Quantifying the Effectiveness of Performance-Based Pavement Marking Maintenance Contracts Srinivas Reddy Geedipally, Praprut Songchitruksa, and Adam M. Pike paper presents the evaluation related to (a) the safety performance of roadways with pavement markings maintained with PBPMMCs, and (b) the average decay in retroreflectivity levels measured on different road segments to determine if there are any differences between PBPMMC and non-PBPMMC contracts. The paper is divided into five parts. The first part summarizes the background information. The second part describes the methodology used for conducting the safety and decay analysis. The third part presents the data collection process and a summary of the data set. The fourth part describes the modeling results. The last part provides the concluding remarks.
Pavement markings play a vital role in the safe and efficient movement of traffic. In 2010, FHWA began the process of amending existing regulations and issued a notice of proposed amendments to adopt minimum pavement marking retroreflectivity levels. Performance-based pavement marking maintenance contracts (PBPMMCs) are one of the latest mechanisms used to maintain adequate pavement marking performance levels. The Texas Department of Transportation has issued two PBPMMCs, but the effectiveness of these contracts compared with other contracting mechanisms from a performance or safety perspective has not been investigated. This study quantified the effectiveness of PBPMMCs by evaluating the delivered pavement marking performance and safety performance. When compared with other contracting mechanisms, the evaluations found inconclusive evidence as to the benefit of the PBPMMC from a safety and marking performance standpoint. The results are inconclusive perhaps because the markings were maintained adequately before the PBPMMC or because the PBPMMC did not provide a significant improvement in the marking systems.
Background Pavement markings are unlike many other engineering safety treatments in that the treatment is continuously changing over time. One common challenge that researchers face when attempting to address this is how to capture these visibility changes over time and synchronize them with crash occurrences for safety evaluation purposes. Typically, as pavement markings age, their retroreflectivity, and subsequently their visibility, degrades. The rate of degradation is dependent on many factors that are not easily accounted for, such as age of the marking, marking material type, bead type, marking color, traffic conditions, roadway surface type, installation quality, initial retroreflectivity level, winter maintenance, and environmental conditions. Some general background information is provided below; a full literature review can be found in the full research report (1).
Pavement markings play a vital role in the safe and efficient movement of traffic. In 2010, FHWA began the process of amending existing regulations and issued a notice of proposed amendments to adopt minimum pavement marking retroreflectivity levels. These minimum levels will need to be maintained on all pavement markings on the nation’s roadways but do not address adverse weather conditions. Performance-based pavement marking maintenance contracts (PBPMMCs) are one of the latest mechanisms used to maintain adequate pavement marking performance and to share the risk of maintaining minimum performance levels. The Texas Department of Transportation (DOT) has issued two PBPMMCs, but the effectiveness of these contracts compared with other contracting mechanisms (annual district-wide, warranty, or hybrid contracts) from a performance or safety perspective has not been evaluated. The Texas A&M Transportation Institute conducted a research project to evaluate the effectiveness of PBPMMCs by evaluating the delivered pavement marking performance, safety performance, potential cost savings, and most suitable performance measures and measurement protocols for inclusion in future PBPMMCs (1). This
Research Findings That Show Some Evidence of a Safety Relationship Migletz et al. used a before–after evaluation to determine the effects of pavement marking retroreflectivity on safety (2, 3). Pavement marking restriping was considered when the retroreflectivity level fell below a minimum level. The study considered daylight and nighttime crashes separately, with nighttime crashes including dawn and dusk crashes. In addition, dry and wet crashes were examined separately to assess the safety of all-weather pavement markings. The paired sign evaluation did not provide any statistically significant conclusions. Yoked-comparison evaluation found that allweather markings may be effective overall in reducing the number of crashes; however, the result was not statistically significant. Abboud and Bowman conducted a study in Alabama to establish a relationship between retroreflectivity and crashes and to identify
S. R. Geedipally, Arlington Office, Texas A&M Transportation Institute, 110 North Davis Drive, Suite 101, Texas A&M University System, Arlington, TX 76013. P. Songchitruksa and A. M. Pike, Texas A&M Transportation Institute, 3135 TAMU, Texas A&M University System, College Station, TX 77843-3135. Corresponding author: S. R. Geedipally,
[email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 2482, Transportation Research Board, Washington, D.C., 2015, pp. 23–31. DOI: 10.3141/2482-04 23
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the minimum retroreflectivity value that corresponds to a maximum allowable crash rate (4). Based on the critical crash rate, the study determined a minimum retroreflectivity threshold of 150 mcd/m2/lx for white pavement markings. Bahar et al. found that the expected crash frequency is not linearly proportional to traffic volume and the conclusions of this study may not be true (5). Bahar et al. also pointed out that this study did not address seasonal effects or apply any analysis methods that could minimize seasonal bias (5). A research study of pavement markings and safety was conducted by Smadi et al. for the Iowa DOT (6). The study investigated the correlation between pavement marking retroreflectivity and cor responding crash and traffic data on all state primary roads. The study found that the retroreflectivity levels have a significant correlation with crash occurrence probability for four data subsets— interstate, white edge line, yellow edge line, and yellow centerline data. For white edge line and yellow centerline data, crash occurrence probability was found to increase with decreasing values of retro reflectivity. The study also suggested that drivers may compensate for the risk by adjusting their driving behavior (e.g., reducing speed) if the markings have low visibility.
