Investigating Safety Effectiveness of Centerline Rumble Strips on Rural Two-Lane Roads in

Louisiana with Empirical Bayes Method

A Thesis

Presented to the

Graduate Faculty of the

University of Louisiana at Lafayette

In Partial Fulfillment of the

Requirements for the Degree

Master of Science

Mohammad Ashifur Rahman

Spring 2016
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Investigating Safety Effectiveness of Centerline Rumble Strips on Rural Two-Lane Roads in
Louisiana with Empirical Bayes Method

Mohammad Ashifur Rahman

APPROVED:

_________________________________ _________________________________
Xiaoduan Sun, Chair Kenneth McManis
Professor of Civil Engineering Professor and Head of Civil Engineering

_________________________________ _________________________________
Mohammad Jamal Khattak Mary Farmer-Kaiser
Professor of Civil Engineering Dean of the Graduate School
 ACKNOWLEDGMENTS

I would like to thank my supervisor, Xiaoduan Sun, for her guidance and encouragement,

and for being incredibly patient with me. I am grateful to my other committee members,

Kenneth McManis and Mohammad Jamal Khattak, for agreeing to be on the committee. I

would like to express my gratitude to my colleagues, Sabina Paudel and Jacob Moreau, for

the help in this thesis. I am indebted to my former colleague, Subasish Das, for his

tremendous support. I would also like to thank LADOTD for providing the data for the

analysis. I want to acknowledge the Graduate School and Department of Civil Engineering

for the support during my graduate studies so far. Finally, I appreciate the encouragement of

all my family members, especially my beloved late mother.

 LIST OF TABLES

Table 1 Road functional class distribution of Louisiana State Highway Network ................... 2

Table 2 Centerline rumble strip projects in Louisiana .............................................................. 9


Table 3 Before-after years of centerline rumble strip projects
analyzed for evaluation ...........................................................................

Table 4 Potential Crash Effects of Installing Centerline Rumble Strips

(Source: HSM 2010) ................................................................................................. 17

Table 5 Results from first two steps in EB method ................................................................ 26

Table 6 Results from the third step in EB method .................................................................. 27

Table 7 Results from the fourth to sixth steps in EB method ................................................. 28

Table 8 Results from the seventh to ninth steps in EB method .............................................. 29

Table 9 Results from the last three steps in EB method for injury crashes ............................ 30

Table 10 Results from the last three steps in EB method for cross centerline crashes ........... 30

Table 11 Results from the last three steps in EB method

for cross centerline injury crashes............................................................................ 30

Table 12 Results from the first step in improved prediction method ..................................... 32

Table 13 Results from the second step in improved prediction method ................................. 32

Table 14 Results from the third step in improved prediction method .................................... 33

Table 15 Results from the fourth step in improved prediction method .................................. 34

Table 16 Results from the last step in Imroved Prediction method for injury crashes ........... 34

Table 17 Results from the last step in Improved Prediction method

for cross centerline crashes ..................................................................................... 34

Table 18 Results from the last step in Improved Prediction method

for cross centerline injury crashes ........................................................................... 35


Table 19 Crash severity and reduction in before-after periods by type ............................... 38

Table 20 Summary of overall crashes in study area over the before after years .................... 42
Table 21 Crash modification factor of all crashes with confidence interval .......................... 43

Table 22 Crash modification factor of injury crashes with confidence interval ..................... 43

Table 23 Crash modification factor of cross centerline crashes

with confidence interval .......................................................................................... 44

Table 24 Crash modification factor of cross centerline injury crashes

with confidence interval .......................................................................................... 44

Table 25 Summary of estimated crash modification factors .................................................. 45

Table 26 Variables used for before and after analysis ............................................................ 51

Table 27 Empirical Bayes method for injury crashes ............................................................. 52

Table 28 Improved Prediction method for injury crashes ...................................................... 52

Table 29 Empirical Bayes method for cross centerline crashes ............................................. 53

Table 30 Improved Prediction method for cross centerline crashes ....................................... 53

Table 31 Empirical Bayes method for cross centerline injury crashes ................................... 54

Table 32 Improved Prediction method for cross centerline injury crashes ............................ 54

vii
 LIST OF FIGURES

Figure 1 Distribution of Louisiana State Highway System Size by Road Class ...................... 1

Figure 2 Percentage of mileage distribution of rural two-lane roads by functional class......... 2

Figure 3 Typical Rural Two-lane Road in Louisiana with narrow pavement width
and shoulder width (Source: Google Street View of LA105)................................... 3

Figure 4 AADT distribution of Louisiana rural two-lane highways by length in mile ............ 4

Figure 5 Fatality rates in Louisiana, Alabama, Mississippi, and national average ................... 4

Figure 6 Crash trend by severity in Louisiana during 2005-2014 ............................................ 5

Figure 7 Fatal crashes and fatalities by highway functional class in Louisiana ....................... 6

Figure 8 Centerline rumble strips installed on LA 1019 (Source: Google Street View) .......... 8

Figure 9 LADOTD converter converts coordinates to control section ................................... 21

Figure 10 LADOTD converter also shows the converted coordinates in a map .................... 21

Figure 11 Presence of Centerline Rumble Strips is verified using Google Street View ........ 22

Figure 12 A section proposed for analysis with no centerline rumble strips .......................... 22

Figure 13 A rural two-lane road wrongly coded as urban four-lane divided highway ........... 23

Figure 14 Final selected sections for crash analysis .............................................................. 24

Figure 15 Density of AADT in before-after periods. ............................................................. 35

Figure 16 Box and whisker plot of AADT in before after period .......................................... 36

Figure 17 Box and whisker plot of estimated speed in before after period ............................ 36

Figure 18 AADT vs. crash rate in before-after periods .......................................................... 37

Figure 19 Crash severity in before-after periods .................................................................... 37

Figure 20 Density plot of crash hour in before-after periods.................................................. 38

Figure 21 Lighting condition for before and after years ......................................................... 39

Figure 22 Type of wather at the time of crash for before and after years ............................... 39
Figure 23 Number of male and female drivers in traffic crashes ........................................... 40

Figure 24 Percentage of male and female drivers in traffic crashes ....................................... 40

Figure 25 Driver age distribution in before after years........................................................... 41

Figure 26 Overview of centerline rumble strips design .......................................................... 49

