Topic 1

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Topic 1 Fundamentals CEE 763
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BASIC TERMS

• Traffic crash event(s) resulting in injury or
  property damage
• Crash frequency number of crashes in a certain
  period (year)
• Crash severity KABCO levels
• K Fatal injury
• A Incapacitating injury
• B Non-incapacitating evident injury
• C Possible injury
• O Property damage only (PDO)

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BASIC TERMS (CONTINUED)

• Crash type
• Rear-end sideswipe angle turning head-on
  run-off the road fixed object animal
  pedestrian out of control work zone
• Collision diagrams

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COLLISION DIAGRAMS
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BASIC TERMS (CONTINUED)

• Expected crash frequency long-term average
• Crash rate number of crashes per unit exposure
• Safety performance function (SPF) one of the
  methods to predict the expected crash frequency
• Accident modification factor crash reduction
  due to a treatment

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EXAMPLE

• A roadway section has a length of 2.5 miles and
  an AADT of 20,000. What is the expected crash
  frequency per year for this roadway section if
  the SPF is as shown
• An intersection with a permitted LT control is
  converted to a protected LT control. If the AMF
  for protected LT is 0.90. What is the percent
  reduction in crash after the control change?
  Suppose the intersection has a crash frequency of
  10 crashes per year with permitted LT control,
  what is the expected number of crashes per year
  after the change of the control?

Comment on the relationship between SPF and AMF
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REVIEW OF STATISTICS

• Traffic crash can normally be estimated according
  to the Poisson Distribution.
• For Poisson distribution, the variance is equal
  to the mean.
• Central Limit Theorem Regardless of the
  population distribution, the sample means follow
  a normal distribution.
• The standard deviation of the mean (also called
  standard error) can be estimated by

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EXAMPLE

• On average, a railroad crossing has about 2
  crashes in three years. What is the probability
  that there are more than 1 crashes in a year?

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EXAMPLE

• Ten random samples were obtained as the
  following
• 2, 4, 6, 1, 6, 8, 10, 3, 5, 3. Calculate the
  standard error of the sample. What is the
  implication of this calculated standard error?
• Exercise In Excel, generate 100 random samples
  from a uniform distribution with a mean of 10
  (i.e., U0,20). Repeat 10 times of the sampling
  process. Compare the estimated standard error
  from the initial 100 samples and the standard
  deviation of the sample means from the 10-time
  sampling data.

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REVIEW OF STATISTICS

• Mean and variance for linear functions of random
  variables
• Coefficient of variation normalized standard
  deviation

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REVIEW OF STATISTICS

• Confidence interval

the standard deviation of the sample
the standard deviation of the population
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EXAMPLE

• Two sites have the following crash data
• Road section X Y
• Length, mi 1 0.2
• Expected crash this site 52.2 11.0 (mean
  and s.d.)
• Expected at similar sites 20.5 0.40.1
• Which site has more reliable data, assuming the
  performance measure is excess of crash
  frequency? If the limiting coefficient of
  variation is set at 0.05, what is the typical
  estimation error with respect to the mean?

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REGRESSION-TO-MEAN BIAS
Perceived
RTM Bias
Expected average crash frequency
Actual reduction due to treatment
Actual crash frequency
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EMPIRICAL BAYES METHODS
Crash Frequence
E(k) is the predicted value at similar sites, in
crash/year Y is the analysis period in number of
years f is over-dispersion factor
Volume
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EXAMPLE

• A road segment is 1.8 miles long, has an ADT of
  4,000 and recorded 12 accidents in the last year.
  The SPF for similar roads is shown in the
  equation, where L is length of the segment in
  miles
• If the standard deviation of the accidents is
  accident/year, what is the expected number of
  accidents and the standard deviation for this
  site?

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Homework

• Now the same road segment has 3 years of accident
  counts (12, 16, 8). What is the expected number
  of accidents and the standard deviation for this
  site?