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APPENDIX A
DETAILS OF CALIBRATED SAFETY PERFORMANCE FUNCTIONS
The tables in this appendix summarize the safety perfor- · TER = 0 if flat terrain, 1 if rolling terrain.
mance functions and annual factors developed as part of this · DOC = degree of curvature.
study. The information is organized by roadway type: · ENV = environmental type (either urban or rural).
· s.e. = standard error.
· Two-lane roadways (Pennsylvania, New Jersey, New · 1, 2, 3, and 4 = model coefficients.
York, and Illinois),
· Four-lane freeways (Pennsylvania, New York, Missouri, To account for the effect of trends in safety not related to
and Wisconsin), and traffic volumes, annual factors were estimated using a pro-
· Four-lane divided expressways (Pennsylvania and cedure documented by Harwood et al. ("Prediction of the
Wisconsin). Expected Safety Performance of Rural Two-Lane High-
ways," FHWA-RD-99-207, Federal Highway Administra-
The symbols and short forms in the following tables are tion, 2000).
defined here: The methodology used this report compared data before
PRPMs were installed with data after PRPMs were installed.
· k = calibrated parameter relating the mean and variance The actual year that the PRPMs were installed cannot be used
of the prediction. for data analysis because for part of the year there were no
· f = factor applied to the calibrated model to predict for PRPMs and for part of the year PRPMs were installed. The
a crash type other than that used for the model calibration. data from the same year as the installation of the PRPMs was
· AADT = annual average daily traffic. not used in the analysis, which is why certain years of data
· SW = shoulder width in feet. are missing.
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TABLE A-1 Safety performance functions for two-lane roadways
Model Form Pennsylvania New Jersey New York I llinois
Crashes per Mile-yr (AADT)1exp(2DOC) (AADT)1exp(3SW) (AADT)1exp(3 SW) (AADT)1exp(3SW + 4TER)
ln()(s.e.) -6.1060 (0.3340) -10.4380 (0.8970) -7.8980 (0.6050) -7.1120 (0.4630)
1 (s.e.) 0.7640 (0.0398) 1.3292 (0.0954) 1.0218 (0.0690) 0.8988 (0.0576)
2 (s.e.) 0.0400 (0.0126) NA NA NA
3 (s.e.) NA -0.0504 (0.0148) -0.0669 (0.0167) -0.0613 (0.0282)
4 (s.e.) NA NA NA 0.1720 (0.0956)
k 3.2 2.2 3.5 3.1
Model parameters f k f k f k f k
Total 1.000 3.2 1.000 2.2 1.000 3.5 1.000 3.1
Fatal and injury 0.195 4.3 0.430 2.2 0.738 3.4 0.262 1.9
Daytime 0.578 2.6 0.656 1.6 0.600 3.7 0.479 3.4
Daytime fatal and injury 0.101 3.8 0.298 2.1 0.468 3.2 0.148 2.2
Nighttime 0.422 3.1 0.344 2.8 0.400 2.2 0.521 2.5
Nighttime fatal and injury 0.094 2.6 0.131 2.0 0.270 2.9 0.135 1.6
Dry 0.657 2.7 0.729 1.9 0.590 3.1 0.690 2.9
Wet 0.337 2.0 0.270 1.8 0.390 7.4 0.247 1.7
Head-on 0.067 3.0 0.064 2.2 Sample size too small 0.031 3.1
Guidance-related 0.209 3.6 0.045 0.7 0.368 2.5
TABLE A-2 Pennsylvania two-lane roadways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Head- Guidance-
Injury and Injury and Injury On Related
1991 0.94 1.00 0.84 0.81 1.09 1.21 1.01 0.84 0.75 1.05
1992 1.00 1.17 0.88 1.04 1.17 1.30 0.92 1.19 0.72 0.96
1993 1.00 1.01 0.99 0.84 1.02 1.18 1.00 1.00 0.89 0.93
1994 0.84 0.84 0.80 0.80 0.89 0.99 0.83 0.83 1.01 0.98
1995 0.98 1.03 1.05 1.05 0.88 1.00 1.02 0.91 1.08 1.14
