Pavement Marking Materials and Markers: Real-World Relationship Between Retroreflectivity and Safety Over Time (2006)

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82 3. Chapter 3 Study Methodology This chapter presents the study methodology for correlating the safety impact of pavement markings and markers with their retroreflectivity. The methodology is based upon time-series approach as opposed to the traditional before-after design. This research study is not the first one designed to address the safety and cost effectiveness of pavement markings and markers, however previous studies have often been inconclusive on several key questions. 3.1. Vision of the Research Study The overall vision of this research study is to provide agencies with the ability to make informed decisions regarding the use of pavement marking materials and markers, including their maintenance/construction activities based on the safety impacts and cost-effectiveness of different pavement marking and marker management policies. In this report, pavement markings (and materials) and markers refer to those in common use for longitudinal delineation of all road types. A review of the literature has determined that the primary research gap concerning pavement markings and markers is a study of the relationship between safety and visibility. Safety is defined here as the number of crashes by severity (e.g., fatal, nonfatal injury, property damage only) per unit of time and distance during non-daylight conditions. Visibility at night is defined here as the retroreflectivity of the delineation. This research study did not explore the daytime relationship between safety and visibility. The relationships between visibility, driver performance and driver preference have been studied (33,83,16,84,55). Previous research has also reviewed the overall safety effect of newly installed pavement markings (85,58,86,54,61,60) and markers (63,87,88,89,90). However, underlying previous studies of the overall safety effect of a marking or marker was the assumption that the visibility of markings and markers is constant throughout the evaluation period. Unfortunately, the reality is that the visibility of markers and markings degrades over time. As a result, the quantitative relationship between visibility and safety has yet to be determined. In other words the question is, how do different levels of visibility of markings and markers affect the safety of highways? Understanding the relationship between visibility and safety is important in: • Establishing guidelines for the use of pavement marking material and markers; and • Setting minimum retroreflectivity guidelines for pavement markings and markers. Previous research that examined the relationship between visibility and safety has been inconclusive (1), or has failed to adequately address issues such as seasonality and the non-linearity of

83 traffic data (30). Currently, recommended minimum retroreflectivity guidelines are based on driver performance and driver preference responses that were measured in the field or during simulator studies (29). Superior recommendations and guidelines for their use will be achieved when a cost analysis of pavement marking and markers include their safety effects. A comprehensive cost analysis requires a formalized structure which takes into account total costs and total benefits for assessing the effectiveness of markings and markers. The following variables have been included in the study methodology: • Road Type: • Multi-lane freeways • Multi-lane highways • Two-lane highways • Time of Day: • Non-daylight crashes (nighttime crashes, which includes dawn and dusk) • Crash Type: • Non-intersection crashes • Crash Severity: • All crashes combined (total) • Fatal and nonfatal injury crashes • Pavement Markings and Markers: • Markings only • Markings and Markers • Pavement: • Surface material type • Climate Region: • As a function of precipitation and temperature • Snow Removal: • Historical snowfall is used as a proxy measure for the amount of snow removal • Traffic Volume: • Full range of traffic volumes by road type • By AADT bin ranges The previous variables define the scope of the study. No distinction was made between roads based upon environment (rural or urban), roadway geometry (tangent or curve), or whether the surface condition (wet or dry). The analysis focused on retroreflectivity and its effect on non-daylight crashes at non-intersection locations.

84 3.2. Methodology Outline The methodology adopted has five major steps. The first two steps involve data collection and preparation. The third step involves modeling the retroreflectivity of pavement markings and markers over time under different conditions. Using the resulting models, the fourth step allows all different markings and all different markers to be compared in terms of their retroreflectivity profiles over time. In the fifth step, the retroreflectivity profiles over time and the number of crashes by severity over time are analyzed in concert to determine the relationship between retroreflectivity of longitudinal markings and markers and crashes. In order to separate the cyclic pavement marking and marker safety effect from the seasonal effect, separate seasonal effect multipliers are estimated, where a constant seasonal effect for all roads of the same type is assumed. The full range of experimental conditions is shown in Figure 20.

