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Title: CE 7600: Highway Safety and Risk Management


1
CE 7600 Highway Safety and Risk Management
Dr. Tapan Datta
2
Paired T Test
Analysis Question Is the before mean of a group
of locations significantly different from the
after mean for
the same locations?. Null Hypothesis There is
no difference between the before mean and
variance of a group of locations and the after
mean and variances for the same locations. XB
XA SD/?N Where XB Before sample mean
XA After Sample Mean S2D S2B S2A 2
? (XB1 XB) (XA1 XA)
t
N Number of Locations
If tcalculated gt tcritical, difference in means
is statistically significant where
degrees of freedom N-1
3
Example of Paired T test
Mean of expected crash rate without treatment
2.01 Mean of after period crash rate
1.07 Variance of the expected crash rate without
treatment 1.31 Variance of the after crash
rate 0.17 t calculated 1.819 t critical
1.476 _at_ ? 0.10 Since, tcalculated gt tcritical,
difference between the before crash rate mean and
the after crash rate mean is statistically
significant at 90 Level of confidence
4
  • E - Perform Economic Analysis
  • Methods to Use
  • Benefit/Cost Ratio Method - The ratio of the
    benefits accrued from accident and/or severity
    reduction to costs needed to implement the
    countermeasures.
  • Cost Effectiveness Method - The cost to the
    agency of preventing a single accident or
    accident type.

5
F - Prepare Evaluation Documentation The
evaluator must draw conclusions regarding the
overall effectiveness and worth of the project
and review the appropriateness of all activities
of the evaluation study which lead to the final
conclusions.
6
  • G - Develop and Update Effectiveness of Database
  • An effectiveness database is an accumulation of
    sound project evaluation results which are
    directly usable as input to project selection and
    project development within the Planning
    Component.
  • The data base should contain information on the
    accident reducing capabilities of a project in
    terms of average accident rate reduction.
  • This information is a requirement for use in
    economic analysis of proposed projects.

7
RISK MANAGEMENT
8
What is Risk Management?
  • Risk Management for a road agency is the
    identification, measurement and treatment of
    potential traffic crashes and associated tort
    liability and monetary losses.
  • A well planned risk management system will enable
    a road agency to handle its exposure to traffic
    crash losses and associated tort liability in the
    most economical and effective way.

9
What is Risk?
  • Risk is defined as the variation in the possible
    outcomes in a given situation
  • Pure Risk
  • When there is a chance of loss, but no chance of
    gain.
  • Speculative Risk
  • When there is a chance of gain as well as loss.

10
Steps Involved in the Process
  • Risk Identification identifying particular
    types of potential loss exposure
  • Estimation of potential losses associated with
    these exposures
  • Probability that each particular type of loss
    will occur
  • Estimation of the total losses likely to occur
    during the planning period
  • Financial impact of these losses

11
Steps Involved in the Process
  1. Selection of appropriate tools to be used in
    alleviating the risk
  2. Implementation of risk management process
  3. Monitoring and Evaluation

12
The Legal System
  • Plaintiff one who makes the original
    complain against the other party
  • Defendant the other party who is defending
    the complain
  • Attorney at Law
  • A person qualified in character and training to
    serve as an official of the court in representing
    people and agencies, and advising them in regard
    to law.

13
American Legal System
  • 1. Federal Statutory Law
  • enacted by the U.S. Congress
  • enforced by the President through executive
    branch of government
  • interpreted by
  • U.S. District Courts
  • U.S. Circuit Courts of Appeals
  • U.S. Supreme Court
  • seldom involved in tort liability
  • Federal Government cannot be sued except with
    their permission

14
American Legal System (Cont.)
  • 2. State Statutory Law
  • enacted by state legislative bodies
  • enforced by the Governor and executive agencies
  • interpreted by state trial courts, appellate
    courts, and State Supreme Court

15
American Legal System (Cont.)
  • 3. Municipal Court or City Court
  • judicial arm of municipal government
  • legislative equivalent is the City Council
  • executive equivalent is the Mayor