Research Findings That Show No Evidence of a Safety Relationship In 1999, Lee et al. conducted a study to develop a correlation between pavement marking retroreflectivity and nighttime crashes with data from four different geographic areas in Michigan (7). A linear regression analysis in this research found no evidence of a relationship between retroreflectivity and nighttime crash frequency. Lee et al. also suggested that part of the reason for the lack of relationship was the insufficient variation of the observed retroreflectivity values in the database and the limited sample size of the nighttime accidents used in the analysis (7). The authors suggested that a larger sample of nighttime accidents may allow the identification of a relationship between pavement marking retroreflectivity and nighttime accidents. In 2001, Cottrell and Hanson conducted a before–after evaluation in Virginia to determine the impact of white pavement marking materials on crashes (8). The study found inconclusive evidence of a relationship between crashes and retroreflectivity, because some sites showed an increase in crash frequency, while others exhibited a decrease in crash frequency. NCHRP Project 17-28 research by Bahar et al. evaluated the safety effects of longitudinal pavement markings and markers over time with retroreflectivity data collected in California for multilane freeways, multilane highways, and two-lane highways (5). The study found no evidence of a relationship between safety and pavement marking retroreflectivity for all roads that are maintained at the level implemented by California. The authors noted that California implements a pavement marking management system that results in very few segments having retroreflectivity dropping below 100 mcd/m2/lx. Masliah et al. applied a time-series methodology to identify the relationship between retroreflectivity of pavement markings and crashes (9). The data used by Bahar et al. were also used in this study (5). The results of the Bahar et al. study showed that, when the roadways are maintained at a minimum level of pavement marking retroreflectivity, the retroreflectivity levels have between no effect and a small effect on safety performance. Smadi et al. attempted to model the correlation between retro reflectivity levels and crash probability (10). For the complete data set and the two-lane roads, the authors found that there is no
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correlation between poor pavement marking retroreflectivity and higher crash probability. At the same time, for records with retro reflectivity values of 200 mcd/m2/lx or less, a statistically significant, albeit weak, relationship was determined. Smadi et al. cautioned that increased visibility may cause drivers to feel too comfortable during nighttime conditions, and drivers may then pay less attention, operate their vehicles at unsafe speeds, or both (10). Donnell et al. performed an exploratory analysis to determine the relationship between pavement marking retroreflectivity and crash frequency (11). Generalized estimating equations were used to model monthly crash frequency. The results of the study showed that yellow and white edge line pavement marking retroreflectivity does not have a statistically significant relationship with two-lane highway nighttime target crash frequency. For multilane highways, the retroreflectivity parameter estimates for white pavement marking were negative, whereas for the yellow pavement marking, they were positive. Retroreflectivity Models The retroreflectivity of pavement markings deteriorates over time and varies with traffic volume, location, environmental conditions, and other factors, and thus complicates the safety evaluation. This characteristic is unlike other engineering treatments, which remain relatively unchanged over time. In addition, markings and markers are restriped or re-marked on a regular or irregular basis, which results in a cyclical pattern for the measured retroreflectivity. This characteristic requires that target crashes should be associated with retroreflectivity readings not only spatially, but also temporally. Thamizharasan et al. developed nonlinear and linear models to predict the retroreflectivity of pavement markings (12). The nonlinear model was developed to predict the number of days required as the retroreflectivity of a newly applied pavement marking rises before dropping back to the initial value. In contrast, the linear model was developed to predict the number of days needed for the retroreflectivity of a pavement marking to drop (after the initial rise) to a minimum specified value. Bahar et al. proposed nonlinear retroreflectivity models of the following form (5): R=
1 β 0 + β1 i age + β 2 i age 2
where R = retroreflectivity of pavement stripe (mcd/m2/lx), age = age of pavement stripe (months), and β0, β1, β2 = model parameters to be estimated. Overview of Performance-Based Contracts The North Carolina DOT began issuing performance-based contracting with a pilot project in 2005. To verify the contractor’s performance, performance targets and semiannual condition assessments are performed. The contractor’s payment is based on how closely it adheres to the targets (13). Pavement markings and markers are also part of the North Carolina DOT’s performance-based contracts. The ratings after the first year of implementation indicated that performance improves over time, but does not reach the required target. Pavement markers and sign lighting were among the lowest rated components with 42% meeting the required conditions.