85 Road Class 2-lane Highway Road Class Multi-lane Highway Road Class Multi-lane Freeway Retroreflectivity Pavement Type Concrete,Asphalt Retroreflectivity Modeling Safety Modeling Volume AADT Snow Removal Heavy, medium-light No Snowfall Climate Region Retroreflectivity and Safety Delineation Markings & Markers Delineation Markings & Markers Delineation Markings & Markers Crash / Severity Crash / Severity Crash / Severity Figure 20. Full range of experimental conditions

86 3.3. Study Enhanced Methodology There are three features of this research methodology that expands on what has been previously accomplished: • The focus is on determining the direct relationship between retroreflectivity and crash frequency and severity (safety); • The focus is on most materials in common use; and • The focus is on the change in safety over time. These three features of this study methodology are discussed in detail in the following sections. 3.3.1. Focus on the Relationship Between Visibility and Safety Pavement markings and markers are unlike many other engineering safety treatments in that the treatment is continuously changing over time. Most treatments remain unchanged over time (for example, installing a dedicated left turn lane to deal with rear-end crashes). In contrast, pavement markings and markers change in a measurable/quantifiable way from the date of installation. The non-daylight retroreflectivity visibility of pavement markings and markers degrades over time as the markings and markers separate from and are worn off the pavement. This change in the condition of the markings and markers may affect their safety performance. In addition, markings and markers are remarked on a regular basis whereas many other engineering treatments require little to no regular maintenance. Waterborne paint, for example, in many jurisdictions is remarked on a yearly basis, which results in a cyclic pattern for the retroreflectivity of the markings and markers. Other markings follow different cyclic patterns. Nearly all variants of the before-after research design assume that the safety effect of a treatment remains constant during each time period. Because of this assumption, the safety of markings and markers as a function of visibility cannot be assessed using a traditional before-after design if time is not taken into account. Most previous studies have used the before-after design without including the changing performance of the markings and markers over time as a factor. 3.3.2. Focus upon Materials in Common Use Not all types of pavement marking materials and markers are used to the same extent (Section 2.1). The most commonly-used marking material is waterborne paint which is applied on 65% of total road mileage in the U.S. Thermoplastic is second accounting for about 25% of total road mileage based

87 upon industry panel sources (91). This research study focuses upon materials in common use. This focus optimizes the research design toward the application of the findings by the transportation agencies. 3.3.3. Focus on Safety Over Time Hauer et al. (92) provide an example of research which examines changes in safety as a function of time, specifically the effect of resurfacing on safety. Hauer et al. (92) conducted a before-after study with the specific intent of understanding the effect of resurfacing on safety over time. Therefore, it is of critical importance to know when the treatment has occurred. Knowing when the treatment occurred would be important for the before period, the after period, or for any comparison sites, since the treatment is the variable of interest. In the Hauer et al. (92) study, only the date of the pavement resurfacing for the after period of the study was known, while the before period resurfacing date was unknown. Post- analysis, Hauer et al. (92) discussed their study design: “There is one deficiency that became apparent only after the analysis was completed. The results indicate that as the pavement ages accidents diminish. Because all treated road sections were resurfaced within 1 year of each other [treatment], their pavements must have been deteriorating approximately in tandem; they were all in need of repair just before resurfacing and in good shape 5 to 7 years earlier. If so there is a systematic factor that the analysis in Step 1 [estimating the expected number of accidents] neglected. The net effect of this deficiency is that prediction of what would be expected without resurfacing has been produced as if a constant pavement condition prevailed during the entire before-resurfacing period.” Hauer et al. (92) p37 Hauer et al. (92) called the overlooking of the date of the treatment (resurfacing) during the before period a “logical deficiency”. This type of logical deficiency is not limited to Hauer et al. (92) as both Migletz et al. (2) and Cottrell and Hanson (3) did not obtain or did not use the date of restriping in their analysis of the before period. In order to avoid this logical deficiency, the proposed design requires that it is necessary to know when striping has occurred for all time periods, and for all roads. Only by using the age of markings in an analysis of pavement markings can the relationship between restriping and safety be understood. 3.4. Methodology for Modeling Retroreflectivity Since retroreflectivity measurements of pavement markings and markers are not usually conducted by state agencies in a systematic manner, it is not possible to attain observed retroreflectivity values when studying historical crash data for any particular locations. Therefore, there is a need to develop such models of retroreflectivity in order to estimate how retroreflectivity changes with time and road use. Retroreflectivity is used as a common metric to compare performance across material types, and where two materials result with the same retroreflectivity, these are assumed to have the same safety

