3.4 Highway Safety and Crash Modification Factors (CMFs)

3.4 Highway Safety and Crash Modification Factors (CMFs)

Introduction to the Highway Safety Manual (HSM)

The AASHTO Highway Safety Manual (HSM) provides a quantitative, science-based approach to safety analysis. Rather than relying on subjective assessments, the HSM provides predictive methods to estimate the expected crash frequency and severity of a facility.

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Safety Performance Functions (SPFs)

A Safety Performance Function (SPF) is an equation that estimates the average crash frequency for a specific facility type under base conditions (e.g., standard lane widths, flat terrain, specific shoulder widths, no rumble strips). SPFs are developed using historical data from a large sample of similar sites.

The independent variables in an SPF are typically the traffic volume (AADT) and, for segments, the length of the road ($L$).

SPF Form for Roadway Segments

$N_{\text{spf}} = L \times e^{a} \times AADT^{b}$ where $a$ and $b$ are regression parameters specific to the facility type (e.g., rural two-lane highway) and crash severity.

SPF Form for Intersections

$N_{\text{spf}} = e^{a} \times AADT_{\text{major}}^{b} \times AADT_{\text{minor}}^{c}$ where $AADT_{\text{major}}$ and $AADT_{\text{minor}}$ are the daily entering volumes on the major and minor streets, respectively.

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Crash Modification Factors (CMFs) and Crash Reduction Factors (CRFs)

Because most real-world sites do not match the ideal "base conditions" of an SPF, or because engineers want to evaluate the safety impacts of a specific countermeasure, Crash Modification Factors (CMFs) are applied.

Defining CMFs

A CMF is a multiplicative factor indicating the expected change in crash frequency resulting from a change in site conditions or the implementation of a countermeasure: $N_{\text{expected}} = N_{\text{base}} \times CMF$

The value of a CMF indicates the safety effect:

• $CMF < 1.0$: The treatment is expected to reduce crashes.
• $CMF = 1.0$: The treatment has no effect on safety.
• $CMF > 1.0$: The treatment is expected to increase crashes.

Crash Reduction Factors (CRFs)

A Crash Reduction Factor (CRF) is the percentage reduction in crashes expected from a countermeasure. It is directly related to the CMF: $CRF = 1 - CMF$ For example, if a treatment has a $CMF = 0.78$, the corresponding $CRF = 1 - 0.78 = 0.22$, meaning a $22\%$ reduction in crashes.

Combining Multiple CMFs

When multiple treatments are implemented at a single site, their combined safety effect is often estimated using the multiplicative method: $CMF_{\text{combined}} = CMF_1 \times CMF_2 \times \dots \times CMF_m$

Engineers must exercise caution when combining CMFs. The multiplicative method assumes the treatments act independently. If two treatments target the same crash type (e.g., both rumble strips and high-friction overlays target run-off-road crashes), multiplying their CMFs will overestimate the safety benefit. The HSM suggests applying no more than three CMFs concurrently, and only if they affect different crash types.

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The HSM Predictive Method

The complete HSM predictive method integrates SPFs, CMFs, and a local calibration factor ($C$) to estimate the expected crash frequency ($N_{\text{predicted}}$) for a specific study site: $N_{\text{predicted}} = N_{\text{spf}} \times \left( \prod CMF_i \right) \times C$ where $C$ is the calibration factor, which adjusts the national/regional SPF models to fit local conditions, driver behavior, and climate. It is calculated as: $C = \frac{\sum \text{Observed Crashes}}{\sum \text{Predicted Crashes (uncalibrated)}}$ for a sample of similar sites in the local jurisdiction.

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The Empirical Bayes (EB) Method

One of the major challenges in safety analysis is regression-to-the-mean (RTM) bias. RTM is the statistical phenomenon where a site with an unusually high crash count in one year will naturally experience fewer crashes the following year, simply due to random variation. If an agency installs a countermeasure during a peak crash year, they may attribute the subsequent reduction to the treatment when it was actually due to RTM.

To eliminate RTM bias, the HSM uses the Empirical Bayes (EB) method. The EB method combines the predicted crash frequency from the SPF ($N_{\text{predicted}}$) with the observed crash history ($N_{\text{observed}}$) using a weighted average to calculate the long-term expected crash frequency ($N_{\text{expected}}$): $N_{\text{expected}} = w \cdot N_{\text{predicted}} + (1 - w) \cdot N_{\text{observed}}$

The weight factor ($w$) is calculated as: $w = \frac{1}{1 + k \cdot N_{\text{predicted}}}$ where $k$ is the overdispersion parameter of the SPF.

• $k$ measures the extra-Poisson variation in the crash data used to develop the SPF.
• If $k$ is small (close to 0), the SPF is highly reliable, resulting in a larger weight $w$, meaning the estimate relies more on the SPF prediction.
• If $k$ is large, the SPF has high variance, resulting in a smaller weight $w$, meaning the estimate relies more on the site-specific observed history.