Geedipally, Songchitruksa, and Pike
Following the completion of the first outsourced highway maintenance contract by the Virginia DOT, Ozbek suggested that the contract terms allowed the contractor to maintain the network at the minimum service level required, by applying less expensive measures with a shorter life span (14). To transfer long-term risk to the contractor—the party with the most control over pavement quality and performance—Ozbek proposed that the contract include a warranty clause to guarantee the work of the contractor beyond the expiration of the contract. Similarly, Kim et al. suggested that performance-based service contracting should use long-term contracts with disincentive clauses (15). Kim et al. showed that if such contracts were considered, the contractor’s optimal maintenance strategy would include actions that substantially add to the structural capacity of a pavement, such as thick overlays, rather than actions that only cover surface distresses (15). Manion and Tighe studied the effectiveness of the performancespecified maintenance contracts in New Zealand from the perspective of the social cost of crashes (16). The contractor’s performance was measured to determine the social cost of crashes that occur on the network regardless of crash causes. The contracts also required that the contractor conduct a preliminary accident investigation at all fatal and selected serious injury crash sites. The contractor must make an assessment of the retroreflectivity as part of the crash investigation. The reduction in the social cost of crashes on the network was compared with national trends on the remainder of the national highway network and the improvement was found to be significantly better than the corresponding national figures. Methodology This section is divided into two parts. The first part presents the methodology used for the safety analysis and the second part presents the methodology used for the decay analysis. Safety Analysis
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Step 2. Define Comparison Group The comparison group represents those crashes that are not associated with pavement marking retroreflectivity. In this study, crashes occurring during the daytime were considered as the comparison group. The purpose of the comparison group was to estimate the change in crash frequency that would have occurred at the sites if they were not maintained under PBPMMCs. The reasoning was that the markings would be visible during daytime regardless of the level of retro reflectivity. Each of the following incidents describes crashes that are not associated with poor pavement marking visibility, although the crash may still fit the aforementioned criteria: • Driver’s alcohol or drug use, • Carelessness or fatigue, • Defective equipment, • Lost control because of shifting load, and • Skidding. Step 3. Predict the Expected Number of Crashes and Variances for the After Period Since other factors may cause an effect, after-period crash frequency and variances that are either not measured or produce an influence on safety must be considered. In this study, the after period refers to the period beginning one year after the start of the PBPMMC. The analytical procedure used in this study was described in detail in Hauer (17). The expected number of after-period crashes and their variances for site i (site i represents a group of roadway segments on a control section) had the treatment not been implemented at the treated site is given as πˆ = rˆT K and
Crash frequency counts on roadway segments were combined within each control section to determine the effectiveness that the PBPMMCs had on safety in the Dallas and San Antonio, Texas, districts. The two districts were also combined to develop an overall estimate of the safety effectiveness of the contracts.
1 vaˆr {rˆT } vaˆr ( πˆ ) = πˆ + K rT2
Step 1. Define Target Crashes
where
Target crashes were used as the absolute measure of safety. Target crashes were defined as those types of crashes that are likely influenced by poor pavement marking visibility (e.g., nonintersection and nondaylight crashes). The team combined the findings from a comprehensive literature review and expertise with Texas crash databases to form a viable definition of target crashes that was used to assess the safety performance of PBPMMCs. The criteria for target crashes used in this study are as follows: • Crashes classified as nonintersection and nondriveway related, • Crashes that occurred in dark conditions, • Crashes related to dry weather, • Single-vehicle run-off-the-road and head-on collisions, and • Crash outcomes that do not include a pedestrian, train, pedacyclist, or animal.
2
N M with rˆT = 1 1+ M and
1 vaˆr {rˆT } 1 ≅ + r T2 M N
K = total crash counts during before period in treated group, rˆT = ratio of expected crash counts for treatment group, M = total crash counts during before period in comparison group, and N = total crash counts during after period in comparison group. If there were no crashes (zero) recorded on a control section in either a treatment or comparison group, then an adjustment factor of 0.5 crashes was evenly made within the control section. Step 4. Compute Sum of Predicted Crashes over All Treated Sites and Their Variances It is widely recognized that the safety effect of a treatment varies from one site to another. Thus, instead of a single site, the average safety
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effect of the treatment for a group of sites must be calculated. Therefore, the expected number of after-period crashes and their variances for a group of sites had the treatment not been implemented at the treated sites is given as
The approximate 95% confidence interval for θ is given by addˆ from θ. ˆ If the confidence interval ing and subtracting 1.96 × SE(θ) contains the value 1, then no significant effect has been observed.