Figure 27 Design specification of centerline rumble strips in Louisiana ............................... 50

ix
 LIST OF ABBREVIATIONS

AADT Annual Average Daily Traffic

Caltrans California Department of Transportation

CMF Crash Modification Factor

DelDOT Delaware Department of Transportation

DOT Department of Transportation

DOTD Department of Transportation and Development

EB Empirical Bayes

FHWA Federal Highway Administration

HSM Highway Safety Manual

IIHS Insurance Institute of Highway Safety

LADOTD Louisiana Department of Transportation and Development

MUTCD Manual on Uniform Traffic Control Devices

NCHRP National Cooperative Highway Research Program

NTP Notice to Proceed

PDO Property Damage Only

SPF Safety Performance Function

VMT Vehicle Miles Traveled

 Table 1 Road functional class distribution of Louisiana State Highway Network

Road Class Functional Class Length (mile) Percentage

Rural Interstate Rural Interstate 563.83 3.4%
Rural Principal Arterial 566.39 3.4%
Rural Minor Arterial 154.16 0.9%
Rural Multi-Lane Rural Major Collector 45.74 0.3%
Rural Minor Collector 1.65 0.0%
Rural Local 5.1 0.0%
Rural Principal Arterial 410.47 2.5%
Rural Minor Arterial 1436.7 8.6%
Rural two-lane Rural Major Collector 4,606.94 27.7%
Rural Minor Collector 2,931.85 17.6%
Rural Local 2,454.02 14.7%
Urban Interstate 361.96 2.2%
Urban Interstate & Freeway
Urban Freeway 49.4 0.3%
Urban Principal Arterial 719.26 4.3%
Urban Minor Arterial 291.57 1.8%
Urban Multi-Lane
Urban Collector 23.13 0.1%
Urban Local 0.44 0.0%
Urban Principal Arterial 194.96 1.2%
Urban Minor Arterial 922.42 5.5%
Urban two-lane
Urban Collector 774.56 4.7%
Urban Local 132.07 0.8%
Total 16646.62 100.0%

Figure 2 Percentage of mileage distribution of rural two-lane roads by functional class

2
Seventy-five percent of rural two-lane roads comprise non-arterial roads (major collector and

minor collector) and local roads (Figure 2). Therefore, rural two-lane roads in Louisiana can

be characterized by undivided roadways with narrow lanes and low AADT encompassing a

large number of uncontrolled accesses from local small communities [3].

Low geometric standards of Louisiana rural two-lane roads can be pictured in Figure 3.

 
     , 39% of rural two-lane state highways in
Louisiana have lane widths of 10 ft. or less and 55% have shoulder widths of 4 ft. or less.

More than 55% of rural two-lane highways have AADT of less than 1500 or less, as

indicated by Figure 4.

Figure 3 Typical Rural Two-lane Road in Louisiana with narrow pavement width and
shoulder width (Source: Google Street View of LA105)

3
 Major type of non-intersection fatal crashes are: non-collision (71%), cross centerline

(20%), rear-end (5%).

Non-intersection multivehicle crashes comprise rear-end (43%) and cross centerline

(16%).

A majority of the crashes in Louisiana are rural two-lane crashes. A large portion of these

rural two-lane crashes are non-intersection crashes, which are scattered all over the rural two-

lane road network. Since these rural two-lane roads are on low hierarchical road classes

which serve very low AADT and VMT, investment on low cost countermeasures are

reasonable, economically feasible and likely to have higher impact. In addition, any effort

targeted at addressing the safety problems of rural two-lane roads is expected to accrue

significant benefits to a large percentage of the state road network.

The risk of centerline crashes can be reduced by median barriers or roadway widening;

however, these countermeasures are expensive. One reasonably low cost countermeasure,

which is expected to have a high impact on preventing centerline crashes, is centerline

rumble strips. Rumble strips along the centerline are inexpensive countermeasures designed

to prevent head-on and opposite direction sideswipe crashes.

Groove patterned rumble strips installed on the center line are designed to alert inattentive

drivers of the potential dangers associated with leaving their intended lane. The rumble strips

cause a tactile vibration and audible rumbling, which are transmitted through from wheels

into the vehicles interior. The noise and vibration generated by the rumble strip grooves is

7
intended towards alerting drivers to take corrective action before further leaving their lane

and potentially colliding with an oncoming vehicle. Centerline rumble strips also serve as an

effective mean in locating a travel lane due to poor visibility during inclement weather.

Louisiana launched an ambitious Strategic Highway Safety Plan aiming at zero deaths, with

an interim goal of reducing traffic fatalities and serious injuries by 50% by 2030. To achieve

this goal, implementation of effective crash countermeasures is necessary to reduce the high

proportion of crashes taking place on rural two-lane roads. Based on positive reports on the

performance of centerline rumble strips installed in May 2006 on LA 1019 (pictured in

Figure 8), DOTD chose to aggressively pursue statewide installation.

Figure 8 Centerline rumble strips installed on LA 1019 (Source: Google Street View)

Potential routes for implementation were considered based on the DOTD highway database

utilizing the search criteria of rural two-lane undivided highways with pavements less than

8
10 years of age, minimum 11 ft. lanes, 55 mph speed limits, and federal aid eligibility. A

series of projects were initiated, and plans were developed to install center line rumble strips

on more than 2,100 miles of rural two-lane roads. Table 2 lists the recent centerline rumble

strip installation projects in Louisiana.

Table 2 Centerline rumble strip projects in Louisiana

Project District Length (mile) Construction Year(s)
737-92-0089 2 109.73 2011
737-93-0070 3 205.12 2011
737-94-0065 4 404.59 2010-2012
737-95-0043 5 257.22 2011
737-97-0048 7 229.47 2011-2012
737-98-0045 8 297.55 2011-2012
737-91-0037 58 195.07 2011
737-96-0085 61 186.86 2011-2012
737-90-0087 62 272.79 2011
Total 2158.4

The systematic approach of installing centerline rumble strips on numerous routes is intended

to have a greater impact on reducing the number of crashes. In addition to the reduction of

crashes, the statewide center line rumble strip installation project is expected to return

substantial benefit. DOTD roughly estimates annual benefit of $91.9 million and cumulative

benefit of $1.38 billion. The total estimated cost of the above nine state projects is $14.3

million, which results in benefit cost ratio 96.4 to 1.

1.2 Goals and Objectives

The overall goal is to investigate and evaluate safety effects of centerline rumble strips in

rural two-lane roads in Louisiana. The specific objectives are:

9
 Perform a state-of-the-art literature review on performance measurement of centerline

rumble strips on rural two-lane highways.

Conduct a complete before-and-after crash analysis with three years before and three

years after crash data to estimate the crash reduction factors utilizing the Empirical

Bayes (EB) method.

Conduct a complete before-and-after crash analysis with three years before and three

years after crash data to estimate the crash reduction factors utilizing the Improved

Prediction method (Naïve before after study with correction due to change of traffic

volume).

Compare crash reduction results from EB and Improved Prediction Method.

Conduct characteristics analysis on crashes which have occurred on road sections

under study.

1.3 Scope of the Study

Road Functional Class: The present study focused only on rural two-lane roads. Four

functional classes were studied: Rural Collectors, Rural Minor Arterials, Rural

Principal Arterials, and Local Roads on the state highway system.

Analysis Period: The annual crash frequencies, along with other relevant attribute

  
 
      
 


      
     
  

Bayes Method requires data from three years before and after for a complete

evaluation. Table 3 lists before-after years of the projects applicable to the analysis.

Crash Severity Types: Fatal, injury, and property damage only crashes.

10
 Methods: Empirical Bayes (EB) and Improved Safety Prediction methods are used in

the analysis.

