9.1 Highway Safety Manual (HSM) Predictive Methodology & Part C Models

9.1 Highway Safety Manual (HSM) Predictive Methodology & Part C Models

PTOE Exam Focus: The Highway Safety Manual (HSM), published by AASHTO, transitions traffic safety from historical, reactive crash counting to a science-based predictive discipline. Expect quantitative exam problems testing the general Part C predictive formulation $N_{\text{predicted}} = N_{\text{spf}} \times \prod CMF_i \times C_x$, facility segmentation criteria, base condition adjustments, and the derivation and application of local calibration factors ($C_x$).

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1. Architecture of the Highway Safety Manual

The Highway Safety Manual is organized into four foundational parts that guide the quantitative safety management lifecycle:

• Part A — Fundamentals: Human factors, vehicle dynamics, roadway design interactions, fundamentals of safety analytics, and the role of safety in the project development process.
• Part B — Roadway Safety Management Process: Systemic and network-level safety management tools, including Network Screening (identifying sites with potential for improvement), Diagnosis, Countermeasure Selection, Economic Appraisal, Project Prioritization, and Safety Effectiveness Evaluation.
• Part C — Predictive Method: Mathematical models (Safety Performance Functions, Crash Modification Factors, and Calibration Procedures) for estimating expected average crash frequency and severity distributions across defined facility types.
• Part D — Crash Modification Factors (CMFs): Catalog of documented treatments, geometric modifications, and operational countermeasures with their associated CMFs and standard errors.

+-----------------------------------------------------------------------------------------+
|                        AASHTO HIGHWAY SAFETY MANUAL ARCHITECTURE                        |
+-----------------------------------------------------------------------------------------+
| Part A: Fundamentals           | Human factors, collision fundamentals, safety physics  |
| Part B: Safety Management      | Network screening, diagnosis, economic appraisal, B/C  |
| Part C: Predictive Method      | Part C models: SPFs + CMFs + Calibration (Ch 10-12, 18)|
| Part D: CMF Catalog            | Quantitative countermeasure library and standard error |
+-----------------------------------------------------------------------------------------+

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2. The General Part C Predictive Formulation

The core mathematical engine of HSM Part C estimates the predicted average crash frequency ($N_{\text{predicted}}$) for a specific site (roadway segment or intersection) over a defined multi-year study period:

$N_{\text{predicted}} = N_{\text{spf}, x} \times \left( \prod_{y=1}^{m} CMF_{yx} \right) \times C_x$

Where:

• $N_{\text{predicted}}$ = Predicted average crash frequency for a specific year on site $x$ (crashes/year).
• $N_{\text{spf}, x}$ = Predicted average crash frequency for nominal baseline geometric and operational conditions determined from a statistical Safety Performance Function.
• $CMF_{yx}$ = Crash Modification Factor $y$ for site $x$, adjusting for specific geometric or operational features that deviate from the nominal baseline condition (e.g., lane width, shoulder width, horizontal curvature, median type, driveway density).
• $m$ = Total number of applicable Crash Modification Factors for site $x$.
• $C_x$ = Local jurisdictional calibration factor developed by a state DOT or municipal agency to adjust national base models to local environmental, driver behavior, and statutory crash reporting practices.

For a contiguous corridor containing multiple roadway segments and intersections, the total facility predicted crash frequency is the linear sum of all individual components:

$N_{\text{predicted, total}} = \sum_{\text{all segments}} N_{\text{predicted, segment}} + \sum_{\text{all intersections}} N_{\text{predicted, intersection}}$

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3. The 18-Step HSM Predictive Workflow

The HSM establishes a rigorous 18-step protocol for conducting predictive safety analyses:

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|                         THE 18-STEP HSM PREDICTIVE WORKFLOW                           |
+----+------------------------------------+----+----------------------------------------+
| 01 | Define facility and study limits   | 10 | Apply local calibration factor (C_x)   |
| 02 | Divide facility into segments/nodes| 11 | Calculate N_predicted for each site    |
| 03 | Determine study period (years)     | 12 | Apply crash severity distributions     |
| 04 | Select applicable facility model   | 13 | Apply collision type distributions     |
| 05 | Obtain AADT for all elements       | 14 | Sum segments and intersections         |
| 06 | Gather geometric and control data  | 15 | Determine if observed data exist       |
| 07 | Apply base SPF (N_spf)             | 16 | Apply Empirical Bayes (EB) method      |
| 08 | Calculate applicable CMFs          | 17 | Assess patterns and design alternatives|
| 09 | Calculate uncalibrated prediction  | 18 | Perform economic appraisal & B/C       |
+----+------------------------------------+----+----------------------------------------+

