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A-1 APPENDIX A Using Prediction Models to Determine Relative Safety of Design Element Choices Model Use used to adjust the predictions to the local conditions. This process is described in the following section. This report presents the use of AMFs as a recommended Step 5: Summarize the predictions of the safety implica- approach for determining the relative safety of design ele- tions of the design choices. The total number of predicted ment choices. An alternative method that will yield similar crashes for the entire roadway section can be obtained by results is the use of the prediction models developed herein; simply summing up all individual predictions from Step 4. this approach is illustrated in this appendix. This process can be applied to determine the safety implications of using dif- ferent values for a single or combination of design elements; Calibration Process it may be implemented using the models with or without calibration to local conditions or by simply using the AMFs Calibration to adjust the model estimates for the local con- to determine the anticipated percent change in crashes. ditions is recommended. A simple, four-step calibration pro- Steps 1 through 5 of the process are also illustrated in cedure is as follows: Figure A-1: Step 1: Randomly select a sample of the data set to be Step 1: Apportion the roadway section in homogenous evaluated; a set of 75 to 100 segments is suitable. The seg- segments where geometry and traffic are constant. This ments should satisfy the basic assumptions of the models requires dividing the roadway section into individual homo- (i.e., four-lane rural highways with 12-ft lanes and divided geneous segments without intersections. Each segment is or undivided). defined when a change in the value of the average daily traf- Step 2: Apply the model of concern for each selected seg- fic, lane, shoulder and median width occurs or a median ment to determine the expected number of crashes for is introduced. The roadway then comprises a number of the segment. For example, if all crashes for divided high- segments of varying length. ways are to be estimated, Equation 8 should be used. Step 2: Determine the geometric design elements and val- Step 3: Compare the expected values obtained in Step 2 ues to be considered. In this step, the choice of shoulder with those actually observed and determine the relative widths, median widths, median presence, and shoulder type differences between observed and expected values. are determined in order to identify the possible roadway Step 4: Calculate a ratio of the observed to the expected geometric design elements to be evaluated. values by summing all crashes for the selected segments. Step 3: Estimate the number of crashes for each condition This is the calibration factor that can be used as a multiply- to be evaluated using the appropriate prediction model ing factor for prediction obtained from the models as for each segment of concern. To do this, the user must described above. decide whether to estimate single-vehicle, multi-vehicle, or all crashes and to address the severity of crashes. Once these This calibration process is required for each for the mod- choices are made, the appropriate models are selected from els to be applied, and it may be difficult to implement since it Equations 6 though 14 (see Chapter 3 for equations). is possible that for certain categories the necessary data will Step 4: Apply a calibration factor to adjust predictions be inadequate or not available. An example of the use of the to local jurisdiction. The calibration factor is a multiplier calibration process is presented in the next section.

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A-2 The California intercept value was used in this analysis. The use of either of the other two intercepts produces similar results, and the percent change between the two choices is the same. The Kentucky intercept produces an estimate of 1.47 and 0.91 crashes per year per mile for the 4-ft and 8-ft shoul- ders; the use of the Minnesota intercept gives estimates of 1.69 and 1.05 crashes per year per mile. All three estimates have a crash reduction of approximately 38% with the use of the 8-ft shoulder compared with the 4-ft shoulder. Example 2: Calibration An agency is designing a roadway project where an 8-ft shoulder is considered. The roadway project has a length of 1.0 miles and an ADT of 15,000 vehicles/day. The roadway will be a principal arterial, it will be undivided with four 12-ft lanes, the shoulders will be paved, and there are no access points along the segment. The agency wishes to estimate the safety effect of the choice of shoulder width on all crashes. Figure A-1. Flow chart of model application. To develop a calibration factor, a set of 100 segments is randomly chosen within the agency's jurisdiction. All seg- Examples ments are undivided four-lane rural highways with 12-ft lanes and paved shoulders. For each segment the total num- Two examples are presented to demonstrate the use of the ber of crashes is estimated for the period of concern. Using models and AMFs for estimating the safety implications from Equation 11, the expected number of total crashes for undi- design choices. The first example demonstrates the use of the vided four-lane rural highways is calculated for each segment models without calibration; the second illustrates the appli- (see Table A-1). cation of calibration factors. Summing over the 100 segments, the ratio of observed to expected crashes is 70/50 = 1.4, and this calibration factor is Example 1: No Calibration applied in Equation 11: cr An agency is evaluating the effects of shoulder widths for a E [ N ]AD = (1.0 e -5.105 - ln12 + 0.960 ln15000 - 0.067(8) )1.4 = 0.419 roadway project with a length of 0.75 miles and an ADT of yr 10,000 vehicles/day. The roadway will be a principal arterial mi with these characteristics: (1) divided with a 30-ft median, (2) four 12-ft lanes, (3) no median barrier, (4) paved shoulders, Using the calibrated equation, the total number of expected and (5) no access points along the segment. Designs with 4-ft crashes per year per mile for this segment with 8-ft shoulders and 8-ft shoulders will be evaluated where the agency is con- will be 0.419. cerned with the effect of the choice on all crashes. Equation 8 is used since all crashes for divided roads must be estimated. It is assumed that the geometric features of the Table A-1. Sample data set calculations for roadway segment are homogeneous (i.e., there is no need to calibration factor. subdivide the segment): Crashes cr Segment Length ADT Shoulder Obs Exp E [ N ]AD 4 = 0.75 e -4.235- ln 12 + 0.835 ln 10000 + 0.781(0) + 0.172(1) + 0.228(1) - 0.118( 4 ) = 1.84 1 0.25 12,000 6 4 2.38 yr 2 0.30 10,000 4 3 3.02 mi 3 0.44 16,000 8 6 4.51 cr E [ N ]AD 8 = 0.75 e -4.235- ln 12 + 0.835 ln 10000 + 0.781(0) + 0.172(1) + 0.228(1) - 0.118(8) = 1.15 4 0.20 18,000 8 4 2.36 yr ... ... ... ... ... ... mi ... ... ... ... ... ... ... ... ... ... ... ... So, the choice of the wider shoulder will result in a reduction 100 0.42 17,000 6 6 6.09 of 0.69 crashes per year per mile for this roadway segment. Total 70 50