N
Decay Analysis
i =1
To examine the retroreflectivity decay rates of PBPMMC versus non-PBPMMC districts, linear mixed-effect regression models were utilized. The measured retroreflectivity was defined as a response variable. The districts and the measurement periods (before and after) were included as fixed effects. The effects of average daily traffic (ADT) and age of markings were also tested as fixed effects. Each measured segment in the before and after periods was recognized as a random effect, as it directly contributes to the levels of retroreflectivity, but it was not of primary interest for the study.
πˆ = ∑ πˆ i and N
var ( πˆ ) = ∑ var ( πˆ i ) i =1
where N is the total number of sites in the treatment group and πˆ is the expected after-period crashes at all treated sites had there been no treatment.
Step 5. Compute the Sum of Actual Crashes over All Treated Sites For a treated site, crashes in the after period are influenced by the implementation of the treatment. The safety effectiveness of a treatment is known by comparing the actual crashes with the treatment to the expected crashes without the treatment. The actual number of after-period crashes for a group of treated sites is given as N
λˆ = ∑ Li i =1
where Li is the total crash count during the after period at site i. Step 6. Compute Unbiased Estimate of Safety Effectiveness of Treatment and Its Variance The index of effectiveness (θ) is defined as the ratio of safety with the treatment to what it would have been without the treatment. The parameter θ gives the overall safety effect of the treatment and is given by λ π θˆ = var ( πˆ ) 1 + ˆ 2 π The percentage of change in the number of target crashes due to ˆ the treatment is calculated by 100(1 − θ)%. If θˆ is less than 1, then the treatment has a positive safety effect. The estimated variance and standard error (SE) of the estimated safety effectiveness are given by 1 var ( πˆ ) + ˆ 2 L π var θˆ = θˆ 2 var ( πˆ ) 2 1 + ˆ 2 π
()
()
()
SE θˆ = var θˆ
Data Collection This section briefly describes the data assembly and reduction activities that were undertaken to develop a database for conducting the safety analysis.
Roadway Data The Texas DOT has issued five-year PBPMMCs in the San Antonio district since September 2006 and in the Dallas district since September 2009. For San Antonio, the sites were obtained from a list of roadways that the agency had maintained for conducting sampling for monthly assessment. The district also provided information on the construction projects that were planned during the period when the PBPMMC was active. However, the construction project data consisted of the street names for the starting and ending limits and the Texas reference markers (TRMs) were not provided. Aerial photography was used to obtain the TRMs of each road segment under construction. The Dallas district provided the data related to the roadways under PBPMMCs and information about the construction that was being planned on those roadways when the contract was active. However, the data that the Dallas district provided did not contain TRMs. TRMs were identified manually with aerial photography. There were difficulties in identifying some of the roadway segments and so not all segments were included in the analysis. The segments under PBPMMCs that fall within the construction limits were excluded from the crash analysis regardless of the construction time. The reasoning was that the construction projects provided were planned schedules, which made it difficult to verify when they actually took place. Further, the PBPMMCs have a provision that relieves the contractor of its duties when the construction projects meet certain criteria.
