SPF

SAFETY PERFORMANCE FUNCTION

A safety performance function (SPF) is an equation used to predict the average number of crashes per year at a location as a function of exposure and, in some cases, roadway or  intersection characteristics. In case of a section of a highway, exposure is represented by the corresponding length and annual average daily traffic (AADT).

One of the main goals is to calibrate Safety Performance Functions (SPFs) that can predict the frequency per year of injuries and fatalities on homogeneous road segments.  Analysis of accident data confirms the effectiveness of the SPFs.  Using previous data of crash, traffic, and road inventory data for various roads, fixed- and random-parameter count data models are calibrated. However, it has been seen that accidents are greater in number than the predictions made by the Safety Performance Functions. Hence, an area specific random parameter poisson’s SPF gives the best-fit random parameter SPF specification for crash frequency. It includes the following variables -  annual average daily traffic, segment length, shoulder width, lane width, speed limit, and the presence of passing lanes. Hence, heterogeneity-based models can be specified and used for obtaining accurate crash predictions.

Predicted Crashes = exp[α + β * ln(AADT) + ln(Segment Length)]

For intersections, exposure is represented by the AADT on the major and minor intersecting roads

Predicted Crashes = exp[α + β1 * ln(AADTmajor) + β2 * ln(AADTminor)]

Example: The SPF from the Highway Safety Manual for total Multiple Vehicle (MV) crashes at urban, four-legged signalized intersections using the above equation where α, β1 and β2 were  calculated separately is:

Predicted MV crashes = exp[-10.99 + 1.07*ln(AADTmajor) + 0.23*ln(AADTminor)]

For an urban, four-legged signalized intersection with a major road traffic volume (AADTmajor) of 25,000 vehicles per day and a minor road traffic volume (AADTminor) of 10,000 vehicles  per day, the predicted number of MV crashes is computed as follows for the given SPF.

Predicted MV crashes = exp[-10.99 + 1.07*ln(25,000) + 0.23*ln(10,000)] = 7.13 crashes/year

SPFs are used to predict crash frequency for a given set of site conditions. The predicted crashes from the SPF can be used alone or in combination with the site-specific crash history  (i.e., Empirical Bayes method) to compare the safety performance of a specific site under various conditions. The Empirical Bayes method is used to estimate the expected long-term  crash experience, which is a weighted average of the observed crashes at the site of interest and the predicted crashes from an SPF

The predicted number of crashes calculated using SPFs is instrumental for a number of activities in the project development process, including

1)      Network screening,

2)      Countermeasure comparison, and

3)      Project evaluation.

 Network Screening

SPFs can be used in the network screening process to determine whether the observed safety performance at a given location is higher or lower than the average safety performance of other sites with similar roadway characteristics and exposure. This is useful in the safety management process to identify sites with potential for safety improvement.

 Countermeasure Comparison

SPFs can be used to predict the baseline crash frequency for given site conditions when comparing potential countermeasures. SPFs are used alone or in conjunction with the crash history to estimate the long-term crash frequency for baseline conditions (without treatment) and crash modification factors (CMFs) are applied to estimate the crashes with treatment as shown in Equation 3. This is useful in activities where there are multiple alternatives to address safety concerns and it is desirable to quantify and compare the potential benefits of each treatment.

 Project Evaluation

It is important to evaluate the safety effectiveness of roadway improvements to provide input to future planning, policy and programming decisions. The current state-of-the-practice is to employ the Empirical Bayes method in an observational before-after study to develop CMFs. SPFs are a critical component of the Empirical Bayes method, which combines the crash history for a given site with the predicted crashes from an SPF. In particular, the SPF helps to account for changes in traffic volume over time.