Table 3 Before-after years of centerline rumble strip projects analyzed for evaluation
Before Construction After
Project District Length (Mile) Years Years Years
737-92-0089 2 109.73 2008-2010 2011 2012-2014
737-93-0070 3 205.12 2008-2010 2011 2012-2014
737-95-0043 5 257.22 2008-2010 2011 2012-2014
737-91-0037 58 195.07 2008-2010 2011 2012-2014
737-90-0087 62 272.79 2008-2010 2011 2012-2014
Total 1,039.93 2008-2010 2011 2012-2014

1.4 Thesis Outline

Chapter 1 gives an introduction to the Louisiana highway network, the significance and role

of rural two-lane highways, information recent rumble strip installation projects in Louisiana

and the scope and objectives of this study. A literature review of safety improvement due to

centerline rumble strips installation and crash information related to previous studies are

presented in Chapter 2. Chapter 3 provides the methodology of the study including a step by

step statistical analysis. Chapter 4 presents the safety effectiveness evaluation results of

centerline rumble strips in terms of Empirical Bayes Method and Improve Prediction

Method. Crash characteristics, from the sections under study, in the before and after years

will also be evaluated. Conclusions are also presented in the same chapter.

11
In 1995, centerline rumble strips were installed in a 23 mile section of a two-lane rural

highway in California. In that California DOT (Caltrans) demonstration project, additional

countermeasures, such as raised pavement markers and shoulder rumble strips, were also

installed along with the centerline rumble strips. Crash data of 25 months after the

demonstration project were compared with 34 months crash data of before period. A 90%

reduction in fatal head-on crashes and a 42% reduction in head-on crashes were reported [5].

The Delaware Department of Transportation (DelDOT) installed centerline rumble strips on

a 2.9 mile section of US 301 highway with a purpose to reduce head-on crashes. A before

and after study compared average yearly crashes during 3-year period before (1992-1994)

and 8-year period after (1995-2002). Average crashes per year decreased by 8% and cross

centerline crashes per year reduced by 60%. However, there was a 4% increase in injury

crashes per year and a 13% increase in PDO crashes per year. It should also be noted that

there was a 4% increase in AADT [6].

A comprehensive study was conducted in Washington State on cost effective safety

improvements to two-lane rural state roads. Safety effectiveness was evaluated on a 47 mile

stretch of roadway where centerline rumble strips were installed. These rumble strips were

installed during 2001-2003. A 15% reduction in total crashes and a 39% reduction in

opposite direction crashes were observed. In addition, there was a 56% reduction in head-on

crashes and a 29% reduction in opposite direction sideswipe crashes [7].

13
A Kansas study using the Naïve Before and After Method was conducted on 26 miles of two

rural two-lane highways (US 50 and US 40) in 2009. This study showed a 51% decrease in

total crashes per mile per year and a 92% decrease in head-on and opposite direction

sideswipe crashes per mile per year [8].

2.3 Naïve Before and After Method with Traffic Flow Correction

One assumption the Naïve Before and After Method makes is that there are no other changes

in the treated section, except for the treatment itself. However, changes in AADT, growth in

surrounding areas, and shift in traffic do occur within the network. This methodology

considers the ability for systematic change of AADT over time on the network while

allowing for a non-linear relationship between AADT and safety outcome. Although this

method takes traffic change into consideration, it still does not account for regression-to-the-

mean

  

  
  
    
   
 


The comprehensive study in Washington State on cost effective safety improvements on two-

lane rural state roads evaluated safety effectiveness of 47 miles of centerline rumble strips.

The study found 24% reduction in all crashes, 81% reduction in opposite direction crashes,

88% reduction in head-on crashes, and 91% reduction in opposite direction sideswipe crashes

considering the traffic volume changes over the years under study in the Naïve Before and

After Method [7]. These results are significantly higher than those previously mentioned

using the standard Naïve Before and After Method.

2.4 Comparison Group

A quasi-experimental design has also been used in which an untreated comparison group of

sites similar to the treated ones selected separately from the treatment site selection process.

14
Comparison between untreated and treated sections are evaluated. A comparison group can

account for unrelated effects, such as time and travel trends, but will not account for

regression-to-the-mean effect.

A comparison group study was performed in Massachusetts on three rural two-lane highways

containing centerline rumble strips. These three highways (route 2, 20, and 88) were

compared with a group of highways having similar geometric and operational features, but

no rumble strips. After evaluation, the number of predicted crashes increased by

approximately 7%, with a standard deviation of ±41%. Only one highway showed a crash

reduction, but with a large standard deviation. The other two highways showed an increase in

predicted crashes. Targeted crashes (head-on collision; angle collision nearly head-on

collision; sideswipe opposite direction collision; run off road collision to the left with

centerline encounter) showed no significant c
 


  

 The

results of the crash data analysis showed no significant change in crash frequencies before

and after the installation of centerline rumble strips [9].

2.5 Empirical Bayes Method

Empirical Bayes method is considered as the most efficient method in overcoming the

limitations of conventional methods by accounting not only for regression-to-the-mean

effect, but also traffic volume changes and trends in crash occurrence due to changes in

factors such as weather, accident reporting habits, and driving habits over time [4].

The Insurance Institute for Highway Safety (IIHS) sponsored a study on centerline rumble

strips in seven states. This was the first widespread study that evaluated centerline rumble

15
strips safety effectiveness using the Empirical Bayes Method. A total of 98 treatment sites

along approximately 200 miles of two-lane rural roads were evaluated. The analysis showed

a 14% reduction in all crashes and a 15% reduction in injury crashes. Targeted crashes (head-

on and opposite direction sideswipe crashes) reduced by 21%, and targeted injury crashes

reduced by 25% [10].

Another study (NCHRP 646) evaluated the safety effects of centerline rumble strips and

shoulder rumble strips on different types of roads. The research analyzed approximately 416

miles of rural two-lane highways in Minnesota, Pennsylvania, and Washington. A

statistically insignificant 4% reduction in overall crashes was found. However, a 9.4%

reduction in fatal and injury crashes and a 37% reduction in targeted crashes were

statistically significant [11].

The 2009 study in Kansas, which used the Naïve Before and After Method on 26 miles of

rural two-lane highways (US 50 and US 40), also used the Empirical Bayes Method in the

analysis. The EB method presented a 49% decrease in total crashes per mile per year and an

89% decrease in head-on and opposite direction sideswipe crashes per mile per year. These

results are slightly different from Naïve Before and After Method [8].

The comprehensive study in Washington State, which evaluated safety effectiveness of 47

miles of centerline rumble strips, found a 13%, 5%, and 22% reduction all, injury, and PDO

crashes respectively, using Empirical Bayes Method. The reduction in the crashes using EB

16
method is considerably lower than the reduction using Naïve Before and After Method with

traffic flow correction [7].

2.6 Literature Gap

The Highway Safety Manual (HSM) 2010 adopted the IIHS study results as a record of crash

modification factor (CMF) of centerline rumble strips installation on rural two-lane highways

[12]. Although IIHS study involved analysis of centerline rumble strips in seven states, it is

only applicable to AADT higher than 5,000 and less than 22,000 (Table 4). But 90% of state

maintained rural two-lane highways in Louisiana has an AADT of less than 5,000. Therefore,

the HSM estimated CMF will not be applicable to Louisiana.