Crash Data The research team collected crash data from the Texas DOT’s crash records information system. The contract for the San Antonio district was from September 2006 to August 2011; the contract for the Dallas district was from September 2009 to August 2014. However, the districts indicated that they did not start charging any penalties
Geedipally, Songchitruksa, and Pike
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until after the first year and thus a period of one year after the start of the contract was not considered in the analysis. These no-penalty periods allow the contractor in both contracts to conduct the initial striping work required to bring the pavement markings up to the conditions set forth in the contract agreement. For the San Antonio district, crash data were retrieved from January 2003 to August 2006 for the before period and from September 2007 to August 2011 for the after period. For the Dallas district, crash data were retrieved from January 2007 to August 2009 for the before period and from September 2010 to December 2012 for the after period. The Dallas data ended in December 2012 because of the timeframe of the research project. Daytime and nighttime crashes were used as control and treatment groups, respectively. Table 1 summarizes the crash frequency for the control and treatment groups for the before and after periods (i.e., without and with PBPMMC) for the San Antonio and Dallas districts. The collected data were assembled into a database with spatial and temporal cross referencing across crash, traffic, and geometric records. The control section numbers and TRMs were used for this purpose. Retroreflectivity Data The research team collected pavement marking retroreflectivity data on a variety of markings in three Texas DOT districts. The Bryan, Dallas, and San Antonio districts were used as the pavement marking retroreflectivity data collection districts. The San Antonio
TABLE 1 Crash Data Summary Period
Control (daytime)
Treatment (nighttime)
Grand Total
San Antonio District After PBPMMC Total Sept. 2007–Dec. 2007 Jan. 2008–Dec. 2008 Jan. 2009–Dec. 2009 Jan. 2010–Dec. 2010 Jan. 2011–Aug. 2011 Before PBPMMC Total Jan. 2003–Dec. 2003 Jan. 2004–Dec. 2004 Jan. 2005–Dec. 2005 Jan. 2006–Aug. 2006 Grand total
1,245 70 355 294 304 222
572 49 147 149 136 91
1,817 119 502 443 440 313
963 215 255 298 195 2,208
436 116 118 131 71 1,008
1,399 331 373 329 266 3,216
820 116 352 352
160 18 61 81
980 134 413 433
729 234 298 197 1,549
196 78 66 52 356
925 312 364 249 1,905
Dallas District After PBPMMC Total Sept. 2010–Dec. 2010 Jan. 2011–Dec. 2011 Jan. 2012–Dec. 2012 Before PBPMMC Total Jan. 2007–Dec. 2007 Jan. 2008–Dec. 2008 Jan. 2009–Aug. 2009 Grand total
Note: Sept. = September; Dec. = December; Jan. = January; Aug. = August.
and Dallas districts each used a PBPMMC in one county at the time of the data collection. The Bryan district was selected because the data collection team was located in that district and to serve as a comparison district that used only the standard pavement marking contracting. San Antonio District Data were collected in the San Antonio district in May 2012 and May 2013. Approximately 800 mi of mobile pavement marking retroreflectivity data were collected. Data were collected on Interstate highways, U.S. routes, state highways, farm-to-market roads, spurs, and loops. All the markings that were measured were thermoplastic markings and most were spray-applied, but some were extruded. Several sections of newly applied markings were measured each year of the data collection. In the first year, several sections that were scheduled to be restriped after the data collection were also evaluated to determine whether these sections were truly in need of new pavement markings. Several other sections of markings that were at various stages were also evaluated. These sections tended to cross the county lines from the PBPMMC county into surrounding counties operating under standard pavement marking contracts. Dallas District Data were collected in the Dallas district in June 2012 and June 2013. Approximately 660 mi of mobile pavement marking retroreflectivity data were collected. Data were collected on Interstate highways, U.S. routes, state highways, spurs, and loops. A combination of spray and extruded thermoplastic and epoxy markings were measured. Several sections of newly applied markings were measured each year of the data collection. In the first year, one section that was scheduled to be restriped after the data collection was also evaluated to determine whether that section was truly in need of new pavement markings. Several other sections of markings that were at various stages were also evaluated. These sections tended to cross the county lines from the PBPMMC county into surrounding counties operating under standard pavement marking contracts. Bryan District Data were collected in the Bryan district in June 2012 and June 2013. Approximately 200 mi of mobile pavement marking retro reflectivity data were collected. Data were collected on state highways and farm-to-market roads. All the markings that were measured were sprayed thermoplastic. Several sections of newly applied markings were measured in the first year of the data collection. In the first year, several sections with older markings were also measured to determine the maintained retroreflectivity level and retroreflectivity degradation in a non-PBPMMC district. Modeling Results This section presents the results related to the safety and decay analysis.
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Safety Analysis This section of the paper provides the evaluation results of the safety effectiveness of PBPMMCs. Table 2 presents the average safety effect of the PBPMMCs by location in Texas. The first analysis was conducted by including dry weather-related crashes only and the results are shown from the third to fifth columns in Table 2. The analysis was done by combining the two districts and by each district separately. The analysis results suggest that there is a positive safety effect and the incidence of crashes is expected to decrease by 5.77% with the implementation of PBPMMCs. The standard deviation of this estimate of the average safety effect is 8%. At a 95% confidence interval, this result is statistically insignificant. This means that the reduction in crashes may not be caused by the contracts, but may be a just a random occurrence. In the San Antonio district, the analysis results suggest that the number of crashes increased by 3.95%; however, the standard deviation of the estimate is 11% and thus this result is highly insignificant at the 95% confidence level. At the same time, the before–after analysis of the PBPMMCs in the Dallas district suggests a decrease in the number of crashes by 26.6% with a standard deviation of 9%. Although this result is statistically significant, the decrease in crashes may not be completely attributed to the performance-based contracts. Some part of the reduction in crashes may have occurred because of other countermeasures that were implemented during the same period, or it may have occurred just by chance. In summary, the overall effect of the PBPMMCs is inconclusive, although the contracts in the Dallas district showed that the segments under contract exhibited a positive change in safety performance. This finding is consistent with the findings from several previous studies, which indicated inconclusive evidence of a relationship between safety and pavement marking retroreflectivity. Although several previous studies indicated that the presence of markings can positively improve safety (18–20), the effects of varying the range of retroreflectivity of different types of markings on safety performance have been inconclusive.