16
U.S. Court System
  • 1. U.S. District Court
  • trial court
  • one or several districts in each state
  • 2. Circuit Courts of Appeals
  • 11 circuits each with a court of appeals
  • intermediate between the trial court and the
    Supreme Court

17
U.S. Court System (Cont.)
  • 3. U.S. Supreme Court
  • highest court in the nation
  • appellate court
  • ultimate decision forum for all legal questions,
    state and federal
  • 4. Specialty Courts
  • maritime courts
  • patent courts
  • U.S. courts of Claims

18
Michigans State Court System
  • 1. Municipal Court
  • independent courts operated by city governments
  • courts of original jurisdiction
  • monetary limitations
  • scope enforce municipal code
  • traffic fines
  • disturbing the peace charges, etc

19
Michigans State Court System (Cont.)
  • 2. Probate with Probate Judge
  • judge hears cases in chambers
  • formal filing of wills
  • 3. District Courts
  • lowest level of original jurisdiction
  • claims up to 10,000
  • cases heard by judge or jury

20
Michigans State Court System (Cont.)
  • 4. Circuit Courts
  • highest ranking trial court
  • lawsuits over 10,000
  • cases heard by a jury
  • unless the state is the defendant
  • 5. Court of Civil Appeals
  • intermediate appellate court
  • claims less than 10,000
  • does not exist in Michigan

21
Types of Law
  • Statutory Law
  • - enacted by a legislative body
  • Case Law
  • - body of the law created by judges
  • Regulatory Law
  • - enacted by a regulatory agency with more
    detailed provisions of a legislative enactment
  • Substantive Law
  • - applies to any substance of any given issue

22
Types of Law (Cont.)
  • Procedural Law
  • - procedures to be followed in pursuing a legal
    remedy
  • Criminal Law
  • - enforcement of standards of conduct by the
    State
  • - State is always a party to the criminal case
  • Civil Law
  • - non-criminal law dealing with regulation

23
Concept of Tort and Negligence
  • Tort - a civil wrong or injury.
  • The person/agency performing the tort is liable
    for damages.
  • Negligence failure to use reasonable care in
    dealing with others.

24
Concept of Tort and Negligence
  • In order to win a judgment on the grounds of
    negligence, the plaintiff must prove
  • Defendant (road agency) had a duty to use
    reasonable care toward plaintiff (road user).
  • Defendant breached that duty (negligence)
  • Defendants negligence was a proximate cause of
    plaintiffs injury.
  • Plaintiff incurred resulting damages.

25
Notice of Defect
  • Actual Notice
  • Simplest form, e.g., a complaint call.
  • Constructive Notice
  • If defects exist for an unreasonable length of
    time, it should have been discovered by the road
    agency.
  • Statutory Notice
  • A readily apparent defect for 30 days, the road
    agency is conclusively presumed to know it with
    sufficient time to correct it.
  • Notice by Own Actions
  • IF entitys own actions cause the defect, no
    notice is required.

26
Jury vs. Judge Trial
  • A dispute not settled or abandoned prior to trial
    may be submitted to a judge or a jury
  • Juries consist of persons selected from the
    community to pass upon guilt in criminal matters,
    and to decide disputed factual questions in civil
    matters.
  • In state courts, attorneys are allowed to
    question the jurors to determine their
    impartiality.

27
Jury vs. Judge Trial
  • One aspect of jury system both praised and
    criticized is that
  • Jurors need not to give any reasons for their
    opinions.
  • Jurors are free to disregard the law if they so
    desire.
  • While the judge instructs the jury as to the law,
    they are, for all practical purposes, free to do
    as they choose.