Table 4 Potential Crash Effects of Installing Centerline Rumble Strips (Source: HSM 2010)
Setting Traffic Volume Crash Type Std.
Treatment CMF
(Road Type) (AADT) (Severity) Error
All types
0.86 0.05
(All severities)
All types
0.85 0.08
(Injury)
Install Head-on and
Centerline Rural opposing direction
5,000 to 20,000 0.79 0.1
rumble (Two-lane) sideswipe
strips (All severities)
Head-on and
opposing direction
0.75 0.2
sideswipe
(Injury)
Base Condition: Absence of centerline rumble strips.

NOTE: Based on centerline rumble strips installation in seven states: California, Colorado, Delaware,
Maryland, Minnesota, Oregon, and Washington.
Bold text used for most reliable CMFs. These CMFs have a standard error of 0.1 or less.
Italic text is used for less reliable CMFs. These CMFs have standard errors between 0.2 to 0.3.

Studies included in this literature review have many different features. Some of these features

are as follows:

17
 Pavement and shoulder width: Although most states follow FHWA guidelines for

pavement and shoulder width, variation may be higher when compared to Louisiana.

AADT: The two-lane roads analyzed for centerline rumble strips safety evaluation

in this literature review have considerably higher AADT than the rural two-lane

roads under study for centerline rumble strips safety evaluation in Louisiana.

Weather effect: Some states face much severe hot and cold season than Louisiana

resulting in different AADT and crash pattern during these seasons.

Type of rumble strips: Some states use rolled or raised type of rumble strips which

might produce different vibratory effect on drivers than the effect from milled

rumble strips in Louisiana.

The results from a
    


   
       



network. This is not only due to different road network setting and the effects listed above,

but also the effect of driving behavior and overall  
  


 n system.

Safety effectiveness of more than 2,000 miles of centerline rumble strips installation on

Louisiana roads cannot be determined based on the analysis established in other states. A

need for evaluation of safety effectiveness on rural two-lane roads in Louisiana is self-

evident.

18
Control section is the general Linear Referencing System (LRS) of LADOTD, which

describes state-maintained highway properties and right of ways. A unique five digit number

represents a control section (i.e. XXX-XX).

Control sections are further divided into smaller sections with respective mileage

information. Each smaller section holds similar highway section properties (i.e. pavement

 


    




 

   
 
each smaller section is the mileage difference between logmile from and logmile to.

Crash databases for the before and after years were collected from LADOTD. These crash

databases contain numerous variables regarding highway section information, crash

information and vehicle information. All variables necessary for anaysis are extracted from

the crash databases and are merged together. A list of all required variables are in Appendix

B. The extracted databases were then filtered for control section and logmiles where rumble

strips were installed.

3.3 Segment Data Verification

Two tools were used to verify sections. LADOTD converter is a free online tool which

converts control section to geographic coordinates (Latitude and Longitude). This converter

(Figure 9 and Figure 10) was used to identify the location where centerline rumble strips

were installed. The second verification tool used was Google street view. This was used to

visually inspect the highway sections, using the coordinates identified by LADOTD

converter.

20
 Figure 9 LADOTD converter converts coordinates to control section

Figure 10 LADOTD converter also shows the converted coordinates in a map

21
The sections/segments were verified for following purposes:

Presence of centerline rumble strips
was verified using Google street view. Sections

containing no centerline rumble strips were removed from prepared database. Figure

11 depicts a section with only centerline rumble strips and Figure 12 presents a

section with no centerline rumble strips.

Figure 11 Presence of Centerline Rumble Strips is verified using Google Street View

Figure 12 A section proposed for analysis with no centerline rumble strips

22
 Control section segments were also verified for type of roads. The analysis is

intended for rural two-lane roads. Road sections improperly coded were corrected

using Google street view (Figure 13).

Figure 13 A rural two-lane road wrongly coded as urban four-lane divided highway

In addition to the mentioned verifications, intersection crashes were removed from the

prepared database. The effective area of an intersection does not contain centerline rumble

strips and centerline rumble strips are not intended to prevent intersection crashes.

Intersection crashes were identified as designated intersection crashes and crashes which

were not identified as intersection crashes but occurred within 150 ft. of the intersection.

According to LADOTD crash data analysi


It is important to note that not all

crashes that occur as a result of the intersection will be included within this 150 ft. radius and

not all crashes within 150 ft. occurred as a result of the intersection. However, for

consistency purposes it is recommended to use the 150 ft. radius. [13]

23
Sections which had no crashes in both before and after period were also removed. There was

no visible impact on these sections, since there were no crashes. The following map

represents the area selected for analysis (Figure 14).

Figure 14 Final selected sections for crash analysis

3.4 Crash Analysis with Empirical Bayes Method

The Empirical Bayes (EB) method combines observed crash frequency with predicted crash

frequency. The Safety Performance Function (SPF) is used to calculate the expected crash

frequency for a site of interest. As discussed in Chapter 2, this method accounts for the effect

of regression-to-the-mean, along with changes in traffic volume and other changes not

related to the treatment in crash frequencies. In the EB method, SPFs are used to estimate

expected crash frequencies at sites where treatments have not been applied. Generalized

linear regression models, specifically negative binomial regression models, are often used to

24
derive the SPFs. In this evaluation, safety performance functions were calibrated for each

year of the before and after periods, rather than just for each period. Generalized linear

regression models, specifically negative binomial regression models, are often used to derive

the SPFs. In this evaluation, safety performance functions were calibrated for each year of

the before and after periods rather than just for each period.

Step 1: The first step in applying the EB method was to develop an SPF. The Highway Safety

Manual (HSM) used the following SPF of for rural two-lane highway segments which was

also used in this research:

 





Where,

  = Predicted crash frequency for road segment in base conditions

AADT = Annual Average Daily Traffic

L = Length of road segment (miles).

Expected number of crashes for each year in the before period were estimated at each

treatment site.

Step 2: The second step was to calculate the sum of the annual SPF predictions for each

treatment site during the before period. This computation is defined by the following

equation:

 
  
 

Where,

 indicates the year during which the centerline rumble strip was installed at site i.

Results from the first two steps are shown in Table 5.

25
 Table 5 Results from first two steps in EB method
DOTD District Section Length Number of control sections Pi
2 52.06 14 200
3 55.62 27 147
5 83.24 21 379
58 27.32 8 75.6
62 75.42 23 433
Total 293.66 93 1235

Step 3: The third step was to obtain an estimate of the expected number of crashes (Mi)

before implementation of the countermeasure at each treatment site and the variance of Mi.

The estimate Mi was calculated by combining the sum of the annual SPF predictions during

the before period (Pi) with the total number of crashes during the before period.

 

 



Where,

is total number of crashes during before period at site i; and


  

 
Where,

k = over dispersion parameter;

k is the estimated over dispersion parameter of the negative binomial regression model. This

is a function of roadway segment length, as specified in HSM. The closer k is to zero, the

more statistically reliable the SPF is. The value of k is calculated as:

   

Where,

L = Length of road segment (miles).

26
Estimated variance of Mi is given by:

   
  
As the relationship is linear, Mi value was calculated for each district by summing up all

consecutive control sections.


