispersion parameters for FI and PDO crashes. Figure 9. Relationship between overdispersion parameters for FI and PDO crashes. Analysis of Parameters Describing Angle and Rear-End Crash Frequency This subsection describes an analysis of the parameters associated with a series of SPFs calibrated by McGee et al. (2003) and by Harkey et al. (2008). McGee et al. (2003) calibrated a series of SPFs for FI angle and FI rear-end crashes at urban intersections. One set of SPFs was calibrated for intersections in the states of California, Florida, Maryland, Virginia, and Wisconsin. Harkey et al. (2008) calibrated a series of SPFs for total (all severities) angle and total rear-end crashes at rural intersections. One set of SPFs was calibrated for intersections in California, and a second set for intersections in Minnesota. A preliminary analysis indicated that the parameters for the Minnesota SPFs had outlier tendencies and were 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Predicted Overdispersion Parameter M ea su re d O ve rd is pe rs io n Pa ra m et er y = 1.111x R2 = 0.58 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 FI SPF Overdisperstion Parameter (x) PD O S PF O ve rd is pe rs io n Pa ra m et er (y ) 52

subsequently excluded from further analysis. All of the parameters that were used in the analysis are shown in Table 16. Table 16. Overdispersion parameters for angle and rear-end crash SPFs. Variable Crash Type Variable Value by Source and Table in Source Document Harkey et al. (2008) McGee et al. (2003) 1 22 23 24 9 10 11 12 132 133 14 15 Overdispersio n parameter All 0.564 0.483 0.645 0.164 0.435 0.476 0.526 0.588 0.313 0.333 0.323 Angle 1.083 1.128 1.121 0.455 0.714 1.429 1.250 1.667 0.270 0.714 0.588 Rear-end 1.025 0.726 0.709 0.345 0.667 0.909 0.833 0.909 0.476 0.435 0.417 Proportion of all crashes Angle 0.021 0.235 0.228 0.228 0.356 0.114 0.286 0.203 0.183 0.070 0.161 Rear-end 0.074 0.072 0.078 0.315 0.217 0.352 0.253 0.379 0.306 0.522 0.458 Notes: 1 – McGee et al. reported the inverse dispersion parameter K. Overdispersion parameter k is computed as k = 1/ K. 2 – Values listed in this column apply to three-leg intersection data in Table 13 from McGee et al. (2003). 3 – Values listed in this column apply to four-leg intersection data in Table 13 from McGee et al. (2003). A variation of Equation 19 was used to describe the relationship between the angle, rear-end, and total crash SPFs. The form of this equation is provided below. Equation 22 where, kt = overdispersion parameter for total crash frequency; kang = overdispersion parameter for angle crash frequency; kre = overdispersion parameter for rear-end crash frequency; kother = overdispersion parameter for other (not angle or rear-end) crash frequency; pang = proportion angle crashes; and pre = proportion rear-end crashes. This variation was needed because, unlike the analysis conducted in the previous subsection, overdispersion parameters were not available for the full set of crash-type categories. As a result, the following variation of Equation 22 was used to develop an equation for predicting the reported overdispersion parameter for total crash frequency. The coefficients d0 and d1 are included in the equation to compensate for the missing parameters and the assumption that the correlation coefficient equals 0.0. Equation 23 where, d0, d1 = regression coefficients. A regression analysis indicated that the best-fit model has coefficients d0 and d1 equal to 0.729 and 2.24, respectively. The magnitude of d1 is noted to be similar to b1 in Equation 20 (i.e., both coefficients have a value of about 2.0). Equation 23 is associated with an R2 of 0.78. The fit of the model to the data is shown in Figure 10. ( ) ( ) ( )222 0.1 reangotherrereangangt ppkpkpkk −−++= ( ) ( )[ ] ( )20221 0.1 reangrereangangt ppdpkpkdk −−++= 53

Figure 10. Comparison of predicted and measured overdispersion parameters for angle and rear- end crashes. A supplemental analysis examined the correlation between the overdispersion parameters for rear-end and angle crashes. The results of this analysis are described using the following equation. Equation 24 where, e1 = regression coefficient. A regression analysis indicated that the best-fit model has a coefficient e1 equal to 0.673. It is associated with an R2 of 0.51. The fit of the model to the data is shown in Figure 11. Figure 11. Relationship between overdispersion parameters for angle and rear-end crashes. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.2 0.4 0.6 0.8 Predicted Overdispersion Parameter M ea su re d O ve rd is pe rs io n Pa ra m et er angre kek 1= y = 0.673x R2 = 0.51 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 2.0 Angle SPF Overdispersion Parameter (x) R ea r-E nd S PF O ve rd is pe rs io n Pa ra m et er (y ) 54