28
PROCEDURES USED IN LAW SUIT
  • Initiating a Complaint
  • Filing a Complaint
  • A complaint is a document asserting a legal
    stance claiming that someone and/or something was
    wrong.
  • Service of Complaint and Summons
  • A Summons is a command to a party to either
    appear for a trial or to file a document of
    denial, which is called an Answer

29
PROCEDURES USED IN LAW SUIT
  • Initiating a Complaint (continued)
  • Filing of Answer
  • After an Answer has been filed, the case is
    said to be at Issue
  • Other Pleadings
  • Plaintiff may wish to file a Response, which is
    a document responding to the Answer.
    Defendant may file a Counterclaim.

30
PROCEDURES USED IN LAW SUIT
  • Discovery of Facts
  • A process sanctioned by the court in which
    attorneys representing each party gather
    information about the case. It is designed to
    reveal strengths and weaknesses of the case and
    thereby permit an appraisal of settlement
    potential.
  • Interrogatories
  • Written questions about the case submitted by one
    party to the other
  • Requests for admissions
  • Written statements of facts addressed to one
    party by other with a demand for admission of
    such statements of fact

31
PROCEDURES USED IN LAW SUIT
  • Discovery of Facts (Continued)
  • Depositions
  • Established procedures for oral questions to be
    asked by an attorney to other parties, witnesses
    or experts, with the answers given under oath. A
    word-for-word transcript is made by a court
    reporter.
  • Production of Documents
  • Requesting and obtaining documents from the other
    party

32
PROCEDURES USED IN LAW SUIT
  • Mediation-Arbitration
  • A third party dispute resolution system that
    resembles litigation, but has important
    differences.
  • Third party seeks to mediate disputes between the
    adversarial parties by aiding in the negotiation
    process with a view toward settlement
  • If the parties do not agree to a settlement of
    the dispute, the third party then uses normal
    arbitration power to decide the case
  • Mediator-Arbitrator is selected in advance by the
    parties
  • Designed to avoid costs, inefficiencies and
    unpredictability of the judicial system

33
PROCEDURES USED IN LAW SUIT
  • The Trial
  • Jury selection (If a jury trial)
  • Challenges for cause
  • Preemptory challenges
  • Opening statements of counsel (Not evidence)
  • Plaintiffs case
  • Witnesses Direct examination
  • Witnesses Cross examination
  • Documentary evidence

34
PROCEDURES USED IN LAW SUIT
  • The Trial (continued)
  • Defendants case (same sequence as Plaintiffs)
  • Closing statements of counsel (Not evidence)
  • Jury instructions by court
  • Jury deliberations and verdict
  • Judgment of court

35
PROCEDURES USED IN LAW SUIT
  • Post-Trial Activities
  • It is important to collect data on the number of
    claims and losses, the categories in which the
    losses occur.
  • Classify functional areas and geographic
    locations that are most likely to generate new
    lawsuits and large judgments
  • Target resources to improve those facilities for
    which the agency is most vulnerable

36
PROCEDURES USED IN LAW SUIT
  • Selecting Cases to Appeal
  • The basis for appealing a court decision is an
    alleged error in trial procedure or application
    of the law.
  • Jurors finding of the facts of the case cannot be
    appealed
  • For small awards, it is impractical to be
    concerned about an appeal
  • A well-conceived loss mitigation program will
    carefully select those cases for appeal that
    would otherwise set adverse precedents

37
Risk Management System
  • An ideal goal for all agencies would be the
    elimination of all traffic crashes, which is not
    realistically achievable.
  • A Risk Management System permits a road agency to
    target specific improvements which will minimize
    traffic crashes, lawsuits, and the fiscal losses.