Detailed Step Progression:

1. Step 1 — Define Facility & Study Limits: Identify spatial limits, project purpose (e.g., corridor reconstruction, alternative evaluation), and target design years.
2. Step 2 — Roadway Segmentation: Divide the physical facility into individual homogeneous roadway segments and distinct intersection nodes.
3. Step 3 — Determine Study Period: Establish the historical or forecast analysis timeframe (individual years or multi-year aggregate).
4. Step 4 — Select HSM Chapter Model: Match facility type to the appropriate HSM chapter (Chapter 10 for Rural Two-Lane Two-Way, Chapter 11 for Rural Multilane, Chapter 12 for Urban/Suburban Arterials, Chapter 18 for Freeways, Chapter 19 for Ramps).
5. Step 5 — Traffic Volume Input: Obtain Annual Average Daily Traffic ($AADT$) for every segment and all intersection approaches (major and minor street $AADT$).
6. Step 6 — Geometric & Operational Data Collection: Compile lane widths, shoulder widths, shoulder types, median configurations, driveway densities, roadside hazard ratings ($RHR$), horizontal curve parameters, grade, lighting, and automated speed enforcement.
7. Step 7 — Calculate Base SPF Crash Frequency ($N_{\text{spf}}$): Execute the statistical regression equation corresponding to the facility type under base conditions.
8. Step 8 — Calculate Crash Modification Factors ($CMF_1, CMF_2, \dots, CMF_m$): Compute each CMF based on how actual site parameters deviate from baseline standards.
9. Step 9 — Calculate Uncalibrated Site Prediction: Multiply $N_{\text{spf}}$ by the product of all computed CMFs: $N_{\text{uncalibrated}} = N_{\text{spf}} \times \prod CMF_i$.
10. Step 10 — Identify Local Calibration Factor ($C_x$): Obtain the state DOT calibrated factor $C_x$ for that specific facility type and year.
11. Step 11 — Compute Final Predicted Crashes ($N_{\text{predicted}}$): Calculate $N_{\text{predicted}} = N_{\text{uncalibrated}} \times C_x$.
12. Step 12 — Crash Severity Disaggregation: Apply local or HSM default severity proportions (Fatal $K$, Incapacitating Injury $A$, Non-Incapacitating $B$, Possible Injury $C$, Property Damage Only $O$, or Fatal-and-Injury $FI$ vs $PDO$).
13. Step 13 — Collision Type Disaggregation: Apportion predicted crashes into collision types (rear-end, angle, sideswipe, run-off-road, head-on, pedestrian/bicycle).
14. Step 14 — Sum Facility Totals: Aggregate predicted crashes across all segments and intersections.
15. Step 15 — Check Observed Crash History: Determine whether historical observed crash data ($N_{\text{observed}}$) are available for the study sites.
16. Step 16 — Apply Empirical Bayes (EB) Method: If historical crash data are available, apply the EB weighting procedure to correct for Regression-to-the-Mean (RTM) bias and estimate expected average crash frequency ($N_{\text{expected}}$).
17. Step 17 — Evaluate Design Alternatives: Compare baseline versus alternative geometric designs (e.g., widening shoulders vs installing a roundabout).
18. Step 18 — Conduct Economic Appraisal: Perform Benefit-Cost analysis ($B/C$), Net Present Value ($NPV$), and incremental economic prioritization.

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4. Roadway Segmentation Rules

A central practical skill on the PTOE examination is segmenting a roadway corridor into homogeneous analysis units. A new roadway segment must begin whenever any of the following characteristics change along the alignment:

1. Average Annual Daily Traffic ($AADT$): Change in traffic volume (e.g., crossing a major commercial generator or municipal boundary).
2. Number of Through Lanes: Lane addition, drop, or transition (e.g., 2 lanes to 4 lanes).
3. Lane Width or Shoulder Width/Type: Physical cross-sectional alteration (e.g., 12-ft lanes narrowing to 11-ft lanes, or 8-ft paved shoulders transitioning to 4-ft gravel).
4. Median Configuration: Transition between undivided, two-way left-turn lane (TWLTL), or raised divided median.
5. Horizontal Curvature: Tangent transitioning into a horizontal curve (classified by radius, length, and presence of spiral transitions).
6. Grade / Vertical Alignment: Change in vertical grade exceeding standard thresholds (e.g., flat $\le 3%$, moderate $3\text{--}6%$, steep $> 6%$).
7. Driveway Density: Significant change in access point density (driveways per mile).
8. Roadside Hazard Rating ($RHR$): Shift in roadside clear zone, side slope, or obstacle density (rated on a 1–7 visual scale in Chapter 10).
9. Intersection Influence Area: Roadway segments terminate at the boundary of an intersection influence area, defined by the HSM as extending 250 ft (75 m) along each approach leg from the intersection center (or the physical curb return/queue storage length, whichever is greater).