Further analysis was conducted by including wet-weather crashes, assuming that the PBPMMCs also influence crashes under wet-weather conditions (retroreflective raised pavement markers were to be maintained under the contract as well). The three right-hand columns of Table 2 present the average safety effects of the PBPMMCs in Texas when wet-weather crashes are included. Except for a small difference, the percentage change in the crashes after the implementation of PBPMMC is similar to the analysis that excluded wet-weather crashes. Thus, irrespective of the weather conditions, it can be concluded that the PBPMMCs have an insignificant effect on safety. In addition to the overall effect, it is important to understand the average safety effects that performance-based contracts have on different crash severities. The following five crash severity levels were considered: • Fatal (K), • Incapacitating injury (A), • Nonincapacitating injury (B), • Minor injury (C), and • Property damage only (PDO). As a first step, the research team conducted the analysis by each severity level separately. However, because of the small number of reported crashes, these analyses did not provide any meaningful results. To obtain statistically reliable estimates, fatal crashes were combined with the other injury types. The analysis was conducted with two severity categories: (a) fatal plus serious injury crashes (KAB) and (b) fatal plus all injury crashes (KABC). In Table 3 presents the average safety effect of PBPMMCs by severity. The results shows that KAB crashes increased by 2.7%, whereas KABC crashes decreased by 4.9%. Statistically, these changes are insignificant at the 95% confidence level, which means the safety effect of performance-based contracts on these severity categories is inconclusive. The analysis was further conducted by classifying the highways into different subgroups based on roadway class and is shown in
TABLE 2 Average Safety Effect of PBPMMCs by Weather Conditions Excluding Wet-Weather Crashes
Including Wet-Weather Crashes
Measure
Description
Overall
San Antonio District
Dallas District
Overall
San Antonio District
Dallas District
λˆ
Number of crashes observed during the after perioda Expected number of crashes during after period had PBPMMC not been implemented Variance of πˆ
789.5
607.0
180.5
940.0
744.5
195.5
833.4
578.8
243.2
936.7
639.9
242.8
3,695.5 0.942
3,001.2 1.039
663.7 0.734
4,020.6 0.999
3,505.3 1.065
515.3 0.798
0.08 5.77
0.11 −3.95
0.09 26.6
0.07 0.10
0.10 −6.52
0.09 20.2
(0.793, 1.091) No
(0.832, 1.247) No
(0.550, 0.918) Yes
(0.853, 1.145) No
(0.873, 1.258) No
(0.616, 0.981) Yes
πˆ
var (πˆ ) θˆ σ(θˆ ) 100(1 − θˆ ) (θlower, θupper) Significance a
Unbiased estimate of index of effectiveness Standard error of θˆ Percentage decrease in the number of crashesb 95% confidence interval for θ Statistically significant at 95% confidence level
Adjusted by 0.5 when zero crashes were recorded on a road segment. Negative sign means increase in crashes.
b
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TABLE 3 Average Safety Effect of PBPMMCs by Crash Severity Effect by Crash Severity Measure
Description
λˆ πˆ
Number of crashes observed during after perioda Expected number of crashes during after period had PBPMMC not been implemented Variance of πˆ Unbiased estimate of index of effectiveness Standard error of θˆ Percentage decrease in number of crashesb 95% confidence interval for θ Statistically significant at 95% confidence level
var (πˆ ) θˆ σ(θˆ ) 100(1 − θˆ ) θlower, θupper Significance
Fatal Plus Serious Injury (KAB)
Fatal Plus All Injury (KABC)
221.5 210.7
306.0 315.6
1,025.7 1.027 0.17 −2.7 (0.700, 1.354) No
1,898.2 0.951 0.14 4.9 (0.678, 1.225) No
a
Adjusted by 0.5 when zero crashes were recorded on a road segment. Negative sign means increase in crashes.
