Safety Evaluation of Permanent Raised Pavement Markers (2004)

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A-1 APPENDIX A DETAILS OF CALIBRATED SAFETY PERFORMANCE FUNCTIONS The tables in this appendix summarize the safety perfor- mance functions and annual factors developed as part of this study. The information is organized by roadway type: • Two-lane roadways (Pennsylvania, New Jersey, New York, and Illinois), • Four-lane freeways (Pennsylvania, New York, Missouri, and Wisconsin), and • Four-lane divided expressways (Pennsylvania and Wisconsin). The symbols and short forms in the following tables are defined here: • k = calibrated parameter relating the mean and variance of the prediction. • α f = factor applied to the calibrated model to predict for a crash type other than that used for the model calibration. • AADT = annual average daily traffic. • SW = shoulder width in feet. • TER = 0 if flat terrain, 1 if rolling terrain. • DOC = degree of curvature. • ENV = environmental type (either urban or rural). • s.e. = standard error. • β1, β2, β3, and β4 = model coefficients. To account for the effect of trends in safety not related to traffic volumes, annual factors were estimated using a pro- cedure documented by Harwood et al. (“Prediction of the Expected Safety Performance of Rural Two-Lane High- ways,” FHWA-RD-99-207, Federal Highway Administra- tion, 2000). The methodology used this report compared data before PRPMs were installed with data after PRPMs were installed. The actual year that the PRPMs were installed cannot be used for data analysis because for part of the year there were no PRPMs and for part of the year PRPMs were installed. The data from the same year as the installation of the PRPMs was not used in the analysis, which is why certain years of data are missing.

A-2 TABLE A-1 Safety performance functions for two-lane roadways Pennsylvania New Jersey New York I llinois Model Form Crashes per Mile-yr
(AADT)1exp(2DOC)
(AADT)1exp(3SW)
(AADT)1exp(3 SW)
(AADT)1exp(3SW + 4TER) ln(α) (s.e.) -6.1060 (0.3340) -10.4380 (0.8970) -7.8980 (0.6050) -7.1120 (0.4630) β1 (s.e.) 0.7640 (0.0398) 1.3292 (0.0954) 1.0218 (0.0690) 0.8988 (0.0576) β2 (s.e.) 0.0400 (0.0126) NA NA NA β3 (s.e.) NA -0.0504 (0.0148) -0.0669 (0.0167) -0.0613 (0.0282) β4 (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 Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Head- On Guidance- 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 Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Head-On 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.

A-3 TABLE A-4 New York two-lane roadways: annual factors Annual Factors Total Fatal and Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Guidance-Related 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 Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Head- On Guidance- 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 Pennsylvania 1 New York Missouri 1 Wisconsin Model Form Crashes per Mile-yr
(AADT/2)1
(AADT)1
(AADT)1
(AADT)1exp(2ENV) ln(α) (s.e.) -7.7170 (0.3850) -1.7320 (0.9490) -11.1500 (0.3370) -9.0480 (0.5980) β1 (s.e.) 0.8657 (0.0408) 0.3450 (0.1010) 1.2765 (0.0357) 1.0666 (0.0602) β2 (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 1Data for Pennsylvania and Missouri are for one direction of travel only. AADT variable: for Pennsylvania both directions, for Missouri one-way volume only.

A-4 TABLE A-7 Pennsylvania four-lane freeways: annual factors Annual Factors Total Fatal and Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Guidance-Related 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 Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Guidance-Related 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 Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Guidance-Related 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

A-5 TABLE A-10 Wisconsin four-lane freeway: annual factors Annual Factors Total Fatal and Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Guidance-Related 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 (Comparison Group 1) 1.24 1.48 1.30 1.41 1.12 1.58 1.04 1.54 1.42 2000 (Comparison Group 2) 1.08 0.98 1.08 0.99 1.08 0.99 1.07 1.08 1.24 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. Pennsylvania 1 Wisconsin Model Form Crashes per Mile-yr
(AADT/2)1
(AADT)1 ln(α) (s.e.) -11.40 (1.17) -3.47 (1.88) β1 (s.e.) 1.241 (0.122) 0.494 (0.199) β2 (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 1Data for Pennsylvania is for one direction of travel only. AADT is for both directions. Annual Factors Total Fatal and Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Guidance-Related 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 TABLE A-11 Safety performance functions for four- lane divided expressways TABLE A-12 Pennsylvania four-lane divided expressways: annual factors

A-6 TABLE A-13 Wisconsin four-lane divided expressways: annual factors Annual Factors Total Fatal and Injury Daytime Daytime Fatal and Injury Nighttime Nighttime Fatal and Injury Dry Wet Guidance-Related 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