The core of the HSM predictive method. An SPF is a mathematical regression model used to predict the average number of crashes per year for a specific facility type (e.g., a rural two-lane highway) under "base" conditions, primarily as a function of its traffic volume (AADT).

$N_{spf} = e^{\beta_0} \times AADT^{\beta_1}$

Because SPFs represent "base" ideal conditions (e.g., 12-ft lanes, 6-ft shoulders), the raw SPF output must be adjusted if the actual road differs from these base conditions.

A CMF is a multiplicative factor used to compute the expected number of crashes after implementing a specific countermeasure or changing a geometric feature.

• $CMF = 1.0$: The treatment has no expected effect on safety.
• $CMF < 1.0$: The treatment is expected to reduce crashes (e.g., a CMF of 0.80 means a 20% reduction in crashes).
• $CMF > 1.0$: The treatment is expected to increase crashes (e.g., narrowing a lane from 12 ft to 10 ft might have a CMF of 1.05).

The final predicted crash frequency ($N_{predicted}$) for a specific site is calculated by multiplying the base SPF by all applicable CMFs:

$N_{predicted} = N_{spf} \times (CMF_1 \times CMF_2 \times \dots)$

The core method of evaluating a countermeasure is comparing the crash frequency at a site before its implementation ($N_b$) to the expected crash frequency after ($N_{expected}$), accounting for changes in traffic volume and secular trends.

• Naïve Approach: Simply comparing $N_{after}$ to $N_{before}$. This is highly flawed as it ignores changes in traffic volume, the regression-to-the-mean effect, and general trends (like the introduction of better vehicle safety features).
• Comparison Group Method: Utilizing a similar group of sites that did not receive the treatment to account for secular trends. A ratio is created comparing the before/after change in the comparison group to the treatment group.

A major statistical trap in observational studies is Regression-to-the-Mean (RTM). A site might be selected for treatment simply because it had a randomly high spike in crashes one year. Even without treatment, crashes would likely have naturally "regressed" down to the long-term historical average the following year. If an engineer doesn't account for RTM, they might falsely attribute the natural drop in crashes entirely to their new safety countermeasure.

The Empirical Bayes (EB) Method is the standard, state-of-the-art statistical approach used in modern safety analysis to mathematically correct for the RTM bias, providing a true estimate of the countermeasure's effectiveness. It combines the site's short-term observed crash history with the long-term predicted crashes from the SPF to establish a much more accurate baseline.

• K (Killed): Fatal injury resulting in death within 30 days of the crash.
• A (Incapacitating): Severe injury preventing the victim from walking or driving normally (e.g., broken bones, severe bleeding).
• B (Non-incapacitating): Visible injury but not life-threatening (e.g., cuts, large bruises).
• C (Possible Injury): Complaint of pain or momentary unconsciousness, but no visible wound.
• O (Property Damage Only - PDO): No injuries sustained by any party.

Because velocity ($v$) is squared, a seemingly small increase in speed results in a massive increase in the energy that must be absorbed during a crash.

• A vehicle traveling at $40 \text{ mph}$ has nearly double the kinetic energy of a vehicle traveling at $30 \text{ mph}$, despite only a 33% increase in speed.
• A vehicle traveling at $60 \text{ mph}$ has four times the kinetic energy of a vehicle traveling at $30 \text{ mph}$.

The Human Tolerance Limit: Modern vehicle crumple zones and airbags are highly effective at absorbing this energy and protecting occupants. However, pedestrians and cyclists lack this protection. Empirical safety data shows that if a pedestrian is struck by a car traveling at $20 \text{ mph}$, they have a roughly 90% chance of survival. If struck at $40 \text{ mph}$, the survival rate plummets to 10%.

This nonlinear relationship is the primary justification for strict speed limits (often 20-25 mph) in dense urban areas, school zones, and residential neighborhoods. "Vision Zero" programs globally aim to design street geometry (via narrow lanes, speed humps, and chicanes) to physically force vehicle speeds down to these survivable limits, acknowledging that human error will cause crashes, but the infrastructure should prevent those crashes from being fatal.

When a driver encounters an unexpected hazard, they do not react instantaneously. The brain must process the information through a sequence of cognitive steps, cumulatively known as PIEV Time (or Perception-Reaction Time):

• Perception: The driver's eyes see the stimulus (e.g., a deer jumping onto the road). The image is transmitted to the brain. This time varies depending on the size, color, and contrast of the object, as well as the driver's visual acuity and peripheral vision.
• Intellection (Identification): The brain processes the visual information and identifies it as a hazard. "That is a deer in my lane." The time depends on the complexity of the situation and the driver's experience.
• Emotion (Decision): The driver decides on a course of action. "I need to hit the brakes hard." This phase is influenced by the driver's emotional state, fatigue, intoxication, and the perceived severity of the threat.
• Volition (Reaction): The physical execution of the decision. The brain sends a signal to the foot to move from the gas pedal to the brake pedal. This is relatively fast and constant but can be slowed by physical impairments or cold weather.

For standard highway design and stopping sight distance calculations, AASHTO assumes a conservative, 90th-percentile PIEV time of 2.5 seconds for an average, alert driver.

Key Elements Shown:

• Arrows: Indicate the direction of travel for each vehicle involved.
• Symbols: Standardized symbols represent the crash type (e.g., a straight line with an arrowhead hitting a straight line at 90 degrees indicates a right-angle crash; two lines merging indicates a sideswipe).
• Severity Markers: Often color-coded or using specific icons to denote Fatal, Injury, or PDO.
• Context: Time of day (Day/Night), weather (Wet/Dry/Ice).

Purpose: Collision diagrams allow engineers to visually identify spatial and directional patterns. For example, if a diagram shows 15 right-angle crashes involving northbound traffic, the engineer knows to investigate sight distance or signal visibility on that specific approach.

Waiting years for enough crash data to accumulate is reactive and ethically problematic. Surrogate Safety Measures allow engineers to evaluate safety proactively using near-miss data and traffic conflicts.

A primary metric is Time to Collision (TTC): The time required for two vehicles to collide if they continue at their present speeds and on the same path. A very low TTC indicates a severe conflict or "near-miss," serving as a proxy indicator for a high-risk location even if a crash hasn't happened yet.

An RSA is a formal safety performance examination of an existing or future road or intersection by an independent, multidisciplinary team. It aims to evaluate the road from the perspective of all road users (drivers, pedestrians, cyclists) to catch safety deficiencies in the design phase or on existing un-treated roads.