Office of Operations Active Transportation and Demand Management

Guide for Highway Capacity and Operations Analysis of Active Transportation and Demand Management Strategies

Appendix B: Incident Probabilities and Duration

Incident probabilities and durations may be needed for an “existing conditions evaluation” in which case the analyst can take advantage of recent historical experience on the facility. If some of the required data is lacking, this Appendix provides methods to estimate incident probabilities.

For future conditions evaluations, where the facility design is significantly changed, historic crash and incident experience may not provide a sufficient basis for forecasting future incident probabilities. The procedures and defaults in this Appendix may be useful for forecasting future incident probabilities.

For an existing facility evaluation, data-rich agencies will have to convert their incident log data to a compatible format for input in the ATDM analysis procedures. Data-poor agencies typically lack local incident data, but may have access to local crash data, which is identified as one of the common incident types. These agencies will have to populate incident frequency based on crash data. A procedure to estimate incidents from crash data is provided in Section 5.7. For planned or future conditions, both data-rich and data-poor agencies will have to perform extra steps in order to estimate incident frequency. When sufficient traffic and geometry information is available, crash frequency for arterials can be estimated using the crash prediction procedures available in the Highway Safety Manual (HSM) (Highway Safety Manual, 2011). Alternatively, in a situation where only planning-level parameters – such as traffic forecast and length of facilities – are known, incident frequency for either urban freeways or arterials can be estimated using HERS (Highway Economic Requirements System - State Version: Technical Report, 2005) or other crash prediction methodologies. Details for each step and suggested default values for both evaluation types are also provided later in this guideline.

Unfortunately, there is no consistency across agencies’ incident data recording systems. Some agencies simply record the incident duration and number of lane closures, without regard to the roadway shoulder. However, the HCM freeway incident classification categorizes shoulder accident, shoulder disablement, and lane closures separately. Most of the incident databases show that shoulder closures are more frequent than lane closures. Consequently, shoulder closures should represent a significant share in the incident type distribution.

The following procedures are recommended for both data-rich and data-poor agencies to prepare and process their incident data or estimate incidents in a compatible format for use in the ATDM analysis.

Estimate Incident Probabilities for the Study Period

Three approaches are described here for estimating incident probabilities. The best approach uses archived incident data for the facility to estimate incident probabilities by incident type. The “Second Best” approach uses historic facility crash rates to estimate incidents. The “Third Best” approach (which must be used if sufficient facility design changes are expected to change crash rates) uses Highway Safety Manual procedures or “rule of thumb” rates from national sources to estimate facility crash rates and then incident probabilities.

Best Approach: Employing Local Incident Data

This option is for agencies with archived incident logs for the facility. The following steps are performed.

  1. All incidents occurring within the study limits and the reliability reporting period are extracted from the agency’s incident logs for the facility.
    1. Preferably 5 years of data is available to provide a robust estimate of incident probabilities for the facility, but one year of data is acceptable.
  2. The incident types in the logs are converted by the analyst into ATDM incident types:
    1. Breakdown, property damage only (PDO), injury, fatal; and
    2. Further subdivided by maximum lanes closed (shoulder, 1, or 2+).
  3. The number of incidents (for each incident type) is divided by the number of study periods within the reliability reporting period to obtain the incident probability by type.
    1. For example, if a one year reporting period is covered in the incident data base, and the desired study period is all weekday PM peak periods of the year, then the number of study periods covered by the incident data base is 260 weekday peak periods per year.
      • If 13 shoulder breakdowns were recorded during weekday PM peak periods in the past year, then the probability of that incident type occurring sometime during the weekday PM peak period in the future is 13/260 = 5%.

Second Best Approach: Incident Prediction Based on Local Crash Data

This approach is appropriate for facilities where incident logs are not routinely prepared, are inadequately detailed, or where the incident logs are not accessible to the analyst. It requires that facility-specific crash data be available, preferably over a 3- to 5-year period (with 1 year acceptable).

This approach expands the reported crashes to total incidents using an expansion factor obtained from the SHRP 2-L08 research. The probabilities of incidents by severity and lane blockage type are computed using the following formula.

Equation 5. Formula to compute the probabilities of incidents by severity and lane blockage type.

Equation 5

Where:

P(inc, sev, block) = Probability of incident, with severity type “sev,” and lane blockage type “block.”
P(sev) = Probability of incident being one of following severity types: fatal, injury, property damage only, noncrash incident.
P(inc) = Probability of incident occurring on facility within the daily study period. This is equal to 1 – probability of no incidents within the study period. Assuming Poisson distribution of incidents for study period, probability of no incidents = exp(-lambda), where lambda is the average number of incidents per study period
P(block) = Probability of incident being one of following lane blockage types: shoulders only, one lane, two or more lanes.