38
Objectives of Risk Management System
  • To minimize the number of lawsuits filed against
    a road agency
  • To minimize the number of those suits that are
    ultimately lost or settled adversely
  • To minimize the total dollar damages from tort
    liability

39
Programs and Processes in Risk Management System
  • Programs
  • Crash reduction
  • Loss reduction
  • Defect surveillance
  • Public relations
  • Processes
  • Risk identification
  • Resource allocation
  • Risk management evaluation

40
Risk Management System
Risk Identification Process
Crash Reduction Program
Loss Reduction Program
Defect Surveillance Program
Public Relations Program
Resource Allocation Process
Countermeasure Implementation
Risk Management Evaluation Process
Transfer Lessons from Evaluation to Various
Programs
41
Program Components of Risk Management System
  • Crash Reduction Program
  • Identify hazardous locations
  • Identify alternative countermeasures
  • Select the most suitable countermeasures
  • Implement and review the selected countermeasures
  • Evaluate effectiveness

42
Program Components of Risk Management System
  • 2. Loss Reduction Program
  • Crash site investigation
  • Review the history of complaints
  • Perform a liability assessment
  • Administer discovery process(es)
  • Coordinate expert witnesses and deposition needs
  • Coordinate all aspects with attorney(s)
  • Determine trial support needs
  • Review and critique all aspects of trial
    procedures
  • Provide risk management recommendations

43
Program Components of Risk Management System
  • 3. Defect Surveillance Program
  • Up-to-date inventories
  • Citizens complaint system
  • Employee review system
  • Complaint deposition system

44
Program Components of Risk Management System
  • 4. Public Relations Program
  • Coordination with local radio stations to
    encourage reporting of defect and crash
    surveillance information
  • Public information news releases to create a
    positive image of the road agency

45
Inputs to the Risk Management System
Past Lawsuits History
History of Judgments Settlements
Crash History
Traffic Data
Roadway Data
Crash Reduction Program
Loss Reduction Program
Risk Management System
Defect Surveillance Program
Public Relations Program
Media Availability
Media Support
Citizens Complaint Data
Complaint Disposition Data
Employee Review Data
46
Key Process Within the Risk Management System
  • Risk Identification Process
  • Consists of one or more of the following
    activities
  • Determine crash rates
  • Determine severity rates
  • Determine fatality rates
  • Determine various exposure measures
  • Determine frequency and rate of lawsuits

47
Key Process Within the Risk Management System
  • Risk Identification Process
  • (Continued)
  • Categorize roadway situations by type
  • high, medium, and low probability of generating
    lawsuits against the agency
  • Determine probability of crashes for each type of
    roadway situation
  • Determine the risk factor (i.e., a factor based
    on crash history and defects)
  • Rank ordering of situations by risk factor

48
Key Process Within the Risk Management System
  • Roadway Categories
  • Urban-Rural
  • Number of lanes
  • Intersection, tangent and curve sections
  • Traffic volumes
  • Percent grades
  • Types of shoulder and shoulder widths
  • Type of traffic control
  • Type of defects, etc.

49
Key Process Within the Risk Management System
  • 2. Resource Allocation Process
  • Identify the types of deficiencies by roadway
    situations
  • Estimate safety improvement costs
  • Estimate judgment/settlement costs
  • Determine benefits derived from risk
    reduction/elimination
  • Determine benefit/cost ratios
  • Determine resource allocation strategy

50
Key Process Within the Risk Management System
  • 3. Risk Management Evaluation Process
  • Conduct a highway safety evaluation program
    following FHWA documents
  • Determine the reduction or increase in the
    lawsuit rate
  • Determine the reduction or increase in the
    judgment settlement rate
  • Perform significance testing
  • Determine the benefit (loss) from the risk
    management program

51
Goals of a Risk Management System
  • Minimization of
  • Highway traffic crashes
  • Highway traffic crash severity
  • Highway traffic crash potential
  • Lawsuits stemming from highway traffic crashes
  • Losses from lawsuits

52
Key Individuals in a Typical Road Agency
  • Policy Makers
  • Highway Designers
  • Highway Operational Personnel
  • Highway Maintenance Personnel
  • Enforcement Personnel
  • Defense Attorneys
  • Risk Management Analysts

53
Data Needs
  • Historic and current data
  • Traffic crashes
  • Roadways
  • Roadsides
  • Traffic control devices
  • Maintenance
  • Lawsuits

