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Are you making the best roadway safety decisions?
How do you know?
One of the most basic components of evidence-based safety is quantifying safety performance
in terms of the estimated frequency and severity of crashes.
Once you quantify the safety performance of a facility, existing or planned, you can use
this information to support decisions throughout the project development process from planning
and design to operations and maintenance.
For example, it allows you to optimize design decisions, assess the safety impacts of design
exceptions, and compare the cost-effectiveness of alternatives.
In this video, you will learn how to:
define observed, predicted, and expected crashes and crash frequency;
describe the strengths and limitations of using observed, predicted, and expected crash
frequency to estimate the safety performance of a facility;
select an appropriate analysis approach to estimate the safety performance of a facility;
and apply observed, predicted, and expected crash frequency
to estimate the safety performance of a facility.
There are three approaches to define the safety performance of a facility:
observed crash frequency,
predicted crash frequency,
and expected crash frequency.
Observed crashes are those reported and documented at a site of interest.
The observed crash frequency is simply the number of observed crashes at a specific location
during a defined time period.
Predicted crashes are based on a safety performance function, or SPF.
When you use an SPF to estimate crashes, the result is the predicted crash frequency.
The expected crash frequency is the combination of observed and predicted crash frequencies.
Specifically, you would use the Empirical Bayes, or EB method, to compute a weighted
average of the observed and predicted crash frequencies.
Each approach has specific strengths and limitations, and these approaches differ in terms of the
reliability and data requirements.
In some cases, data availability may limit the approach you choose.
The observed crash frequency approach is relatively simple and requires minimal data.
The reliability of this approach improves with a larger sample of observed crashes and
smaller degree of fluctuation in annual observed crashes.
The primary limitation is that it does not account for potential changes that affect
safety performance at the location of interest from year-to-year.
For example, it does not account for changes in traffic, weather, crash reporting,
road conditions, land use, vehicle fleet, or driver behavior, all of which could impact the
safety performance of the facility.
The observed crash frequency approach assumes the historical observed crashes represent
the expected future safety performance in the absence of any changes to the site.
As such, it may not be reliable when the site characteristics change drastically from the
past condition to the present or future condition of interest.
If you were given an exam with the data shown on this chart and asked to estimate the crash
frequency for the present or future year, what value would you select?
a. 3 crashes per year (5-year average) b. 4 crashes per year (3-year average)
c. More than 5 crashes per year d. None of the above
The answer is likely 'c' (more than 5 crashes per year) because there is a clear
increasing trend in observed crashes.
This underlying trend could be due to several factors, but the important point is that the
average observed crash frequency does not capture this trend.
The predicted crash frequency is a measure of safety performance based on other segments
or intersections of a common facility type.
For example, you can predict the safety performance of an urban, four-legged, signalized intersection
based on the safety performance of other similar urban, four-legged, signalized intersections.
If you were given this chart and asked to predict the crash frequency for a facility
with 5000 vehicles per day, what value would you select?
a. 6 crashes per year b. 7 crashes per year
c. 8 crashes per year d. 9 crashes per year
The answer is 'd' (9 crashes per year)
because this is where the line for predicted crashes crosses the traffic volume
of 5000 vehicles per day.
You will need an SPF to compute the predicted crashes.
Refer to the resources web page at the end of this video for sources of SPFs.
This approach assumes the SPF prediction is representative of future safety performance.
While it accounts for annual fluctuations in observed crashes as well as changes in
traffic volume, roadway characteristics, and general time trends,
it does not consider historical crash data for the location of interest.
Therefore, this approach is appropriate when the observed crash history is not informative
of future conditions.
The observed crash history is generally not informative when there are major changes to
the land use, traffic operations, or facility type.
For example, if the existing condition is a two-lane road and the future condition of
interest is a four-lane road, then the historical observed crashes under the two-lane condition
probably do not reflect the safety performance under the future four-lane condition.
In these cases, the predicted crash frequency is generally appropriate.
The expected crash frequency combines the observed and predicted crash frequency using
the EB method.
This approach accounts for annual fluctuations in observed crashes as well as changes in
traffic volume, roadway geometrics, and general time trends.
The expected crash frequency approach assumes the combined information from observed and
predicted crashes is representative of future safety performance.
As such, it may not be reliable when the site characteristics change drastically from the
past condition to the present or future condition of interest.
Again, it is important to understand the strengths and limitations of these approaches because
the reliability of the approach will impact the reliability of analysis results,
and therefore, decision-making.
In selecting an appropriate analysis approach to estimate safety performance,
you should consider the level of rigor, scope of the project, and data availability.
You should also consider:
annual fluctuations in observed crashes;
changes in geometric or traffic control characteristics;
SPF availability and reliability;
and potential for changes in traffic volume.
This table provides an overview of the characteristics associated with observed, predicted,
and expected crashes to help determine when each is (or is not) appropriate.
For example, if there is a high degree of annual fluctuation in the observed crashes,
then using observed crash frequency may lead to inaccurate estimates
of the long-term safety performance.
If a calibrated SPF is available, you can consider using the predicted or expected crashes
to normalize annual fluctuations in observed crashes and account for changes in traffic volume.
The expected crashes are typically more reliable than predicted crashes when site characteristics
remain relatively constant from the past condition to the present or future condition of interest.
Use predicted crashes if the site characteristics change drastically from the past condition
to the present or future condition of interest.
