Chapter 4 Expected Average Crash Frequency

[gamparano]

Step 4 example problem for "Expected Average Crash Frequency with EB Adjustments" (page 4-62) uses Equations 4-28 and 4-29 and "Annual Correction Factors" computed from Equation 4-26 to calculate the Expected (Total and FI) Crashes. This method differs slightly from the Part C "Site-Specific EB Method" (Appendix A) which provides Equations A-4 and A-5 (page A-19) with no mention of annual correction factors. I've used both methods for a given set of project data but get different results for the Nexpected and Excess Expected values which also affects the expected crash values in dollars. In an effort to quantify the dollars saved by the expected reduction in crash frequencies and severities, which of these (Part B example or Part C equations) provide the most reliable results? Thanks.

[Mohamad Banihashemi]

It seems to me that Equation 4-28 estimates the expected frequency of crashes for year 1 and Equation A-4 does this estimation for all study years combined. This is the only difference between these equations and that is why we have the term related to "Annual Correction Factors" in the first one and not in the second one. I suppose if we multiply both sides of equation 4-28 by summation of all "Annual Correction Factors" as they are defined on page 4-60, we come up with Equation A-4. Am I missing something?

[gamparano]

My question is in regards to applying these equations (Eqs 4-28 & 4-29, or A-4 & A-5) to determine Nexpected crashes for the example problem on page 4-62.
In applying Equations 4-28 and 4-29 EB analysis from Part B for 3 years of data, I obtain the following results:
Year Nexpected(Total) Nexpected(FI) Nexpected(PDO)
1 9.8 6.7 3.1
2 10.0 6.8 3.2
3 10.8 7.4 3.4

In applying Equations A-4 and A-5 EB analyiss from Part C to the same data, I obtain the following results:
Year Nexpected(Total) Nexpected(FI) Nexpected(PDO)
1 8.0 6.7 1.3
2 9.6 6.7 2.9
3 13.0 7.5 5.5

The average values from both methods are the same Nexpected(Total) = 10.2, Nexpected(F&I)= 7.0, and Nexpected(PDO)= 3.2, but why is there such a big difference between the annual values (i.e., year 3)? I understand that these are just predictions but are the differences acceptable and/or is the critical concern the average of the three years rather than the annual results? I would be glad to share the full spreadsheet with you.

[Mohamad Banihashemi]

By my understanding Equations in Chapter 4 (4-28 and 4-29) are designed to produce the EB adjusted expected number of crashes for all years of past period (by using the total observed number of crashes in the equation) and then split the total for each year. The Equations in Appendix A of Part C (A-4 and A-5) do not have any means to split the total estimated value for different years of past period. If you use these equations for each year separately, even though the summation may turn out the same, it is not actually the split of total for different years. The values will simply be the EB adjusted expected number of crashes for each year with the assumption of having only that year of observed crashes since only one year of observed number of crashes is used in the equation each time that you use the equation. Therefore my recommendation is that you use chapter 4 equations in your study.