54
Crash Data
  • A comprehensive historical crash database (for a
    minimum of 3 years), as well as current crash
    data, inclusive of the entire roadway network,
    which entails
  • A roadway location index
  • A system for entering and locating all reported
    traffic crashes
  • A procedure for retrieving crash data on demand

55
Roadway Data
  • Roadway database should contain the following
    information for each segment of roadway
  • Classification by urban, suburban, rural
  • Number of lanes by direction
  • Lane widths
  • Shoulder type and width
  • Alignment
  • Grades
  • Roadway condition
  • Traffic volume
  • Others

56
Roadway Data
  • Road agencies should establish a computerized
    database.
  • Photologs
  • Videologs
  • Asset management systems

57
Pavement Condition Inventory
  • Location reference and length of section
  • Classification
  • Geometry
  • Number of lanes, lane width,
  • shoulder type and width,
  • Pavement Type
  • Condition Assessment of Pavement Distress
  • Location, Type and Severity
  • Cracking alligator, longitudinal or transverse
  • Patches
  • Rutting and depressions
  • Weathering and raveling
  • Potholes
  • Others

58
Traffic Sign Inventory
  • Location Information
  • Sign Information
  • Sign message and code
  • Sign Condition
  • Retro-reflectivity
  • Support information
  • Type and condition
  • Standard or Nonstandard
  • Date of Last Maintenance
  • Life Expectancy

59
Traffic Signal Inventory
  • Location Information
  • Signal Information
  • Number and size of signal heads
  • Controller Information
  • Type, make, model
  • Pedestrian Signal Information
  • Signal Timing Information
  • Number of Plans
  • Days/Hours of Operation
  • Cycle length, phasing and timing details
  • Maintenance Information

60
Pavement Marking Inventory
  • Longitudinal Pavement Markings
  • Transverse Pavement Markings
  • Word/Symbol Pavement Markings
  • Location Information
  • Type/Color
  • Condition
  • Retro-reflectivity

61
Sidewalk/Handicap Ramp Inventory
  • Location Information
  • Width/Length/Material
  • Condition of Sidewalk
  • Presence of Handicap Ramp

62
GIS Base-map for the City of Detroit
63
Word Pavement Marking Inventory
Pavement Marking Inventory on Warren Avenue
Longitudinal Pavement Marking Inventory
Pavement Marking Data Inventory in GIS
64
Loss Data
  • The following data should be compiled for the
    lawsuit complaints, depositions, judgments,
    post-trial analyses, etc
  • Type of roadway situation involved in the
    lawsuit, e.g., intersection, curve, tangent,
    urban-rural, number of lanes, etc.
  • Type of crash, including severity
  • Vehicle speeds involved in the crash
  • Nature of alleged defect
  • Expert witnesses used by defense and plaintiff
  • Details of post-trial analysis
  • Any other information which can assist in the
    loss reduction program

65
Defect Data
  • Irrespective of the size of a roadway system
    under the jurisdiction of an agency, the agency
    should perform a comprehensive inventory of
    roadway defects. Following typical roadway
    defects should be identified and inventoried
  • Shoulder
  • Significant drop-off
  • Soft shoulder
  • No shoulder
  • Drainage ditch too close to the edge of pavement

66
Defect Data
  • Designs
  • Improper super elevation
  • Sight distance restrictions
  • Surface
  • Slippery
  • Large pot holes
  • Washboarding and rutting (gravel roads)

67
Defect Data
  • Work Zone
  • Nonstandard traffic control devices
  • Inadequate advance warning
  • Nonreflecting signing
  • Improper delineation
  • lack of barriers separating traffic and workers

68
Defect Data
  • Signs
  • Nonstandard
  • Obstructed view of sign
  • Nonreflectorized
  • Absence when needed
  • Roadside Obstacles
  • Utility poles, sign posts
  • Bridge abutments and piers
  • Trees
  • Boulders

69
Defect Data
  • Bridges
  • Too narrow
  • Inadequate bridge rails
  • Railroad Crossings
  • Absence of standard signs and markings
  • Absence of flashers and/or gates when warranted
  • Drainage
  • Inadequate drainage of the pavement surface
  • Ponding
  • Clogged inlet gates