88 effect. As discussed in the literature review (Section 2.2.3), the National Transportation Product Evaluation founded in 1994 has been collecting retroreflectivity data from trafficked roads at test decks in various states. The retroreflectivity models based upon NTPEP data were developed by following top- down approach: 1. Examine the variables affecting retroreflectivity starting with the variable with the largest influence proceeding with the next most important variable to the variable with the smallest influence, based upon the test deck data available. So for example, the variable with the largest effect on retroreflectivity is age, and the second largest effect is color. 2. By setting on the largest effect variable, based upon graphs and model residuals, determine the most appropriate model form describing the relationship between the variable and retroreflectivity. Calibrate the model parameters to optimize the fit to the average retroreflectivity value for the data. 3. Once the most appropriate model form has been identified, subdivide the data by the next largest variable affecting retroreflectivity. So for example, after fitting a model as a function of marking age, the next models to fit would be for white and yellow markings over time. 4. Based upon graphs and model residuals determine the most appropriate model form for the data subset, and calibrate the model to optimize the fit. 5. If the subset model form is the same as the parent category, and the residuals show no pattern, collapse the subset variable data into one model. So if there is no pattern to the residuals for models of retroreflectivity collected on asphalt compared to concrete, for example, then the same model form is adopted for both types of pavement surface. 6. Repeat this analysis for each variable affecting retroreflectivity. Once the retroreflectivity models are complete, they need to be linked to roadway and crash data in order to examine the relationship between safety and retroreflectivity as described in the next section. 3.5. Methodology for Examining the Relationship Between Safety and Retroreflectivity As described, the methodology aims to quantify the relationship between the retroreflectivity of markings and markers and non-daylight, non-intersection crashes by severity (target crashes). The most likely cause-effect scenario is that pavement markings and markers affect perception and thereby may

89 affect the probability of target crash occurrence and/or of crash severity (if perception affects speed choice). From the time when a marking is freshly painted or a new marker installed, retroreflectivity (denoted as R) diminishes until new markings or markers are installed. This cyclical pattern of decline and restoration of R may be reflected in the corresponding time-series of reported non-daylight crash counts. In order to analyze the relationship between crashes and safety, the concept of retroreflectivity bins is introduced where there are ‘n’ retroreflectivity bins i=1, 2, ...., n. Thus, for example, i=1 when R>250, i=2 when 200<R≤250, i=3 when 150<R≤200 and i=4 when R≤150. In this example, n=4. On this basis there are n multipliers qi , i=1, 2, ...., n. If a marking with R in category i reduces the probability of reported non-daylight crash occurrence relative to markings in category n by 5%, qi /qn=0.95; if the marking with R in category i increases the probability of target crash occurrence relative to markings in category n by 4%, qi/qn will be 1.04. This research study aims to estimate the magnitude of qi, i=1, 2, ..., n and, if appropriate, fit a smooth function to these estimates. In other words, this research aims to estimate the magnitude of these multipliers as a function of the retroreflectivity of the pavement markings and markers over time. Thus, data for the safety modeling of R will be in the form of: • The monthly count of reported non-daylight, non-intersection crashes on roads segments; • The dates of remarking without resurfacing for same roads; and • A model that predicts R on these roads for each calendar month (based on models built from NTPEP data). Data from several sources (Chapter 4) will be entered into a large database. Each row in this database corresponds to one road segment that all its attributes are the same and the markings were painted on the same calendar month, thus have the same R. That is, it has been remarked as a unit by the same materials and has the same traits that influence R. These are named “homogeneous segments” (Section 3.6). Thus, should it turn out in the course of modeling the relationship between R and safety, that, e.g., pavement surface type and AADT do not materially affect R, there is no need to discontinue a segment when pavement surface type or AADT change, and homogeneous segments will be redefined accordingly. As an example consider apportioning retroreflectivity into one of four bin ranges as shown in Table 21. For a specific homogeneous segment, the monthly target crash counts for, say, the years 1998, 1999 and 2000 are grouped (Table 22), and indexed by year and month so that for January 1998 y=1, m=1 and for December 2000 y=3 and m=12. Assuming that this road segment has been remarked in May 1998,