  



   
 



The results of step three are shown in Table 6.

Table 6 Results from the third step in EB method

DOTD District Section Length Number of control sections Mi var(Mi)
2 52.06 14 362.443 356.7708
3 55.62 27 249.3914 238.2904
5 83.24 21 203.0748 199.0076
58 27.32 8 42.79573 41.92597
62 75.42 23 581.5751 576.52
Total 293.66 93 1439.28 1412.515

 for each year in the after

Step 4: The fourth step was to determine SPF predictions 

period at each treatment site, and compute Ci (the ratio of the sum of the annual SPF

predictions for the after period, Qi and the sum of the annual SPF predictions for the before

period, Pi).

   
  
   

27
Step 5: The fifth step was to obtain the predicted crashes and its estimated variance during

the after period had the countermeasure not been implemented. The predicted crashes 

 are

given by:



 


The estimated variance of 

 is given by:

 


 
 
 
 
 

Step 6: The sixth step was to compute the sum of the predicted crashes over all sites in a

treatment group of interest and its estimated variance by:


  








  




Where,

I = total number of sites in a treatment group of interest.

The results of step four to step six are shown in Table 7.

Table 7 Results from the fourth to sixth steps in EB method

DOTD District Section Length Number of control sections ci  

2 52.06 14 0.57 372 384.51

3 55.62 27 0.63 265 285.94
5 83.24 21 1.59 174 149.76
58 27.32 8 1.70 42 43.33
62 75.42 23 0.70 560 546.27
Total 293.66 93 0.81 1414 1409.81

Step 7: The seventh step was to calculate the sum of the observed crashes over all sites in a

treatment group of interest by:

28
 

 

Where,

Li is the total crash counts during the after period at site i.

Step 8: The index of effectiveness of the countermeasure was estimated by:




 
 

Where,

 = Estimated unbiased expected crash modification factor.

Step 9: The ninth step was to calculate the estimated variance and standard error of the index

of effectiveness and the approximate 95% confidence interval for . The estimated standard

error of the index of effectiveness are given by:


     





 


The results of step seven to step nine are shown in Table 8.

Table 8 Results from the seventh to ninth steps in EB method

No. of
 sd(  )  !"#$ % !"#$
DOTD Section
control Li
District Length
sections
2 52.06 14 284 0.76 0.0603 0.58 0.94
3 55.62 27 268 1.01 0.0884 0.74 1.27
5 83.24 21 182 1.04 0.1059 0.72 1.36
58 27.32 8 48 1.12 0.2321 0.42 1.81
62 75.42 23 482 0.86 0.0529 0.70 1.02
Total 293.66 93 1264 0.89 0.0345 0.79 1.00

29
All nine steps were used for the analysis of Injury crashes, Cross centerline crashes (Head on

+ Opposite direction sideswipe), and Cross centerline injury crashes. The results of the last

three steps are in following tables (Table 9, Table 10, and Table 11).

Table 9 Results from the last three steps in EB method for injury crashes
No. of
DOTD Section
control Li  sd( ) 
   
 
District Length
sections
2 49.62 13 107 0.89 0.1184 0.54 1.25
3 52.19 24 94 0.78 0.1077 0.45 1.10
5 82.65 20 66 0.75 0.1176 0.40 1.10
58 23.72 7 22 1.05 0.3083 0.13 1.98
62 75.42 23 157 0.75 0.0788 0.52 0.99
Total 283.6 87 446 0.80 0.0509 0.65 0.96

Table 10 Results from the last three steps in EB method for cross centerline crashes
No. of
DOTD Section
control Li  sd( ) 
   
 
District Length
sections
2 31.86 9 11 0.49 0.1732 -0.03 1.01
3 41.42 20 19 0.93 0.2911 0.06 1.81
5 31.8 6 6 0.67 0.3179 -0.28 1.63
58 19.67 5 4 1.07 0.6137 -0.77 2.92
62 63.83 15 25 0.72 0.1844 0.17 1.28
Total 188.58 55 65 0.75 0.1226 0.38 1.12

Table 11 Results from the last three steps in EB method for cross centerline injury crashes
No. of
DOTD Section
control Li  sd( ) 
   
 
District Length
sections
2 16.71 5 3 0.28 0.1658 -0.22 0.77
3 22.7 11 5 0.38 0.1875 -0.18 0.94
5 24.4 5 5 0.92 0.4828 -0.53 2.37
62 40.96 9 8 0.39 0.1571 -0.08 0.87
Total 104.77 30 21 0.45 0.1160 0.10 0.80

30
 3.5 Crash Analysis with Improved Prediction Method

To account for the change in traffic volume, Improved Prediction procedure, introduced by

E. Hauer [14], was used in estimating the unbiased crash changes before and after installation

of the centerline rumble strips.

Step 1: Estimating the safety if the centerline rumble strips were not installed during the after

period,  , and the safety with the centerline rumble strips project,
.



  

Where,

= Estimated expected number of crashes in the after time period with the centerline rumble

strips

N = Observed annual crashes after centerline rumble strips project

 = Estimated expected number of crashes in the after period without the centerline rumble

strips

K = Observed annual crashes before the centerline rumble strips project

 = Traffic flow correction factor

 


 


  = Average traffic flow during the after period



 = Average flows during the before period

The results of this application are listed in Table 12.

31
 Table 12 Results from the first step in improved prediction method

:6789
No. of
DOTD Section
control 34 56789 ;<=> ?@
District Length
sections
2 52.06 14 284 106,927 97,707 1.09 367
3 55.62 27 268 140,527 129,270 1.09 265
5 83.24 21 182 100,777 116,577 0.86 206
58 27.32 8 48 27,167 28,120 0.97 43
62 75.42 23 482 174,740 181,993 0.96 584
Total 293.66 93 1264 550,137 553,667 0.99 1,461

Step 2: Estimating the variance
 and
.

 = Estimated variance of 
rd = Ratio of time duration of after period to time duration of before period

v = Percent coefficient of variance for AADT estimates

 !"#

    
  + ##
$$%&'()*
(Number of count-
 , ,
 -./ , 
00
,

12 = Estimated variance of 12

The results up to this step are listed in Table 13.

Table 13 Results from the second step in improved prediction method

No. of
DOTD Section
control ABC D AEFGHI J AEKGHI J ABC(LMNO ABCEPJ
District Length
sections
2 52.06 14 284 0.036907 0.037002 0.003271 143
3 55.62 27 268 0.036658 0.036728 0.003182 131
5 83.24 21 182 0.036969 0.036822 0.002035 53
58 27.32 8 48 0.039482 0.039376 0.002902 16
62 75.42 23 482 0.036496 0.036469 0.002454 211
Total 293.66 93 1,264 0.03599 0.035989 0.002558 6,979

32
Step 3: Estimating the crash difference  and the ratio .



  

 

 





Where,

= Estimated safety impact of the project

 = Estimated unbiased expected crash modification factor

The results up to this step are listed in Table 14.