70
Defect Data
  • Signals
  • Unwarranted signals
  • Absence when needed
  • Improper timing design
  • Improper phasing
  • Markings
  • Absence of edgelines when warranted
  • Obliterated or badly worn lines

71
Defect Data
  • Guardrail
  • Nonstandard
  • Improper end treatment
  • Maintenance
  • Lack of appropriate ice and snow removal and/or
    treatment
  • Inadequate grading of gravel roads
  • Permitting any of above-mentioned defects to
    develop and/or remain for an unreasonable time

72
Risk Identification Process
  • A process by which a road agency systematically
    identifies its liability exposure using past data
    and state-of-the-art analysis techniques.
  • Knowledge of where future traffic crashes are
    most likely to occur, and situations where the
    risk of being sued is greatest is essential
    information for a road agency.
  • This knowledge can then be used
  • To alter the roadway features (make it safer)
  • To alter strategies, maintenance policies and
    procedures
  • In order to identify potential risks one must
    have access to and analyze
  • Crash category
  • Lawsuit history within the agency, and/or
  • Lawsuit history in the region

73
Risk Identification Process
  • In order to identify potential risks one must
    have access to and analyze
  • Crash category
  • Lawsuit history within the agency, and/or
  • Lawsuit history in the region

74
Risk Identification Process
  • The risk identification process is rigorous for
    larger road agencies, like State DOT, large
    county and large cities.
  • For small road road agencies, risk identification
    may have to be based on
  • Risk trends in the region
  • Roadway situations which have been identified by
    others as high risk locations for local roadway
    environments, and/or
  • Observed defects on the roadway and its
    environment

75
Crash History
  • A complete review of past crash data is necessary
    to provide answers to questions like
  • Where are the roadway crashes occurring?
  • What types of roadway situations are experiencing
    roadway crashes?
  • Where are the injury and fatal crashes happening?
  • What are the crash, injury and fatality rates at
    various roadway situation types?

76
Crash History
  • For larger road agencies with computerized crash
    database, these questions can be answered by
    performing the following analysis
  • Divide the roadway system into urban, suburban
    and rural categories
  • Subdivide crash database into the above
    categories
  • Identify in each of the three categories the
    following situation types
  • Intersections of various numbers of approach
    lanes and configurations
  • Tangent sections
  • Curves isolated, winding
  • Grades isolated, rolling

77
Crash History
  • (Continued)
  • 4. Accumulate crash data by each type of the
    situation types for urban, suburban and rural
    categories
  • 5. Perform a count of each type of situation
    within each category
  • 6. Determine 3-year crash history for each
    situation type within the category

78
Example
  • A county road agency has the following road
    mileage categories
  • 500 road miles in urban areas
  • 800 road miles in suburban areas
  • 700 road miles in rural areas
  • The three year crash history distributed among
    three categories is
  • 6,000 total crashes (60 fatal, 2,000 injury
    3,940 PDO)
  • 4,000 total crashes (40 fatal, 1,500 injury
    2,460 PDO)
  • 2,000 total crashes (100 fatal, 1,000 injury
    900 PDO)

79
Example (contd.)
  • The county has the following roadway situations
    within each category of the road systems
  • Urban
  • 2,400 intersections
  • 800 5 lane-5 lane
  • 800 4 lane-4 lane
  • 300 5 lane-2 lane
  • 300 4 lane-2 lane
  • 200 2 lane-2 lane
  • 400 miles of tangent sections
  • 150 miles of 5 lane
  • 150 miles of 4 lane
  • 100 miles of 2 lane
  • 100 isolated curves
  • 50 winding sections
  • 30 roadway segments with grades
  • 25 roadway segments with rolling terrain

80
Example (contd.)
  • Similar characteristics for the suburban and
    rural road systems would also be available.
  • For each category and situation type
  • Determine the crash, injury and fatality rates
    to assess the crash experience and associated
    risk
  • Should also consider exposure factors Traffic
    Volumes