b
Table 4. The analysis focused on these subgroup combinations to identify the subgroups that are potentially influenced by PBPMMCs. The roadway classes that were examined include Interstates, U.S. and state highways, state loops and spurs, and farm-to-market roads. Other road classes, such as business routes and frontage roads, were considered but not reported here because of unreliable estimates that occurred as a result of small sample size. The estimates in Table 5 suggest that performance-based contracts have almost no effect on U.S. and state highways and a negative effect (an increase in crashes) on state loops and spurs and farm-to-market roads, although the results are statistically insignificant. The examination of performance-based contracts on Interstate highways showed a significant positive effect. The estimates show that crashes on Interstates are reduced by 33.5% with a standard deviation of 8%. Although this result is statistically significant, the decrease in crashes may not be completely attributed to the performance-based contracts. Some part of the reduction in crashes may have occurred because of the other countermeasures that were implemented during the same period or it may have occurred just by chance.
The Iowa study found that retroreflectivity has a statistically significant effect on crash occurrence probability for four data subsets: Interstate, white edgeline, yellow edgeline, and yellow centerline data (6). Those findings of statistically significant effects on crashes on Interstate highways are consistent with the findings in this study.
Decay Analysis Two models were calibrated for each marking color. The first model includes districts, measurement periods, and interaction terms between districts and measurement periods. The interaction terms were designed to capture any differences in decay among different districts in the after period (second measurement). The second model is similar to the first model except that the interaction terms were dropped. The log likelihood ratio test can be used to test between the two models whether the interaction term is statistically significant. The significance of the interaction terms indicates that the decay
TABLE 4 Average Safety Effect of PBPMMCs by Road Class Effect by Road Class Measure
Description
λˆ πˆ
Number of crashes observed during after perioda Expected number of crashes during after period had PBPMMC not been implemented Variance of πˆ
var (πˆ ) θˆ σ(θˆ ) 100(1 − θˆ ) (θlower, θupper) Significance a
Unbiased estimate of index of effectiveness Standard error of θˆ Percentage decrease in number of crashesb 95% confidence interval for θ Statistically significant at 95% confidence level
Adjusted by 0.5 when zero crashes were recorded on a road segment. Negative sign means an increase in crashes.
b
Interstate Highways
U.S. and State Highways
State Loops and Spurs
Farm-toMarket Roads
166.5 248.1
177.5 176.2
98.5 85.7
195.0 184.6
570.1 0.665 0.08 33.5 (0.505, 0.825) Yes
526.6 0.990 0.15 1.0 (0.703, 1.277) No
199.2 1.119 0.21 −11.9 (0.707, 1.531) No
599.8 1.038 0.15 −3.8 (0.737, 1.340) No
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TABLE 5 White Marking Mixed-Effects Retroreflectivity Models
TABLE 6 Yellow Marking Mixed-Effects Retroreflectivity Models
Fixed Effect
Fixed Effect
Estimate
SE
t-Value
Model 1, with PBPMMC fixed effects by districts Intercept Log of ADT 1 if DAL, 0 if otherwise 1 if SAT, 0 if otherwise 1 if PBPMMC, 0 if otherwise 1 if PBPMMC for DAL, 0 if otherwise 1 if PBPMMC for SAT, 0 if otherwise
591.24 −21.95 82.81 17.25 −85.58 −0.66 0.22 591.30 −21.95 82.49 17.35 −85.79
SE
t-Value
Model 1, with PBPMMC fixed effects by districts 124.42 13.62 33.82 26.87 6.43 7.86 8.17
4.75 −1.61 2.45 0.64 −13.31 −0.08 0.03
124.37 13.62 33.63 26.61 2.98
4.75 −1.61 2.45 0.65 −28.81
Model 2, without PBPMMC fixed effects by districts Intercept Log of ADT 1 if DAL, 0 if otherwise 1 if SAT, 0 if otherwise 1 if PBPMMC, 0 if otherwise
Estimate
Note: SE = standard error; DAL = Dallas district; SAT = San Antonio district; number of observations, number of segment groups, deviance, and variance of segment random effect, respectively: Models 1 and 2 = 3,451, 43, 40,620, 3,187; Akaike information criterion: Model 1 = 40,594 and Model 2 = 40,601; log likelihood: Model 1 = −20,288 and Model 2 = −20,294; variance of residual random effect: Model 1 = 7,275 and Model 2 = 7,271.