Table 14 Results from the third step in improved prediction method

DOTD Section No. of control
District Length sections
 
2 52.06 14 83 0.77302
3 55.62 27 -3 1.00944
5 83.24 21 24 0.88240
58 27.32 8 -5 1.10689
62 75.42 23 102 0.82483
Total 293.66 93 197 0.86246

Step 4: Estimating the standard deviation of  and  .

   
    
 


   
  

    




 





The results of this application are listed in Table 15.

33
 Table 15 Results from the fourth step in improved prediction method
DOTD Section No. of control

) )

District Length sections
2 52.06 14 20.65650 0.05226
3 55.62 27 19.97409 0.07537
5 83.24 21 15.32399 0.07235
58 27.32 8 7.97975 0.18791
62 75.42 23 26.33366 0.04279
Total 293.66 93 90.79360 0.05479

All nine steps were used for the analysis of: Injury crashes, Cross centerline crashes (Head on

+ Opposite direction sideswipe), and Cross centerline injury crashes. The results of the

estimation of  are in following tables (Table 16, Table 17, and Table 18).

Table 16 Results from the last step in Improved Prediction method for injury crashes
DOTD Section No. of control

) )

District Length sections
2 49.62 13 0.89 0.1184
3 52.19 24 0.78 0.1077
5 82.65 20 0.75 0.1176
58 23.72 7 1.05 0.3083
62 75.42 23 0.75 0.0788
Total 283.6 87 0.80 0.0509

Table 17 Results from the last step in Improved Prediction method

for cross centerline crashes
DOTD Section No. of control

) )

District Length sections
2 31.86 9 0.40 0.1981
3 41.42 20 0.78 0.3886
5 31.8 6 0.65 0.2766
58 19.67 5 1.18 0.6442
62 63.83 15 0.73 0.1571
Total 188.58 55 0.78 0.1334

34
 Table 18 Results from the last step in Imroved Prediction method
for cross centerline injury crashes
DOTD Section No. of control

) )

District Length sections
2 31.86 9 0.20 0.1196
3 41.42 20 0.35 0.1935
5 31.8 6 0.59 0.3272
62 63.83 15 0.40 0.1432
Total 188.58 55 0.47 0.1237

3.6 Traffic, Crash, and Driver Characteristics

Traffic, Crash, and Driver characteristics were also analyzed along with the analysis using

both the EB and Improved Prediction Methods. An increase of about 6% on weighted

average AADT in terms of the section length was observed during the after period. The

density plot of AADT is presented in Figure 15. Two spikes in lower AADT are observed

during the after period. This denotes higher concentration of crashes in lower AADT in after

period than before period. Higher concentration of crashes in low AADT can also be visible

in Figure 16.

Figure 15 Density of AADT in before-after periods.

35
 25000

20000

15000

AADT 10000

5000

0
1 2
1. Before years (2008-2010), 2. After years (2012-2014)

Figure 16 Box and whisker plot of AADT in before after period

The box and whisker plot of estimated operating speed in before-after periods (Figure 17)

clearly shows that operating speed have increased significantly. The median speed of the

vehicles involved in crashes is 50 mph in but the second quartile is more concentrated

towards median speed and narrower than second quartile in the before speed data. However,

insufficient amount of data and varying sample sizes indicates that the claim of increased

operating speed needs further verification.

100 100

90 90

80 80

70 70
Est imat ed Speed

60 60

50 50

40 40

30 30

20 20

10 10

0 0

Before Years (2008-2010) A ft er Years (2012-2014)

Figure 17 Box and whisker plot of estimated speed in before after period
36
 Table 21 Crash modification factor of all crashes with confidence interval
Section No. of Empirical Bayes Improved Prediction
District Length control
 ) - +  ) - +
(mile) sections
2 52.06 14 0.76 0.06 0.58 0.94 0.77 0.05 0.62 0.93
3 55.62 27 1.01 0.09 0.74 1.27 1.01 0.08 0.78 1.24
5 83.24 21 1.04 0.11 0.72 1.36 0.88 0.07 0.67 1.10
58 27.32 8 1.12 0.23 0.42 1.81 1.11 0.19 0.54 1.67
62 75.42 23 0.86 0.05 0.70 1.02 0.82 0.04 0.70 0.95
Total 293.66 93 0.89 0.03 0.79 0.997 0.86 0.05 0.70 1.03

Every district except for District 58 experiences injury crash reduction after centerline

rumble strips installation. But the overall reduction of injury crashes are estimated to be 20%

by EB method and 23% by Improved Prediction Method (Table 22).

Table 22 Crash modification factor of injury crashes with confidence interval

Section No. of Empirical Bayes Improved Prediction
District Length control
 ) - +  ) - +
(mile) sections
2 49.62 13 0.89 0.12 0.54 1.25 0.90 0.10 0.60 1.21
3 52.19 24 0.78 0.11 0.45 1.10 0.81 0.09 0.53 1.10
5 82.65 20 0.75 0.12 0.40 1.10 0.64 0.08 0.39 0.89
58 23.72 7 1.05 0.31 0.13 1.98 1.03 0.25 0.28 1.79
62 75.42 23 0.75 0.08 0.52 0.99 0.73 0.06 0.54 0.92
Total 283.6 87 0.80 0.05 0.65 0.96 0.77 0.06 0.59 0.96

The reduction in targeted crashes (Head-on and Opposite Direction sideswipe crashes) is

22% (Improved Prediction Method) to 25% (EB Method) (

Table 23). District 58 still experiences an increase by about 7%. This might require further

investigation.

43
 Table 23 Crash modification factor of cross centerline crashes with confidence interval
Section No. of Empirical Bayes Improved Prediction
District Length control
 ) - +  ) - +
(mile) sections
2 31.86 9 0.49 0.17 -0.03 1.01 0.40 0.20 -0.20 0.99
3 41.42 20 0.93 0.29 0.06 1.81 0.78 0.39 -0.39 1.95
5 31.8 6 0.67 0.32 -0.28 1.63 0.65 0.28 -0.18 1.48
58 19.67 5 1.07 0.61 -0.77 2.92 1.18 0.64 -0.75 3.11
62 63.83 15 0.72 0.18 0.17 1.28 0.73 0.16 0.26 1.20
Total 188.58 55 0.75 0.12 0.38 1.12 0.78 0.13 0.38 1.18

Targeted (Head-on + Opposite Direction Sideswipe) injury crashes reduced substantially,

A 53% reduction was determined by the EB Method, and a 51% reduction by the Improved

Prediction Method (Table 24). District 58 was removed from this part of the analysis due to

not having any crashes of this type.

Table 24 Crash modification factor of cross centerline injury crashes with confidence interval
Section No. of Empirical Bayes Improved Prediction
District Length control
 ) - +  ) - +
(mile) sections
2 16.71 5 0.28 0.17 -0.22 0.77 0.20 0.12 -0.16 0.56
3 22.7 11 0.38 0.19 -0.18 0.94 0.35 0.19 -0.23 0.93
5 24.4 5 0.92 0.48 -0.53 2.37 0.59 0.33 -0.40 1.57
62 40.96 9 0.39 0.16 -0.08 0.87 0.40 0.14 -0.03 0.83
Total 104.77 30 0.47 0.12 0.11 0.83 0.49 0.13 0.11 0.88

Crash modification factors can be summarized as in Table 25.