You might also consider using the predicted crash frequency instead of the expected crash frequency
when you only have one or two years of observed crashes, which can lead to a higher
degree of annual fluctuations in observed crash frequency.
The observed crash frequency may provide a reasonable estimate when you have at least
five years of historical crash data and there is limited fluctuation in crashes from year to year.
In addition to these factors, you should consider the trade-off between the reliability of the approach
and the resources needed to conduct the analysis.
Consider the following scenario:
You do not have the observed crash history for the location of interest;
there are minor changes in geometric and traffic control characteristics;
You have a reliable, calibrated SPF for the facility type of interest.
What is an appropriate analysis approach to estimate the long-term safety performance of the site?
a) Observed crash frequency
b) Predicted crash frequency
c) Expected crash frequency
In this case, the appropriate answer is 'b' (predicted crash frequency) because a reliable
SPF is available and both the observed and expected crash frequency approaches require
historical crash data.
Now, let's assume the same scenario, but you now have at least five years of historical
crash data and there is limited fluctuation in crashes from year to year.
What is an appropriate analysis approach to estimate the long-term safety performance of the site?
a) Observed crash frequency
b) Predicted crash frequency c) Expected crash frequency
In this case, the expected crash frequency approach would provide the most reliable estimate,
but any of the approaches would provide a reasonable estimate.
At this point, you have selected an appropriate analysis approach and need to apply that approach
to estimate the safety performance for the condition of interest.
Let's walk through the application of each approach.
Again, the observed crash frequency is the historical record of reported crashes.
To estimate the current or future safety performance using the observed crashes, you simply compute
the average of the observed crash frequency over some past time period.
For example, if there were 3, 1, 5, 4, and 6 observed crashes in the last five years,
then the average observed crash frequency is 19 divided by 5, or 3.8 crashes per year.
The solid line in the figure represents the 5-year average of 3.8 observed crashes per year.
Note the weakness of using observed crashes. The result depends on the study period.
For example, if you only used the last three years of observed crashes, the 3-year average
is 5.0 crashes per year, represented by the dashed line in the figure.
A longer study period is generally preferred because it provides a larger sample of crashes
for analysis; however, a longer study period also increases the chances for other changes
over time such as: safety and operational improvements; natural degradation of surface friction and
sign reflectivity; and general land use and traffic patterns.
So, you should balance the length of the study period with the potential for other changes over time.
To estimate the predicted crash frequency, you need a calibrated SPF for the facility type of interest.
Let's assume the facility type of interest is a four-leg, signalized intersection
on a rural, two-lane road.
Let's also assume this SPF from the Highway Safety Manual represents an appropriate calibrated
SPF for the facility type of interest.
The SPF requires the major road traffic volume and minor road traffic volume as data inputs.
If, for the condition of interest, the major road volume is 5700 vehicles per day and the
minor road volume is 3300 vehicles per day, then the predicted crash frequency is 2.94
crashes per year.
Refer to the resources web page at the end of this video for further information on the
calibration and application of SPFs.
To estimate the expected crash frequency, you need to combine the observed and predicted
crashes using the EB method.
This equation represents the EB weighted average of observed and predicted crashes, where 'w'
is the weight computed from the second equation.
In these equations, the observed, predicted, and expected crashes are all in terms of crashes
over the study period.
So, if the study period is five years, then the observed crashes should be the sum of
observed crashes over the five-year period, the predicted crashes should be the sum of
predicted crashes over the five-year period, and the expected crashes would represent the
expected crashes over the five-year period.
The weight is based on the quality of the SPF.
The more confidence we have in the SPF, the more weight we will place on the predicted crashes.
The quality of the SPF is indicated, at least in part, by the amount of over dispersion.
Think of it this way, overdispersion is undesirable because it introduces uncertainty
in the SPF.
This is typically reported with the SPF, but be aware that some resources report this parameter
while others report the inverse.
In the second equation, 'k' is the inverse of the overdispersion parameter where larger
values of 'k' indicate a lesser quality SPF and result in a smaller weight, 'w'.
The HSM reports 'k' for the given SPFs.
For this example, let's assume the facility type of interest is a four-leg, signalized
intersection on a rural, two-lane road and the results from the previous two examples apply.
The total observed crash frequency was 19 crashes over the five-year study period.
The predicted crash frequency was 2.94 crashes per year, which would be 14.7 predicted crashes
over the five-year study period if the traffic volume remained constant.
The HSM indicates the value of 'k' is 0.11 for this SPF.
First, the weight is computed as shown, using 'k' and the sum of the predicted crashes
over the five-year study period.
Now, you can estimate the expected crashes using the EB method.
The result is an expected crash frequency of 17.37 crashes over the five-year period,
or 3.47 crashes per year.
For further instruction on the use of these approaches, refer to the HSM and the resource
web page at the end of this video.
If you wish to estimate the change in safety performance from installing a countermeasure
such as centerline rumble strips along a rural, two-lane road, then you will need to apply
a crash modification factor, or CMF, to the estimated long-term safety performance.
You can refer to the training video on the application of crash modification factors
for further guidance on how to select and apply CMFs.
This video demonstrated the use of three analysis approaches to estimate safety performance:
observed, predicted, and expected crash frequency.
This resource web page provides additional guidance on the strengths and limitations,
selection, and application of these approaches.
At the Federal Highway Administration, safety is our top priority.
For more information, visit us online at safety.fhwa.dot.gov.