Estimated Overdispersion Parameter Values This subsection describes the procedure used to compute the estimated overdispersion parameters. The procedure varies slightly depending on whether the underlying SPFs and parameters originated from Chapter 10, 11, or 12 of the HSM. HSM Chapter 10 Chapter 10 describes SPFs and associated overdispersion parameters for intersections on rural two-lane highways. The SPFs and parameters in this chapter are specific to total crashes (all types and severities). These parameters were used to estimate the overdispersion parameters for the equivalent SPFs described in Table 11 to Table 14. As a first step in the process, a parameter for the equivalent SPF for FI crashes of all types was computed by combining Equation 20 and Equation 21 and solving for kfi. Then, a parameter for the equivalent SPF for PDO crashes of all types was computed using the same two equations. This step was repeated for the SPFs associated with three-leg stop-controlled intersections, the SPFs associated with four-leg stop-controlled intersections, and the SPFs associated with four-leg signalized intersections. The estimated parameters are listed in Table 17 in the rows associated with “All types” as a crash type. Table 17. Estimated overdispersion parameters for rural two-lane highway intersections. Area Type Number of Legs Control Type Major- Road Lanes Crash Type Overdispersion Parameter by Severity Proportion of Crashes by Severity1 FI PDO FI PDO Rural 3 Stop control on minor road 2 All types 0.531 0.590 0.415 0.585 Angle 1.377 1.801 0.275 0.210 Rear-end 0.927 1.212 0.260 0.292 Signal 2 All types not available Angle not available Rear-end not available 4 Stop control on minor road 2 All types 0.239 0.266 0.431 0.569 Angle 0.272 0.414 0.532 0.354 Rear-end 0.183 0.279 0.210 0.266 Signal 2 All types 0.100 0.111 0.340 0.660 Angle 0.101 0.086 0.336 0.242 Rear-end 0.068 0.058 0.403 0.438 Note: 1 - Proportions obtained from HSM Tables 10-5 and 10-6. As a second step of the process, a parameter for the equivalent SPF for angle FI crashes was computed using Equation 23, Equation 24, and the estimated parameter for FI crashes of all types. Then, a parameter for the equivalent SPF for angle PDO crashes was computed using the same equations and the estimated parameter for PDO crashes of all types. These calculations were repeated for the two SPFs for rear-end crashes. All four calculations were repeated for the three combinations of intersection legs and control type. The estimated parameters are listed in Table 17 in the rows associated with “Angle” and “Rear-end” crash types. 55

HSM Chapter 11 Chapter 11 describes SPFs and associated overdispersion parameters for intersections on rural multilane highways. The SPFs and parameters in this chapter are specific to total crashes (all types and severities) and to FI crashes. These parameters were used to estimate the overdispersion parameters for the equivalent SPFs described in Table 11 to Table 14. As a first step in the process, a parameter for the equivalent SPF for PDO crashes of all types was computed using Equation 20. This step was repeated for the SPFs associated with three-leg stop- controlled intersections, the SPFs associated with four-leg stop-controlled intersections, and the SPFs associated with four-leg signalized intersections. The estimated parameters are listed in Table 18 in the rows associated with “All types” as a crash type and columns associated with PDO crashes. Table 18. Estimated overdispersion parameters for rural multilane highway intersections. Area Type Number of Legs Control Type Major- Road Lanes Crash Type Overdispersion Parameter by Severity Proportion of Crashes by Severity1 FI PDO FI PDO Rural 3 Stop control on minor road 4 All types 0.569 0.445 0.421 0.579 Angle 1.163 1.146 0.369 0.198 Rear-end 0.782 0.771 0.247 0.315 Signal 4 All types not available Angle not available Rear-end not available 4 Stop control on minor road 4 All types 0.742 0.334 0.499 0.501 Angle 0.983 0.626 0.534 0.292 Rear-end 0.662 0.421 0.213 0.240 Signal 4 All types 0.218 0.315 0.389 0.611 Angle 0.331 0.528 0.315 0.215 Rear-end 0.223 0.355 0.472 0.505 Note: 1 - Proportions for angle and rear-end crashes obtained from HSM Table 11-9. Equation 20 requires the proportion of FI and PDO crashes. However, this proportion was not available for “All Types” as a crash type from the HSM. As a result, the SPFs for FI and total crashes published in Chapter 11 of the HSM were used, with the average AADT values published by Lord et al. (2008; Tables 4.6, 4.7, and 4.12), to estimate the desired proportions. The computed proportions for FI and PDO crashes are listed in Table 18. The second step of the process was to compute the estimated parameters for angle and rear-end crashes. The calculations for this step were the same as those described in the previous subsection for Chapter 10. The estimated parameters are listed in Table 18 in the rows associated with “Angle” and “Rear-end” crash types. HSM Chapter 12 Chapter 12 describes the SPFs and associated overdispersion parameters for intersections on urban and suburban arterial streets. The SPFs and parameters in this chapter are specific to total single-vehicle and total multiple-vehicle crashes (all severities), as well as to FI and PDO crashes for the single-vehicle and multiple-vehicle categories. These parameters were used to estimate the overdispersion parameters for the equivalent SPFs described in Table 11 to Table 14. 56