1996 0.97 0.87 0.95 0.79 0.99 0.94 0.95 0.99 0.69 1.06
1997 0.97 0.85 1.02 0.78 0.90 0.93 0.87 1.18 1.30 1.12
1998 0.97 0.85 1.02 1.01 0.90 0.68 1.05 0.81 1.14 0.82
1999 1.07 0.94 1.16 1.37 0.96 0.49 1.15 0.92 1.12 1.10
2000 1.19 1.35 1.21 1.41 1.16 1.29 1.13 1.25 1.19 0.76
TABLE A-3 New Jersey two-lane roadways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Head-On
Injury and Injury and Injury
1991 0.89 0.91 0.92 0.94 0.84 0.84 0.91 0.84 0.89
1992 0.93 0.91 0.90 0.88 0.98 0.99 0.91 0.98 0.94
1993 PRPM Implementation Year
1994 1.11 1.05 1.11 1.05 1.11 1.05 1.11 1.11 1.12
1995 1.05 0.95 1.05 0.95 1.05 0.95 1.05 1.05 1.05
1996 PRPM Implementation Year
1997 1.14 0.89 1.14 0.89 1.14 0.90 1.14 1.14 1.14
1998 1.00 0.85 1.00 0.85 1.00 0.85 1.00 1.00 1.01
NOTE: It was not possible to extract guidance-related crashes from the New Jersey database.
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TABLE A-4 New York two-lane roadways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Guidance-Related
Injury and Injury and Injury
1993 1.00 1.04 1.01 1.06 0.98 1.00 1.05 0.90 1.16
1994 1.01 0.99 1.02 0.95 0.99 1.04 0.97 1.06 1.04
1995 0.98 1.05 1.00 1.09 0.94 0.96 0.97 0.97 0.87
1996 0.90 0.81 0.85 0.77 0.97 0.87 0.89 0.95 0.79
1997 1.16 0.84 1.12 0.96 1.22 0.64 1.19 1.05 0.52
1998 PRPM Implementation Year
1999 1.69 0.83 1.45 0.80 2.05 0.88 1.91 1.35 0.68
2000 2.04 0.87 1.77 0.92 2.43 0.79 2.04 1.99 0.87
2001 2.20 1.14 2.15 1.27 2.27 0.93 1.25 3.61 0.88
NOTE: Head-on crashes were not included because of sample size limitations.
TABLE A-5 Illinois two-lane roadways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Head- Guidance-
Injury and Injury and Injury On Related
1991 1.20 0.93 1.20 1.20 1.40 0.93 1.24 1.28 1.20 1.20
1992 1.10 1.07 1.10 1.10 1.16 1.07 1.17 1.10 1.10 1.10
1993 1.20 1.16 1.20 1.20 1.15 1.16 1.12 1.45 1.20 1.20
1994 1.04 1.11 1.04 1.04 1.00 1.11 1.00 0.89 1.04 1.04
1995 1.13 1.41 1.13 1.13 0.94 1.41 1.13 0.96 1.13 1.13
1996 0.91 1.01 0.91 0.91 0.86 1.01 0.90 0.94 0.91 0.91
1997 0.95 1.10 0.95 0.95 0.84 1.10 0.94 0.88 0.95 0.95
1998 0.89 0.81 0.89 0.89 0.78 0.81 0.88 0.83 0.89 0.89
1999 1.03 1.00 1.03 1.03 0.91 1.00 1.03 0.96 1.03 1.03
2000 1.02 0.96 1.02 1.02 0.90 0.96 1.02 0.95 1.02 1.02
TABLE A-6 Safety performance functions for four-lane freeways
Model Form Pennsylvania1 New York Missouri 1 Wisconsin
1 1 1
Crashes per Mile-yr (AADT/2) (AADT) (AADT) (AADT)1exp(2ENV)
ln() (s.e.) -7.7170 (0.3850) -1.7320 (0.9490) -11.1500 (0.3370) -9.0480 (0.5980)
1 (s.e.) 0.8657 (0.0408) 0.3450 (0.1010) 1.2765 (0.0357) 1.0666 (0.0602)
2 (s.e.) NA NA NA 0.3194 (0.0774)
k 2.3 2.9 3.2 2.3
Model parameters f k f k f k f k
Total 1.000 2.3 1.000 2.9 1.000 3.2 1.000 2.3
Fatal and injury 0.131 2.9 0.444 2.6 0.318 3.5 0.250 2.3
Daytime 0.598 1.9 0.570 2.6 0.618 2.7 0.652 2.4
Daytime fatal and injury 0.075 2.6 0.263 2.0 0.199 3.1 0.151 2.3
Nighttime 0.402 2.3 0.430 3.3 0.382 4.0 0.348 2.0
Nighttime fatal and injury 0.055 4.0 0.181 3.6 0.120 4.3 0.099 2.4
Dry 0.581 2.2 0.503 2.2 0.666 4.2 0.604 2.4
Wet 0.414 1.3 0.480 2.9 0.334 1.6 0.396 1.7
Guidance-related 0.221 1.6 0.017 0.9 0.476 3.0 0.606 2.0
1 Datafor Pennsylvania and Missouri are for one direction of travel only. AADT variable: for Pennsylvania both directions,
for Missouri one-way volume only.