90 July 1999 and July 2000, the month of remarking will be indexed “0” and subsequent months as a (a=0,1,…A). Based on ‘a’ (and other traits of the road segment), and using the retroreflectivity model (Section 3.4), one can compute the estimated retroreflectivity R in year y and month m after each remarking (Ry,m) Table 21. Example retroreflectivity bin ranges and numbers Retroreflectivity Range Retroreflectivity Bin Number Rwhite>300 1 250<Rwhite≤300 2 200<Rwhite≤250 3 Rwhite≤200 4

91 Table 22. Illustration of retroreflectivity table for analysis (months of remarking in bold) Year Month M A Ry,m i Retroreflectivity Bin Target Crash Counts Jan 1 7 386 1 0 Feb 2 8 335 1 3 Mar 3 9 295 2 0 Apr 4 10 264 2 1 May 5 0 386 1 1 Jun 6 1 335 1 0 Jul 7 2 295 2 1 Aug 8 3 264 2 1 Sep 9 4 239 3 0 Oct 10 5 218 3 1 Nov 11 6 200 4 1 1998 Dec 12 7 186 4 2 Jan 1 8 173 4 0 Feb 2 9 162 4 2 Mar 3 10 152 4 2 Apr 4 11 143 4 3 May 5 12 135 4 2 Jun 6 13 129 4 2 Jul 7 0 386 1 0 Aug 8 1 335 1 3 Sep 9 2 295 2 2 Oct 10 3 264 2 1 Nov 11 4 239 3 1 1999 Dec 12 5 218 3 3 Jan 1 6 200 4 2 Feb 2 7 186 4 3 Mar 3 8 173 4 3 Apr 4 9 162 4 0 May 5 10 152 4 0 Jun 6 11 143 4 3 Jul 7 0 386 1 1 Aug 8 1 335 1 3 Sep 9 2 295 2 2 Oct 10 3 264 2 0 Nov 11 4 239 3 1 2000 Dec 12 5 218 3 1