Intercept 1 if DAL, 0 if otherwise 1 if SAT, 0 if otherwise 1 if PBPMMC, 0 if otherwise 1 if PBPMMC for DAL, 0 if otherwise 1 if PBPMMC for SAT, 0 if otherwise
273.70 92.60 −36.47 −42.83 −10.86 −22.65
8.20 12.36 11.41 5.56 6.75 7.03
33.37 7.49 −3.20 −7.71 −1.61 −3.22
7.65 11.59 10.48 2.55
36.59 7.53 −4.67 −21.78
Model 2, without PBPMMC fixed effects by districts Intercept 1 if DAL, 0 if otherwise 1 if SAT, 0 if otherwise 1 if PBPMMC, 0 if otherwise
279.94 87.26 −48.93 −55.53
Note: Number of observations and number of segment groups, respectively: Models 1 and 2 = 1,508 and 16; Akaike information criterion: Model 1 = 15,945 and Model 2 = 15,962; log likelihood: Model 1 = −7,964 and Model 2 = −7,975; deviance: Model 1 = 15,961 and Model 2 = 15,972; variance of segment random effects: Model 1 = 311 and Model 2 = 294; variance of residual random effects: Model 1 = 2,261 and Model 2 = 2,275.
Conclusions between two measurement periods differs among districts (i.e., with and without PBPMMCs). The logarithm of ADT was found to be a significant fixed effect for white markings, but not for yellow marking models. The age of the markings was subsequently excluded because the differences in retroreflectivity attributed to age were already captured in the roadway segments (random effect). The roadway segments were a random effect because the retroreflectivity performance can vary across different segments, but the study was not specifically interested in the effects of each individual segment on the retroreflectivity values. Table 5 shows the two mixed-effects models estimated for the white markings. The results indicate that on average white marking retroreflectivity varies among districts. From the estimated model coefficients, the Dallas district has the highest white marking retro reflectivity values in the first measurement. The fixed-effect estimates also indicated that the difference in the first measurement of the white marking values between the San Antonio and Bryan districts is not statistically significant. The average decay between two measurement periods regardless of the districts was 86 mcd/m2/lx. The differences in the decay when considering the district differences are within ±1 mcd/m2/lx. The log likelihood ratio test between the two white marking models indicates that the variables that capture the differences among the districts in the after period are not statistically significant at the 95% confidence level (p-value > .05). Table 6 shows the estimated models for the yellow markings. The results indicate that on average yellow marking retroreflectivity is also the highest for the Dallas district, followed by the Bryan district and then by the San Antonio district. The average overall decay regardless of the district was 56 mcd/m2/lx, which is smaller than for the white marking. However, the average decay varies among the districts more than for the white marking. In this case, the log likelihood ratio test between the two yellow marking models indicates that the differences among the districts in the decay of yellow markings are statistically significant at the 95% confidence level.
This paper has presented the results of before–after analyses conducted to evaluate the effect of PBPMMCs on traffic safety. The before period is the time before the implementation of the PBPMMC and the after period is one year after the implementation of the PBPMMC. The findings of this investigation provide inconclusive evidence that performance-based pavement marking maintenance contracts are an effective safety countermeasure that aids in reducing crashes. The before–after analysis showed that PBPMMCs decrease crashes on average by an estimated 0.1%, and the result is not significant at the 95% confidence level. Further analysis for each district separately showed that performance-based contracts had no significant change in safety in the San Antonio district, whereas a statistically significant positive effect was found in the Dallas district. When the crashes were evaluated by severity, the study results showed inconclusive evidence of a change in safety. Analysis by roadway class showed that PBPMMCs have no statistically significant effect on crashes occurring on U.S. and state highways, state loops and spurs, and farm-to-market roads. However, the performance-based contracts have a significant positive effect on the safety of Interstate highways. There could have been some other countermeasures implemented during the same period that might have affected nighttime crashes and it is difficult to isolate the effect of the performance-based contracts. It is recommended to conduct further analysis by removing the effects of other countermeasures. Further research is also needed to evaluate the level of performance of contracts over time. The decay analysis results indicated that there are differences in retroreflectivity decay among districts for yellow markings but not for white markings. The differences, however, may not be directly attributed to the practice of PBPMMCs. The decay in yellow markings is larger for the PBPMMC districts (Dallas and San Antonio) than for the non-PBPMMC district (Bryan), but this difference could be because of the higher traffic volume expected in the urban districts. The study attempted to include the ADT effect in the yellow marking models, but it was not significant. The smaller sample size of yellow
Geedipally, Songchitruksa, and Pike
markings may have contributed to the inability to detect any differences. Overall, the analysis concluded that there is no statistical evidence of whether PBPMMC contracts yield better retroreflectivity of pavement markings. The reason why the safety and decay results were inconclusive may be because the markings were maintained adequately before the PBPMMC, or because the PBPMMC did not provide a significant improvement in the marking systems.
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The Standing Committee on Signing and Marking Materials peer-reviewed this paper.