Substituting the Poisson probability of zero incidents within the study period, we obtain:

Equation 6. Formula to compute the probabilities of incidents by severity and lane blockage type and substituting the poisson probability of zero incidents within the study period.

Equation 6

Where:

Lambda = the average number of incidents per daily study period.

The following steps are used to apply this approach to estimate incident probabilities by severity and blockage type.

1. Estimate annual crashes occurring within the reliability reporting period for the year.

  • Assume that crashes are proportional to the volume on the facility.
  • Multiply total crashes per year by percent of AADT occurring during the study period.
  • For example if the peak hour is typically 10% of average daily traffic on the facility, then assume that 10% of the annual crashes on the facility occur during the peak hour.

2. Estimate the average crashes per daily study period

  • Divide the annual crashes in the reliability reporting period by the number of days in the reliability reporting period.
  • For example, if the reliability reporting period is the PM peak hour for every weekday of the year, there will be 260 days within the reliability reporting period (52 weeks times 5 days per week).
    • If the facility has 520 crashes per year with 10% occurring during the weekday PM peak hour, then there are on average 520*10%/260 = 0.20 crashes per daily study period.

3. Expand crashes per daily study period to total incidents (crashes plus noncrash incidents) per daily study period.

  • Use SHRP 2-L08 expansion factor for freeways of 4.9 to expand crashes to incidents.
  • Continuing the previous example: 0.20 crashes per daily study period times 4.9 = 0.98 incidents per daily study period.

4. Compute probability of NO incidents occurring during a daily study period.

  • Assume incidents occur independently of the time since the last event, making their probability of occurring within the study period a Poisson distribution with a mean equal to the average number of incidents per daily study period.
  • Compute the probability of zero incidents within the study period using a Poisson distribution with a mean equal to the average number of incidents per daily study period.
    • Continuing the example, If the mean number of incidents per study period is 0.98, then the probability of no incidents occurring is 37.5%.

5. Allocate Total Incidents by severity.

  • The proportions of Noncrash incidents, property damage only (PDO), injury, and fatal crashes can be obtained from Table 37.
  • If facility-specific data on crash proportions is available, those proportions should be used instead. The facility-specific proportions will need to be adjusted to account for noncrash incidents so as to ensure that crash plus noncrash proportions add up to one.

6. Allocate Crashes and Noncrashes by lane closures using the proportions for freeways for freeways estimated from incident data tabulated for various U.S. freeways in Table 38.

Table 37: Default Proportions for Incident Severity
Noncrash Incident Property Damage Only (PDO) Injury Crash Fatal Crash Total
83.05% 14.04% 2.85% 0.06% 100.0%

Source: The ratio of total incidents to crashes used in this table is 4.9, taken from SHRP 2-L08 Final Report. The crashes are proportioned between PDO, injury, and fatal based on national statistics reported in Chapter 2, Table 24 of FHWA Traffic Safety Facts (FHWA, 2010).

Table 38: Default Proportions for Incident Lane Blockage
Incident Type Blocking Shoulder Blocking One Lane Blocking 2 or More Lanes Total
Crashes (PDO, Injury, Fatal) 55.8% 27.8% 16.4% 100.0%
Noncrash Incidents 83.7% 14.8% 1.6% 100.0%

Source:   Freeway incident data in SHRP 2-L08 Final Report (Vandehey, Ryus, Bonneson, Rouphail, Margiotta, & Dowling, 2013).

Estimate Average Incident Duration

For capacity analysis purposes it is necessary to know the incident duration and the number of lanes blocked. The best source of incident durations for a facility is the incident log for the facility, however; the analyst must understand how the time entries in the log are determined to ensure that full incident durations are tallied. Table 39 may be used if superior local data on incident durations is not available.

Table 39: Incident Duration by Crash Severity Type
Severity Shoulder One lane Two+ Lanes All
Noncrash 29.8 29.1 47.4 30.0
PDO 38.1 42.3 56.9 44.5
Injury 57.4 43.9 46.8 47.6
Fatal 229.6 175.5 187.1 190.2

Note: Entries are average duration in minutes. Adapted from SHRP 2-L08 Final Report White Paper on Incidents. When available, local, facility-specific incident durations should be used in lieu of this table.

Prediction of Facility Crashes

In the absence of facility crash records for a sufficiently long historic period to establish expected crash rates, and in the case when forecasting crashes for a new or upgraded facility the Highway Safety Manual methods may be used to estimate crash rates. The analyst should consult the HSM for details.

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