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5. HSM Part C Facility Types & Base Conditions

Each HSM chapter establishes specific baseline geometric conditions for which $CMF = 1.00$. Any deviation from baseline requires an explicit CMF calculation.

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6. Local Calibration Factor Formulation ($C_x$)

Because base SPFs were calibrated using multi-state statistical datasets (such as California, Washington, and Texas data from specific historical years), they cannot be applied directly in other jurisdictions without calibration. Differences in crash reporting thresholds, reporting completeness, driver demographics, wildlife populations, winter maintenance, and pavement friction require local calibration.

Calibration Equation:

$C_x = \frac{\sum_{\text{all sample sites}} N_{\text{observed}}}{\sum_{\text{all sample sites}} N_{\text{predicted(uncalibrated)}}}$

Where:

• $\sum N_{\text{observed}}$ = Total number of recorded crashes observed across all sample sites during the calibration period.
• $\sum N_{\text{predicted(uncalibrated)}}$ = Total number of crashes predicted across the same sample sites using the uncalibrated HSM model ($N_{\text{spf}} \times \prod CMF_i$).

AASHTO Sampling Guidelines for Calibration:

• Minimum Sample Size: 30 to 50 randomly selected sites for each facility type.
• Minimum Total Crashes: The sample must represent at least 100 crashes per year (or 300 crashes over a 3-year study window) to ensure statistical stability.
• Unbiased Selection: Sites must be selected randomly across the jurisdiction, not cherry-picked from high-crash locations.
• Interpretation:
  • $C_x > 1.00$: The local jurisdiction experiences more crashes than the national base model predicts (e.g., $C_x = 1.25$ indicates local crashes are 25% higher than baseline).
  • $C_x < 1.00$: The local jurisdiction experiences fewer crashes than the national base model predicts (e.g., $C_x = 0.85$ indicates local crashes are 15% lower).

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7. Worked PTOE Calculation Example

Problem Statement:

A 2.5-mile rural two-lane highway segment carries an $AADT = 4,000\text{ veh/day}$. The base SPF equation for rural two-lane segments is: $N_{\text{spf}} = AADT \times L \times 365 \times 10^{-6} \times \exp(-0.312)$

Field inspection identifies the following non-base geometric characteristics:

• Lane width: 11 ft ($CMF_{\text{lw}} = 1.05$)
• Shoulder width: 4 ft gravel ($CMF_{\text{sw}} = 1.10$)
• Horizontal alignment: Tangent ($CMF_{\text{c}} = 1.00$)
• Driveway density: 5 driveways/mi ($CMF_{\text{d}} = 1.00$)
• Roadside Hazard Rating: $RHR = 3$ ($CMF_{\text{rhr}} = 1.00$)

The state DOT has published a regional calibration factor for rural two-lane highways of $C_x = 1.20$.

Calculate the predicted average annual crash frequency ($N_{\text{predicted}}$) for this segment.

Solution:

1. Base SPF Output ($N_{\text{spf}}$): $\exp(-0.312) = 0.7320$ $N_{\text{spf}} = 4,000 \times 2.5 \times 365 \times 10^{-6} \times 0.7320 = 10,000 \times 0.000365 \times 0.7320 = 2.6717\text{ crashes/year}$

2. Combined Crash Modification Factor ($\prod CMF_i$): $\prod CMF_i = 1.05 \times 1.10 \times 1.00 \times 1.00 \times 1.00 = 1.1550$

3. Uncalibrated Crash Prediction: $N_{\text{uncalibrated}} = N_{\text{spf}} \times \prod CMF_i = 2.6717 \times 1.1550 = 3.0858\text{ crashes/year}$

4. Final Calibrated Crash Prediction ($N_{\text{predicted}}$): $N_{\text{predicted}} = N_{\text{uncalibrated}} \times C_x = 3.0858 \times 1.20 = 3.703\text{ crashes/year}$

The segment is predicted to experience 3.70 crashes per year.