As a first step in the process, a parameter for FI crashes of all types was computed using the following variation of Equation 20, as well as the overdispersion parameters for FI single-vehicle and FI multiple- vehicle crashes. Equation 25 where, kt = overdispersion parameter for total crash frequency; kmv = overdispersion parameter for multiple-vehicle crash frequency; ksv = overdispersion parameter for single-vehicle crash frequency; pmv = proportion multiple-vehicle crashes; and psv = proportion single-vehicle crashes (= 1.0 − pmv). A parameter for PDO crashes of all types was computed using Equation 25 and the overdispersion parameters for PDO single-vehicle and multiple-vehicle crashes. This step was repeated for the SPFs associated with three-leg stop-controlled intersections, the SPFs associated with four-leg stop-controlled intersections, the SPFs associated with three-leg signalized intersections, and the SPFs associated with four-leg signalized intersections. The estimated parameters are listed in Table 19 in the rows associated with “All types” as a crash type. Table 19. Estimated overdispersion parameters for urban and suburban arterial intersections. Area Type Number of Legs Control Type Major -Road Lanes Crash Type Overdispersion Parameter by Severity Proportion of Crashes by Severity1 FI PDO FI PDO Urban 3 Stop control on minor road 2 or 4 All types 0.973 1.084 0.350 0.650 Angle 1.756 2.288 0.343 0.262 Rear-end 1.182 1.540 0.421 0.440 Signal 2 or 4 All types 0.494 0.572 0.341 0.659 Angle 0.750 0.971 0.280 0.204 Rear-end 0.505 0.653 0.549 0.546 4 Stop control on minor road 2 or 4 All types 0.719 0.598 0.381 0.619 Angle 1.127 1.160 0.440 0.335 Rear-end 0.758 0.780 0.338 0.374 Signal 2 or 4 All types 0.549 0.707 0.326 0.674 Angle 0.902 1.345 0.347 0.244 Rear-end 0.607 0.906 0.450 0.483 Note: 1 - Proportions for angle and rear-end crashes obtained from HSM Exhibit 12-11. Equation 25 requires the proportion of multiple-vehicle crashes and the proportion of single-vehicle crashes. However, these proportions were not available for “All Types” as a crash type from the HSM. As a result, the SPFs for FI and PDO multiple-vehicle and single-vehicle crashes published in Chapter 12 of the HSM were used, with the average AADT values published by Harwood et al. (2007; Table 23), to estimate the desired proportions. The second step of the process is to compute the estimated parameters for angle and rear-end crashes. The calculations for this step were the same as those described in a previous subsection for Chapter 10. ( ) ( )[ ]2284.1 svsvmvmvt pkpkk +×= 57