92 It is assumed that each crash count (rightmost column in Table 22) is a realization of a Poisson random variable the mean of which is μy, m, i to indicate that it varies as a function of Year (y), Month of Year (m), and the retroreflectivity in bin ‘i’. More specifically, it is assumed that μy, m, i can be represented as a product of three elements: μy which represents how the annual mean number of target crashes for the road segment would change from year to year (because of changes in annual AADT, vehicle fleet, driver demography, annual precipitation etc.) if retroreflectivity was that of category ‘n’. pm which is the typical seasonal monthly proportion of yearly target crashes on the road segment (such that 112 1 =∑ =m mp ) and represents the typical within-year variations in traffic, precipitation, kind of road use and condition. qi which is the aforementioned multiplier representing the influence of retroreflectivity in bin i. As illustrated in Table 21, the retroreflectivity prevailing in year y and month m (Ry,m) determines the retroreflectivity bin. Since qi changes with y and m, the notation qi(y,m) will be used. Thus, the expected number of crashes in year y and month m in which the retroreflectivity is in bin ‘i’ is: )m,y(qp imi,m,y ××μ=μ y Equation 3 For a road segment for which there are, for example, three years of data, there are three unknown values of μy, 11 unknown values of pm, and n unknown values of qi. For the road segment in Table 22, there are 36 crash counts. It is assumed that the unknown seasonal monthly proportions (pm), and marking effect multipliers (qi) are common to all road segments of the same kind (2-lane highways, etc). Thus, every additional road segment adds Y unknown μy’s (depending on the number of years, Y) and 12×Y data points. Therefore, it is evident that estimation by least square or by maximizing likelihood would be feasible even if no model for μy is carried out. The likelihood function can be derived as follows. Let cy,m the count of target crashes in year y and month m. By the Poisson assumption:

93 ∏ ∏= = = − Y 1y 12 1m μ my, c im,y, Y,12Y,2Y,11,121,21,1 im,y, my, e !c μ )c..., ,c,c,...,c,...,c,P(c Equation 4 Viewing this as the likelihood component for one road segment, and omitting the constant cy,m!, the natural logarithm is: ))]m,y(qp())m,y(qlnpln(lnc[lnc imy Y 1y 12 1m imym,yi,m,y Y 1y 12 1m i,m,ym,y μ∑ ∑ −++μ=μ∑ ∑ −μ = == = Equation 5 This study is interested in the estimated values of the multipliers qi. The estimates of μy and pm are of no direct interest - they are nuisance parameters. Therefore, it is advantageous to take the μy out of estimation by assuming that ∑ == 12 1 ,y m mycμ . The methodology for determining the relationship between retroreflectivity and crashes involves maximizing Equation 5. Equation 5 is the maximum likelihood function and it can be solved by selecting values for the parameters uy, pm, qr, which maximize the function. These values that maximize the function are the values which “make the observed data most probable or most likely” (93). The values for the parameters are selected in an iterative fashion using an optimization procedure, such as the Solver add-in tool in Microsoft Excel. Suppose now that a road segment has yellow and white markings and that these differ in lifetime so that the remarking of each color follows its own cycle. Thus in any year and month the retroreflectivity bins of the white lines will be ‘i’ and the retroreflectivity bins of the yellow color will be ‘j’. Thus, a matrix of retroreflectivity bins might look like Table 23 and the number of parameters qi,j will vary, and in this illustration case there are 12 qi,j. For example, for a certain month when Rwhite=172 and RYellow=212, then i=3 and j=1, their parameter is q7. A road segment with markers will add another dimension to the matrix of retroreflectivity bins. Table 23. Illustration of retroreflectivity bins RYellow>200 150<RYellow≤200 RYellow≤150 j=1 j=2 j=3 Rwhite>300 i=1 q1 q2 q3 250<Rwhite≤300 i=2 q4 q5 q6 200<Rwhite≤250 i=3 q7 q8 q9 Rwhite≤200 i=4 q10 q11 q12