44
 Table 25 Summary of estimated crash modification factors
Setting Traffic Volume Crash Type Std.
Treatment CMF
(Road Type) (AADT) (Severity) Error
All types
0.89 0.03
(All severities)
All types
0.8 0.05
(Injury)
Install Head-on and
Centerline Rural up to 22,000 opposing direction
0.75 0.12
rumble (Two-lane)
   sideswipe
strips (All severities)
Head-on and
opposing direction
0.47 0.12
sideswipe
(Injury)
Base Condition: Absence of centerline rumble strips.

4.2 Conclusions

Based on the analysis results and discussion, the concluding points are as follows:

 Installation of centerline rumble strips on rural two-lane highways in Louisiana can

reduce crashes.

 Based on the Empirical Bayes method, the most reliable CMF for centerline rumble

strips on narrow, rural two-lane highways (pavement width of minimum 11 ft.) is

0.89 with a standard deviation of 0.03.

 The CMF range for all crashes is 0.73 to 0.997, which indicates a certainty in crash

reduction with centerline rumble strips.

 The CMF range for injury crashes is 0.8 with a standard deviation of 0.05. This

results in a CMF range of 0.65 to 0.96, which indicates an inevitability reduction in

injury crashes with the installation of centerline rumble strips.

45
 Crash reductions are consistent in all crash types and is particularly significant in

cross centerline crashes. The estimated CMF for cross centerline crashes is 0.75 with

a standard deviation of 0.12.

CMF of targeted injury crashes is 0.47 with a standard deviation of 0.12. This denotes

a very high probability of reduction.

Considering the safety trend in Louisiana, the final estimated CMF can be calculated by

applying EB method. This CMF value will hold greater significance if estimated in all

districts when 2015 crash data are available.

46
 REFERENCES

[1] LADOTD, "Right-Sizing the State Highway System: A Voluntary Road Transfer

Program," LADOTD, Baton Rouge, 2013.

[2] D. W. Harwood, A. D. May, I. . B. Anderson, L. Leiman and A. R. Archilla, "Capacity

and Quality of Service of Two-lane Highways," Transportation Research Board,

Washington D.C., 1999.

[3] FHWA, "Highway Functional Classification Concepts, Criteria and Procedures,"

Federal Highway Administration, Washington, D.C., 2013.

[4] B. N. Persaud and C. Lyon, "Empirical Bayes before-after safety studies: Lessons

learned from two decades of experience and future directions," Accident Analysis &

Prevention, vol. 39, no. 3, pp. 546-555 pp, May 2007.

[5] K. Fitzpatrick, K. Balke, D. Harwood and A. I.B., "NCHRP Report 440: Accident

Mitigation Guide for," Transportation Research Board, National Research Council,

Washington, D.C., 2000.

[6] DelDOT, "Centerline Rumble Strips, the Delaware Experience," Delaware Department

of Transportation, [Online]. Available:

www.deldot.gov/static/projects/rumblestripindex.html. [Accessed 2015].

[7] I. v. Schalkwyk and S. Washington , "Cost Effective Safety Improvements on Two-

Lane Rural State Roads in Washington State," Washington State Department of

Transportation, Olympia, 2008.

[8] D. E. Karkle, R. J. Margaret and E. R. Russell Sr, "Evaluation of Centerline Rumble

Strips for Prevention of Highway Crossover Accidents in Kansas," in 2009 Mid-

Continent Transportation Research Symposium, Ames, Iowa, 2009.

[9] D. A. Noyce and V. V. Elango , "Safety Evaluation of Centerline Rumble Strips,"

University of Massachusetts Transportation Center, Amherst, 2003.

[10] B. N. Persaud, R. A. Retting and C. Lyon, "Crash reduction following installation of

centerline rumble strips on rural two-lane roads," Accident Analysis & Prevention, vol.

36, no. 6, pp. 1073-9, 2004.

[11] D. J. Torbic, J. M. Hutton, C. D. Bokenkroger, K. M. Bauer, D. W. Harwood, D. K.

Gilmore, J. M. Dunn, J. J. Ronchetto, E. T. Donnell, H. J. Sommer III, P. M. Garvey,

B. N. Persaud and C. Lyon, "Guidance for the Design and Application of Shoulder and

Centerline Rumble Strips," Transportation Research Board, Washington, D. C., 2009.

[12] AASHTO, Highway Safety Manual, Washington, D. C.: American Association of State

Highway & Transportation Officials, 2010.

[13] LADOTD, Guidelines for Crash Data Analysis, Baton Rogue: Louisiana Department of

Transportation and Development, 2014, p. 13.

[14] E. Hauer, Observational Before After Studies in Road Safety: Estimating the Effect of

Highway and Traffic Engineering measures on Road Safety, New York: Pergamon

Press, 2002.

48
 Appendix A Design of Centerline Rumble Strips

Figure 26 Overview of centerline rumble strips design

No guidelines by MUTCD.

FHWA suggestion: Width (C) = 7 inches, Length (B) = 16 inches, Depth (D) = 0.5 inch.

Design in Louisiana: Width (C) = 6 inches, Spacing (E) = 5 inches, Length (B) = 12

inches, Depth (D) = 0.5 inch.

Figure 27 Design specification of centerline rumble strips in Louisiana

50
 Appendix B Variables for Before-After Analysis

Table 26 Variables used for before and after analysis

Geometric Variables Driver Variables Crash Variables Vehicle Variables
MEDIAN_WIDTH VEH_NUM CR_HOUR VEH_YEAR
NUM_LANES DR_AGE DAY_OF_WK VEH_COND_CD
PAVEMENT_TYPE ALCOHOL SEVERITY_CD VEH_LIGHTING_CD
PAVEMENT_WIDTH DRUGS MAN_COLL_CD
SURF_COND_CD DR_COND_CD NUM_VEH
ALIGNMENT_CD DR_DISTRACT_CD PRI_CONTRIB_FAC_CD
HWY_TYPE_CD DR_INJ_CD SEC_CONTRIB_FAC_CD
TRAFF_CNTL_CD DR_SEX LIGHTING_CD
TRAFF_CNTL_COND_CD EST_SPEED WEATHER_CD
ROAD_COND_CD VIOLATIONS_CD
ROAD_TYPE_CD
INTERSECTION
ADT
FUNCTIONAL_CLASS
HIGHWAY_CLASS
MEDIAN_WIDTH
POSTED_SPEED
 Appendix C Tables for Injury Crashes, Cross Centerline Crashes, and Cross Centerline Injury Crashes

Table 27 Empirical Bayes method for injury crashes

District Length Pi K Mi var(Mi) Qi ci 
   

2 49.62 191.2157 3.7148 117.7679 115.5177 195.8521 1.6630 118.9233 121.2557 0.89 0.1184
3 52.19 140.5962 18.5117 113.0254 108.2151 149.0408 1.3186 120.0212 128.8987 0.78 0.1077
5 82.65 377.8921 2.8044 102.1393 99.7539 321.0695 3.1434 87.0376 74.6791 0.75 0.1176
58 23.72 68.4724 0.7990 21.1115 20.5642 65.7578 3.1148 19.9573 19.6695 1.05 0.3083
62 75.42 433.0524 12.2943 216.6568 214.9493 408.8797 1.8872 207.4827 201.1646 0.75 0.0788
Total 283.6 1211.2287 38.1241 570.7010 559.0003 1140.5999 1.9986 553.4221 545.6677 0.80 0.0509