The estimated parameters are listed in Table 19 in the rows associated with “Angle” and “Rear-end” crash types. Development of Crash Costs This section describes the estimation of crash cost for selected crash type and severity categories. The severity index is used to provide a single-valued indication of overall safety that reflects both the frequency and relative severity of different crash types. The following equation is used to compute this index. Equation 26 with Equation 27 where, Ip,t = severity index for total crashes; cp,t = road-user cost associated with total crashes, $/year; cfi,ang = average cost of FI angle crash, $/year; cfi,re = average cost of FI rear-end crash, $/year; cfi,other = average cost of FI other (not angle or rear-end) crash, $/year; cpdo,ang = average cost of PDO angle crash, $/year; cpdo,re = average cost of PDO rear-end crash, $/year; and cpdo,other = average cost of PDO other (not angle or rear-end) crash, $/year. In Equation 27, the predicted average crash frequency variables Np are replaced by the expected average crash frequency variables Na when the EB Method is applied. The variance of the severity index is computed using the following equation. Equation 28 with Equation 29 where, V[Ip,t] = variance of severity index among intersections; V[cp,t] = variance of road-user cost among intersections, ($/year)2; and V[Np,i,j] = variance of predicted average crash frequency among intersections for severity category i and crash type j, crashes/yr2. In Equation 29, the variance of the predicted average crash frequency variables V[Np] are replaced by the variance of the expected average crash frequency variables V[Na] when the EB Method is applied. Equation 29 does not include the variance of the crash cost estimates. This approach is used because the focus of the safety evaluation procedure is on relative changes in crash severity among alternatives for a given set of road-user costs, as opposed to the degree of certainty that can be placed on a specific estimate of crash cost. ( ) ( ) ( ) ( ) ( ) ( )otherpdootherpdoprepdorepdopangpdoangpdop otherfiotherfiprefirefipangfiangfiptp cNcNcN cNcNcNc ,,,,,,,,, ,,,,,,,,,, ×+×+×+ ×+×+×= 000,1 , , tp tp c I = [ ] [ ]( ) [ ]( ) [ ]( ) [ ]( ) [ ]( ) [ ]( )2 ,,,2 ,,,2 ,,, 2 ,,, 2 ,,, 2 ,,,, otherpdootherpdoprepdorepdopangpdoangpdop otherfiotherfiprefirefipangfiangfiptp cNVcNVcNV cNVcNVcNVcV ×+×+×+ ×+×+×= [ ] [ ]2,, 000,1 tp tp cV IV = 58

[ ] ( )2pp NkNV ×= The variance of the predicted average crash frequency is computed using the following equation. Equation 30 where, V[Np] = variance of predicted average crash frequency among intersections, (crashes/yr2); and k = overdispersion parameter. The variance of the expected average crash frequency is computed using the equations described by Hauer (1997). The crash costs used in Equation 27 and Equation 29 are based on estimates developed by Council et al. (2005). This report identifies crash costs for several crash types and severities, including FI angle, FI rear-end, PDO angle, PDO rear-end, and FI vehicle-pedestrian crashes. These costs are listed in Table 20. Table 20. Unit crash costs. Area Type Control Type Crash Severity Crash Cost by Crash Type1, $ Angle Rear-end Vehicle-Ped. Other Rural (speed limit of 50 mi/h or more) Signal FI 126,878 52,276 183,461 164,041 PDO 8,544 5,901 not needed2 5,337 Stop FI 199,788 34,563 183,461 201,282 PDO 5,444 3,788 not needed2 5,795 Urban (speed limit of 45 mi/h or less) Signal FI 64,468 44,687 169,090 121,665 PDO 8,673 11,463 not needed2 5,641 Stop FI 80,956 56,093 169,090 113,088 PDO 7,910 12,295 not needed2 5,583 Notes: 1 – Source: Council et al. (2005). Costs are in 2001 dollars. 2 – Based on guidance in HSM Chapter 12, all vehicle-pedestrian crashes are assumed to be fatal or injury. The development of a crash cost estimate for the “other” crash category is described in this section. The crash cost estimates provided in the report by Council et al. (2005) were used for this purpose. In addition to angle, rear-end, and vehicle-pedestrian crash costs, the report by Council et al. provides a cost for vehicle-animal, fixed-object, parked-vehicle, rollover, sideswipe, and head-on crashes. These “other” crash types were used to estimate the cost for the “other” crash category. This cost was computed as a weighted average of the crash cost for each crash type, where the weight used was the proportion of crashes associated with the specified crash type. Typical proportions for the other crash types are provided in the crash type distributions in the HSM Part C chapters. The calculation of cost for the other crash category for rural intersections is shown in Table 21. The total proportion in column 7 is computed as the product of the proportion in column 4 and the proportion in column 6. The total proportions are used as the weighting factor in the calculation of “weighted average” crash cost. One average is computed for each combination of control type and crash severity. The calculation of cost for the other crash category for urban intersections is shown in Table 22. It is noted that the weighted average cost for FI “other” crashes exceeds the cost of FI angle and FI rear-end crashes. This trend can be observed by comparing the cost summary in the last four columns of Table 20. The reasons for this trend are that (1) FI fixed-object and FI head-on crashes have very high crash costs, and (2) they constitute about 60 percent of the crash types listed in Table 21 and Table 22. 59