94 By applying Equation 5 and simultaneously solving for pm and qr, the seasonal effect and the safety effect of retroreflectivity will be estimated. The values for pm and qr are multipliers may be thought of as crash or accident modification factors. 3.6. Homogeneous Segments In order to allow comparisons between segments to be made the road segments must first be homogeneous. A homogeneous segment is defined as a segment in which the variables of interest (road identification, traffic volume, pavement material type, marking remarking or restriping dates, and marker installation dates) are either “all” consistent within the segment, or “some” are consistent based on their relevance toward the definition of the model form by means of the modeling as explained in Section 5.1. For example, consider a 5-mile segment of Sinclair Road (2-lane highway) that stretches from milepost (MP) 13.5 to 18.5, with the following variables of interest: • Road Identification: California, District 12, 2-lane highway of Sinclair Rd, from milepost 13.5 to 18.5, data available from 1998 to 2000. (Table 24). • Pavement Surface: MP 13.5-15.0 was reconstructed with concrete in January 1998. (Table 25). • Traffic Volume: MP 13.5-17.2 experienced 8,000 AADT in years 1998-2000, MP 17.2-18.5 experienced 9,000 AADT in years 1998-2000. (Table 26). • Marker Installation Dates: January 1998 makers were installed on all 5 miles. In January 2000, makers were reinstalled from between MP 13.5 to 15.5. (Table 27). • Marking Installation Dates: January 1998, 1999, 2000 markings were restriped for all five miles. (Table 28). Table 24 to Table 28 illustrate how the inclusion of more and more variables of interest causes the number of rows and columns increases. Table 28 illustrates a full table including all five classes of variables of interest. Table 24. Variables: road identification Year State District 2-lane Highway Start MP End MP 1998 California 12 Sinclair Rd 13.5 18.5 1999 California 12 Sinclair Rd 13.5 18.5 2000 California 12 Sinclair Rd 13.5 18.5

95 Table 25. Variables: pavement material type Year State District 2-lane Highway Start MPEnd MPPavement 1998 California 12 Sinclair Rd 13.5 15.0 Concrete 1998 California 12 Sinclair Rd 15.0 18.5 Asphalt 1999 California 12 Sinclair Rd 13.5 15.0 Concrete 1999 California 12 Sinclair Rd 15.0 18.5 Asphalt 2000 California 12 Sinclair Rd 13.5 15.0 Concrete 2000 California 12 Sinclair Rd 15.0 18.5 Asphalt Table 26. Variables: traffic volume Year State District 2-lane Highway Start MPEnd MPPavement Volume (AADT) 1998 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 1998 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 1998 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 1999 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 1999 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 1999 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 2000 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 2000 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 2000 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 Table 27. Variables: marker installation dates Year State District 2-lane Highway Start MPEnd MPPavement Volume (AADT) Last Marker Installation Date 1998 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 Jan, 1998 1998 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 Jan, 1998 1998 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 Jan, 1998 1999 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 Jan, 1998 1999 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 Jan, 1998 1999 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 Jan, 1998 2000 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 Jan, 2000 2000 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 Jan, 2000 2000 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 Jan, 1998

96 Table 28. Variables marking restriping dates Year State District 2-lane Highway Start MP End MP Pavement Volume (AADT) Last Marker Installation Date Last Marking Installation Date 1998 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 Jan, 1998 Jan, 1998 1998 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 Jan, 1998 Jan, 1998 1998 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 Jan, 1998 Jan, 1998 1999 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 Jan, 1998 Jan, 1999 1999 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 Jan, 1998 Jan, 1999 1999 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 Jan, 1998 Jan, 1999 2000 California 12 Sinclair Rd 13.5 15.0 Concrete 8,000 Jan, 2000 Jan, 2000 2000 California 12 Sinclair Rd 15.0 17.2 Asphalt 8,000 Jan, 2000 Jan, 2000 2000 California 12 Sinclair Rd 17.2 18.5 Asphalt 9,000 Jan, 1998 Jan, 2000 3.7. Data Requirements - Simulation The research team conducted a comprehensive experimental design using simulated crash data as a function of pavement markings. An extensive effort was needed to generate artificial but credible data to validate the estimation procedure for pavement markings and determine the amount of data required to achieve sufficiently accurate results. This is believed to be the first time such approach has been applied for such a purpose. A detailed description of the simulation exercise may be found in Appendix E. Detailed simulation results are given in Appendix G. Appendix G presents in graphical format the results of 40 simulation exercises representing more than 5 million crashes. Since this is a simulation, generating millions of crashes is not as costly as collecting the real data. For smaller sample sizes, more advanced validation methods would have been necessary, such as bootstrapping or jackknife testing (e.g., (94)).The conclusions of the simulation exercise are summarized in the following paragraphs. For this study one target crash represents one data point. To have a realistic probability of success, one must answer the question how much data are needed to detect a nominal safety effect? Specifically, this question may be rephrased as: How many target crashes are needed to detect a 5% change in the safety effect of new pavement markings when compared to old markings? The simulation results give the minimal amount data needed to detect a 5% difference in safety (Table 29) for non-daylight, non-intersection locations. At least 50,000 target crashes are needed for 2- lane roads, 200,000 crashes for multi-lane highways, and 200,000 crashes for multi-lane freeways.