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TABLE A-7 Pennsylvania four-lane freeways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Guidance-Related
Injury and Injury and Injury
1991 0.92 0.92 0.92 0.92 0.92 0.92 0.98 0.83 0.92
1992 0.92 0.92 0.92 0.92 0.92 0.92 0.98 0.83 0.92
1993 1.02 1.02 1.02 1.02 1.02 1.02 0.96 1.11 1.02
1994 1.02 1.02 1.02 1.02 1.02 1.02 0.96 1.11 1.02
1995 1.02 1.02 1.02 1.02 1.02 1.02 0.96 1.11 1.02
1996 1.02 1.02 1.02 1.02 1.02 1.02 0.96 1.11 1.02
1997 0.95 0.95 0.95 0.95 0.95 0.95 1.01 0.85 0.95
1998 0.95 0.95 0.95 0.95 0.95 0.95 1.01 0.85 0.95
1999 0.95 0.95 0.95 0.95 0.95 0.95 1.01 0.85 0.95
2000 0.95 0.95 0.95 0.95 0.95 0.95 1.01 0.85 0.95
TABLE A-8 New York four-lane freeways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Guidance-Related
Injury and Injury and Injury
1993 0.42 0.66 0.46 0.72 0.37 0.56 0.41 0.43 0.51
1994 0.46 0.71 0.46 0.66 0.46 0.79 0.44 0.47 0.31
1995 0.60 0.86 0.66 0.92 0.52 0.77 0.62 0.56 0.41
1996 0.66 0.95 0.65 0.87 0.67 1.06 0.58 0.73 0.91
1997 0.82 1.08 0.87 1.09 0.76 1.05 0.72 0.95 1.11
1998 PRPM Implementation Year
1999 1.04 0.66 0.99 0.66 1.11 0.67 1.15 0.94 0.50
2000 1.21 0.63 1.19 0.65 1.24 0.61 1.23 1.17 1.30
2001 1.42 0.76 1.37 0.86 1.48 0.63 0.78 2.09 1.21
TABLE A-9 Missouri four-lane freeway: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Guidance-Related
Injury and Injury and Injury
1991 0.86 0.94 0.81 0.90 0.94 0.99 0.87 0.84 0.91
1992 0.74 0.77 0.73 0.76 0.76 0.77 0.83 0.57 0.71
1993 0.97 0.95 0.93 0.90 1.04 1.03 0.90 1.11 1.01
1994 0.96 0.96 0.93 0.90 1.02 1.06 1.04 0.80 0.94
1995 0.93 0.89 0.89 0.85 0.99 0.94 0.97 0.86 0.90
1996 1.05 1.03 1.07 1.04 1.02 1.01 1.00 1.15 1.03
1997 1.01 1.07 1.05 1.12 0.95 0.97 0.98 1.08 1.08
1998 1.05 1.02 1.11 1.04 0.95 0.97 1.01 1.11 1.03
1999 1.11 1.07 1.27 1.25 0.86 0.76 1.07 1.20 1.02
2000 1.01 0.98 1.00 1.01 1.02 0.91 0.97 1.08 0.99
2001 0.95 0.87 1.01 0.93 0.86 0.76 0.92 1.02 0.94
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TABLE A-10 Wisconsin four-lane freeway: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Guidance-Related
Injury and Injury and Injury
1994 0.73 0.69 0.69 0.70 0.82 0.68 0.72 0.75 0.95
1995 0.73 0.69 0.71 0.71 0.77 0.67 0.78 0.69 0.96
1996 0.95 1.02 0.95 0.97 0.95 1.12 0.85 1.09 1.04
1997 0.93 0.98 0.94 1.00 0.92 0.96 0.88 0.99 1.03
1998 0.90 0.86 0.97 0.89 0.80 0.83 1.00 0.75 0.89
2000 1.24 1.48 1.30 1.41 1.12 1.58 1.04 1.54 1.42
(Comparison
Group 1)
2000 1.08 0.98 1.08 0.99 1.08 0.99 1.07 1.08 1.24
(Comparison
Group 2)
Comparison Group 1: based on 43 miles of comparison sites of four-lane freeways; Comparison Group 2: based on a sample of urban Interstate highway
in Milwaukee County.