Table 28 Improved Prediction method for injury crashes

Distr- Len-
           ( 
 
) )
ict gth

2 49.62 107 102027 93273 1.0938 118 107 0.0370 0.0371 0.0033 46.8438 11 0.90 12.4034 0.1015
3 52.19 94 132193 122303 1.0809 115 94 0.0367 0.0368 0.0032 39.7028 21 0.81 11.5630 0.0949
5 82.65 66 98677 114120 0.8647 103 66 0.0370 0.0368 0.0020 17.4349 37 0.64 9.1343 0.0828
58 23.72 22 24700 25653 0.9628 21 22 0.0398 0.0397 0.0029 6.9558 -1 1.03 5.3811 0.2512
62 75.42 157 174740 181993 0.9601 215 157 0.0365 0.0365 0.0025 54.9659 58 0.73 14.5590 0.0633
Total 283.6 446 532337 537343 0.9907 5741 446 0.0360 0.0360 0.0025 1421.4972 128 0.77 43.2145 0.0624
 Table 29 Empirical Bayes method for cross centerline crashes

District Length Pi K Mi var(Mi) Qi ci 
  

2 31.86 172.6203747 2.7671 20.7653 19.9785 173.8475 8.3720 21.5929 22.9217 0.49 0.1732
3 41.42 126.0963732 3.9937 18.0966 16.9950 135.8498 7.5069 19.2959 20.9032 0.93 0.2911
5 31.8 216.3758735 0.3347 9.3036 9.2729 186.4613 20.0418 8.0573 6.9966 0.67 0.3179
58 19.67 62.91689765 0.3147 3.2944 3.2743 59.0362 17.9200 2.8437 2.5006 1.07 0.6137
62 63.83 405.963834 1.1113 34.8933 34.6888 383.7720 10.9984 33.6390 32.8665 0.72 0.1844
Total 188.58 983.973353 8.5214 86.3533 84.2095 938.9668 10.8736 85.4289 86.1886 0.75 0.1226

Table 30 Improved Prediction method for cross centerline crashes

53
Distr- Len-
          ( 
  ) 
)
ict gth

2 31.86 11 82417 74700 1.1033 20 11 0.0372 0.0373 0.0034 152.3929 9 0.40 12.7825 0.1981
3 41.42 19 102320 92903 1.1014 16 19 0.0370 0.0371 0.0033 133.6708 -3 0.78 12.3560 0.3886
5 31.8 6 45883 52943 0.8666 9 6 0.0381 0.0379 0.0022 1.5108 3 0.65 2.7406 0.2766
58 19.67 4 19767 21300 0.9280 3 4 0.0406 0.0403 0.0028 1.1533 -1 1.18 2.2701 0.6442
62 63.83 25 126703 130703 0.9694 34 25 0.0367 0.0367 0.0025 8.0072 9 0.73 5.7452 0.1571
Total 188.58 65 377090 372550 1.0122 82 65 0.0361 0.0361 0.0027 101.0205 17 0.78 12.8849 0.1334
 Table 31 Empirical Bayes method for cross centerline injury crashes

District Length Pi K Mi var(Mi) Qi ci 
  

2 16.71 125 2.2291 9.3201 8.6240 129.1037 13.8521 9.7742 10.5680 0.28 0.1658
3 22.7 78 1.8260 11.3547 10.9253 82.6773 7.2813 12.0856 13.1727 0.38 0.1875
5 24.4 208 0.3028 5.2773 5.2520 179.4426 34.0029 4.5662 3.9664 0.92 0.4828
62 40.96 348 0.6378 20.5909 20.5444 329.9487 16.0240 19.3168 18.4315 0.39 0.1571
Total 104.77 758 4.9957 46.5431 45.3457 721.1724 15.4947 45.7428 46.1386 0.45 0.1160

Table 32 Improved Prediction method for cross centerline injury crashes

54
Distr- Len-
          ( 
  ) 
)
ict gth

2 16.71 3 57467 49600 1.1586 9 3 0.0377 0.0380 0.0038 54.3945 6 0.20 7.5759 0.1196
3 22.7 5 57557 52443 1.0975 10 5 0.0377 0.0379 0.0034 43.4993 5 0.35 6.9641 0.1935
5 24.4 5 44700 51500 0.8680 5 5 0.0382 0.0379 0.0022 17.6305 0 0.59 4.7571 0.3272
62 40.96 8 108450 111287 0.9745 20 8 0.0369 0.0369 0.0026 2.5508 12 0.40 3.2482 0.1432
Total 104.77 21 268173 264830 1.0126 44 21 0.0363 0.0363 0.0027 49.2818 23 0.47 8.3834 0.1237
Rahman, Mohammad Ashifur. Bachelor of Science in Civil Engineering, Bangladesh
University of Engineering and Technology, Bangladesh, 2012; Master of Science,
University of Louisiana at Lafayette, Spring 2016
Major: Engineering, Civil Engineering option
Title of Thesis: Investigating Safety Effectiveness of Centerline Rumble Strips on Rural
Two-Lane Roads in Louisiana with Empirical Bayes Method
Thesis Director: Dr. Xiaoduan Sun
Pages in Thesis: 66; Words in Abstract: 177

ABSTRACT

Louisiana two-lane rural roads possess a low geometric standard with very low AADT but

more fatalities and fatal crashes compared to other type of roads. Previous studies present

results of significant safety improvement due to installation of centerline rumble strips,

especially in preventing head on and opposite direction sideswipe crashes. LADOTD has

installed over 2,100 miles of centerline rumble strips all nine district wide during 2010-2012.

This study used three years of crash data for the before and after time period, and applied the

Empirical Bayes (EB) method in the analysis to estimate the crash modification factors of

centerline rumble strips for rural two-lane roads. Estimated CMF is 0.89, which means there

is an 11% expected crash reduction in implementation of centerline rumble strips on rural

two-lane highways. The statistically estimated standard deviation for the CMF is 0.03.

Moreover, crash characteristics analysis was performed in this study to compare the

difference before and after center line rumble strip implementation. The crash reduction is

consistent in all crash types and particularly significant in targeted cross centerline injury

crashes.
 BIOGRAPHICAL SKETCH

Mohammad Ashifur Rahman was born on December 11, 1989 in Naogaon, Bangladesh. He

received a Bachelor of Science in Civil Engineering from Bangladesh University of

Engineering and Technology in 2012. He joined FERBA Instrumentation Logistics, Dhaka in

June 2012 and continued there as Project Manager for two years until July 2014. Ashifur has

studied in the M



 


  

 

 

 

the University of Louisiana at Lafayette since August 2014 and graduated in spring 2016. He

is continuing his PhD in Systems Engineering with a concentration in Civil Engineering at

University of Louisiana at Lafayette.