97 Table 29. Number of total target crashes required by road type Road Type Required number of target crashes to detect a 5% change in safety 2-lane roads 50,000 Multi-lane highway 200,000 Multi-lane freeway 200,000 Given a typical given crash rate, the total number of crashes can also be expressed in terms of miles of road and years of data (Table 31). Converting 50,000 crashes into a number of years of data and miles of road is equal to: Number of target crashes ÷ crash rate ÷AADT= yearsmile×=÷÷ 364,26311200061.0000,50 Where the average ADT of 3112 and a non-daylight crash rate of 0.00061 for 2-lane highways is taken from HSIS data as shown in Table 31.

98 Table 30. HSIS volume and crash information for six states, and the values used in the simulation Simulation Values Road Class Variable MN CA NC IL UT OH Average Minimum Maximum Traffic Volumea 472,233 1,719,700 954,718 1,523,788 821574 1323218 Average ADTb 1,294 4,712 2,616 4,175 2,251 3,625 3112 1212 5012 Crash Rate (All day)c 0.8219 2.3 1.63 3.08 2.11 2.57 2-Lane Highways Non-daylight Crash Rate c 0.22654 0.59 0.5 0.82 0.54 0.98 0.61 0.00024 0.00098 Traffic Volumea 5,019,484 8,202,905 6,456,359 7,895,313 6494722 5431506 Average ADTb 13,752 22,474 17,689 21,631 17,794 14,881 18037 13537 22537 Crash Rate (All day) c 10.53 14.9 12.83 33.11 27.38 6 Multi-Lane Highways Non-daylight Crash Rate c 2.55 3.56 2.64 7.59 5.99 1.86 4.03 0.00193 0.00613 Traffic Volumea 13,760,000 30,560,000 14,440,000 11,300,000 7,896,936 15250000 Average ADTb 37,699 83,726 39,562 30,959 21,635 41,781 42560 22560 62560 Crash Rate (All day) c 12.73 30.11 10.35 10.13 7.97 7.07 Multi-Lane Freeways Non-daylight Crash Rate c 3.71 8.23 2.75 3.41 2.21 2.41 3.79 0.00229 0.00529 a Traffic Volume = average annual traffic volume = (AADT * segment length * 365) / summation of segment lengths by road class b Average ADT = traffic volume / 365, i.e., average vehicles / day c Crash Rate = 1000 × crashes / miles

99 Thus, if 26,364 miles × years are divided by 2 years of data, it means that 13,182 miles of 2-lane rural roads over two years would be needed to detect a 5% change in the safety effect of pavement markings. Based on similar calculations, Table 31 was developed. Table 31. Number years and miles of road per year required by road type Years of Data 2 3 4 5 6 7 8 9 10 12 2-lane highway 50,000 Crashes Miles of Road 13182 8788 6591 5273 4394 3766 3296 2929 2636 2397 Multi-lane highway 200,000 Crashes Miles of Road 1375 917 688 550 458 393 344 306 275 250 Multi-lane freeway 200,000 Crashes Miles of Road 620 414 310 248 207 177 155 138 124 113 Previous pavement marking and marker studies have rarely collected data of this magnitude, which may explain why previous studies have often been inconclusive. These data requirement estimates would not have been known without conducting the simulation exercise.