TABLE A-11 Safety performance functions for four-
lane divided expressways
Model Form Pennsylvania1 Wisconsin
1
Crashes per Mile-yr (AADT/2) (AADT)1
ln() (s.e.) -11.40 (1.17) -3.47 (1.88)
1 (s.e.) 1.241 (0.122) 0.494 (0.199)
2 (s.e.) N/A N/A
k 2.3 2.2
Model parameters f k f k
Total 1.000 2.3 1.000 2.2
Fatal and injury 0.154 1.8 0.165 3.7
Daytime 0.625 2.3 0.691 1.6
Daytime fatal and injury 0.098 1.8 0.090 3.4
Nighttime 0.375 2.5 0.309 4.6
Nighttime fatal and injury 0.056 2.5 0.075 2.7
Dry 0.666 2.5 0.761 1.8
Wet 0.331 1.7 0.239 2.3
Guidance-related 0.094 0.8 0.634 3.1
1 Datafor Pennsylvania is for one direction of travel only. AADT is for
both directions.
TABLE A-12 Pennsylvania four-lane divided expressways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Guidance-Related
Injury and Injury and Injury
1991 0.76 0.86 0.78 0.82 0.72 0.93 0.75 0.77 0.88
1992 0.76 0.86 0.78 0.82 0.72 0.93 0.75 0.77 0.88
1993 0.61 0.60 0.61 0.65 0.60 0.50 0.58 0.68 0.63
1994 0.61 0.60 0.61 0.65 0.60 0.50 0.58 0.68 0.63
1995 0.61 0.60 0.61 0.65 0.60 0.50 0.58 0.68 0.63
1996 0.61 0.60 0.61 0.65 0.60 0.50 0.58 0.68 0.63
1997 0.72 0.62 0.68 0.54 0.78 0.76 0.81 0.54 0.49
1998 0.72 0.62 0.68 0.54 0.78 0.76 0.81 0.54 0.49
1999 0.72 0.62 0.68 0.54 0.78 0.76 0.81 0.54 0.49
2000 0.72 0.62 0.68 0.54 0.78 0.76 0.81 0.54 0.49
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TABLE A-13 Wisconsin four-lane divided expressways: annual factors
Annual Factors Total Fatal and Daytime Daytime Fatal Nighttime Nighttime Fatal Dry Wet Guidance-Related
Injury and Injury and Injury
1994 0.77 0.65 0.69 0.64 0.95 0.67 0.81 0.65 1.05
1995 0.69 0.60 0.69 0.66 0.69 0.52 0.76 0.48 0.99
1996 1.00 1.10 1.00 0.94 1.00 1.29 0.98 1.08 0.89
1997 1.14 1.18 1.20 1.28 1.03 1.07 1.06 1.41 0.91
1998 1.28 1.35 1.31 1.35 1.23 1.35 1.29 1.27 1.05
1999 PRPM Implementation Year
2000 1.42 1.71 1.43 1.70 1.43 1.72 1.43 1.43 1.42