81
Risk Analysis
  • 1. Develop of probability density functions P(x)
    for the occurrence of crashes
  • Develop using a vast amount of actual data
  • Assume a probability density function
  • Poisson distribution
  • Assume mean value of occurrence using the mean of
    the historical data
  • 2. Develop loss probability functions
  • Monetary loss data associated with the crash
    would also be obtained
  • Using a vast amount of actual data or the Poisson
    Distribution
  • Determination of the most probable causes of
    crashes from past history
  • Determination of the costs of countermeasures

82
Risk Analysis
  • Determination of loss risk functions
  • Simple form
  • Expected loss at X failures ?P(x) loss
    amount
  • where x No. crashes
  • Complex form
  • Expected loss at X failures ?P(x) loss
    amount ?f(defects)
  • where f(x) function of defects in the system
    related to accidents based on historical
    data
  • ?f(defects) w1d1 w2d2 wndn
  • where wi weighting factors in the same unit
    as loss values, often in monetary
    units

83
Risk Analysis
  • 6. Economic analysis
  • Development of alternative decision strategies
  • Management decision making
  • Implementation of countermeasures

84
Determination of Probability of Traffic Crashes
Expected values of future crashes at any
particular situation/category site can be
determined as follows
  • M TOTAL Mean total crashes in a particular
    situation type for a specific roadway category
    per unit time per location.
  • M INJURY Mean injury crashes in a particular
    situation type for a specific roadway category
    per unit time per location.
  • M FATAL Mean fatal crashes in a particular
    situation type for a specific roadway category
    per unit time per location.

85
Example (contd.)
  • Suppose, there are 30 injury crashes at the 100
    isolated curves in the study area.
  • The expected value of future crashes at these
    types of curves can be computed as
  • 30 injury crashes per 100 curves per 3 years,
    or
  • 10 injury crashes per 100 curves per year

86
Probability of Occurrences
  • where P (x) Probability that there will be x
    number of occurrences over a specific time
    frame
  • M Mean or expected value of total, fatal or
    injury crash over the same time frame
  • X Number of occurrences
  • ? ?M, where ? standard deviation

87
Example (contd.)
  • M 30 crashes per 3 years/100 curves
  • 0.10 injury crashes/curve/year
  • Standard deviation 0.316 crashes /curve/yr
  • (0.1)0 . e-0.1
  • Similarly,
  • P (1) 0.0905, P (2) 0.0045, P (3) 0.001
  • Probability of 0 to 3 injury crashes, P (0 to 3)
  • P (0) P (1) P (2) P (3) 0.9999
  • Therefore, P (gt 3 injury crashes) 1 0.9999
  • 0.0001

0.905
P (0)
0!
88
Example (contd.)
1.0
0.905
0.8
Poisson Distribution with a mean crash occurrence
0.10
0.6
P(Xx)
0.4
0.2
0.0905
0.0045
0.001
3
0
1
2
x
89
Loss Probability Functions Example
  • Suppose an agency has the following loss data and
    probabilities
  • Annual Loss (/year) Probability
  • 0 0.606
  • 5,000,000 0.273
  • 10,000,000 0.100
  • 20,000,000 0.015
  • 50,000,000 0.003
  • 100,000,000 0.002
  • 200,000,000 0.001

90
  • Probability that agency will not suffer any
    losses is 0.61
  • Probability that agency will suffer some loss
    0.39 ( 1- 0.61)
  • Probability that agency will suffer losses gt
    20M
  • 0.015 0.003 0.002 0.001 0.021

91
  • Expected loss can be computed as
  • 0(0.606) 5M(0.273) 10M (0.1) 20M
    (0.015) 50M (0.003) 100M (0.002) 200M
    (0.001) 3.215 x106 per year
  • Next step is to determine the cost of eliminating
    exposure to potential loss through various
    countermeasure strategies
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