Table 21. Crash cost calculations for rural intersections. Control Type Crash Severity Crash Type Pro- portion Crash Type Pro- portion2 Total Pro- portion Crash Cost1, $ HSM Table for Proportions Signal PDO Any 0.660 Animal 0.003 0.0020 5,619 10-5, 10-6 Object 0.081 0.0535 5,565 Parked veh. 0.000 0.0000 6,223 Rollover 0.003 0.0020 13,525 Sideswipe 0.153 0.1010 5,762 Head on 0.040 0.0264 2,617 Weighted average: 5,337 FI Single 0.340 Animal 0.000 0.0000 61,341 Object 0.032 0.0109 246,235 Parked veh. 0.000 0.0000 214,511 Rollover 0.003 0.0010 366,821 Sideswipe 0.051 0.0173 169,438 Head on 0.080 0.0272 120,118 Weighted average: 164,041 Stop PDO Any 0.560 Animal 0.014 0.0080 5,619 Object 0.144 0.0819 5,565 Parked veh. 0.000 0.0000 6,223 Rollover 0.004 0.0023 13,526 Sideswipe 0.144 0.0819 5,762 Head on 0.025 0.0142 6,169 Weighted average: 5,795 FI Single 0.340 Animal 0.006 0.0026 61,341 Object 0.094 0.0405 246,235 Parked veh. 0.000 0.0000 214,511 Rollover 0.006 0.0026 366,821 Sideswipe 0.044 0.0190 169,438 Head on 0.060 0.0259 151,647 Weighted average: 201,282 Notes: 1 – Source: Council et al. (2005). Costs are in 2001 dollars. 2 – Proportions used are based on those for a four-leg intersection. Proportions used for “Object” crash type are assumed to equal those specified as “ran off road” in the HSM. 60

Table 22. Crash cost calculations for urban intersections. Control Type Crash Severity Crash Type Pro- portion3 Crash Type Pro- portion2 Total Pro- portion Crash Cost1, $ HSM Table for Proportions Signal PDO Single vehicle 0.046 Animal 0.002 0.0001 2,617 12-13 Object 0.870 0.0399 5,721 Parked veh. 0.001 0.0000 3,738 Rollover 0.000 0.0000 9,697 Multiple vehicle 0.628 Sideswipe 0.032 0.0201 6,007 12-11 Head on 0.030 0.0188 5,101 Weighted average: 5,641 FI Single vehicle 0.016 Animal 0.002 0.0000 90,943 12-13 Object 0.744 0.0121 202,918 Parked veh. 0.001 0.0000 57,980 Rollover 0.000 0.0000 160,218 Multiple vehicle 0.310 Sideswipe 0.099 0.0307 74,519 12-11 Head on 0.049 0.0152 152,240 Weighted average: 121,665 Stop PDO Single vehicle 0.067 Animal 0.026 0.0017 2,617 12-13 Object 0.847 0.0563 5,721 Parked veh. 0.001 0.0001 3,738 Rollover 0.000 0.0000 9,697 Multiple vehicle 0.552 Sideswipe 0.044 0.0243 6,007 12-11 Head on 0.030 0.0166 4,806 Weighted average: 5,583 FI Single vehicle 0.043 Animal 0.001 0.0000 90,943 12-13 Object 0.679 0.0292 202,918 Parked veh. 0.001 0.0000 57,980 Rollover 0.000 0.0000 160,218 Multiple vehicle 0.338 Sideswipe 0.121 0.0409 74,519 12-11 Head on 0.041 0.0139 37,976 Weighted average: 113,088 Notes: 1 – Source: Council et al. (2005). Costs are in 2001 dollars. 2 – Proportions used are based on those for a four-leg intersection. Proportions used for “Object” crash type are assumed to equal those specified as “fixed object” in the HSM. 3 – Proportions are computed using the HSM SPFs for four-leg intersections with average AADT values. 61