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6.6.4 Step 4: Compare Expected Crashes is 10 fatal, 1,200 injury, and 4,200 PDO. Therefore,
with and without PRPMs the RIC can be calculated as follows:
The difference between the expected number of nighttime
(1, 304.3 10 + 27.4 1, 200 + 4, 200)
nonintersection crashes estimates from Steps 2 and 3 is cal- RIC =
(10 + 1, 200 + 4, 200) (6-7)
culated as
= 9.25
^ 2002 - E( K2002 )
=K PRPM
= 1.841 - 1.0005 (6.5) b) Estimate the potential reduction in crash costs. The
average cost of a crash is the product of the RIC and
= 0.841 crashes per mile-year the cost of a PDO crash:
Cost per crash = 9.25 $2,300
(6-8)
6.6.5 Step 5: Conduct a Benefit-Cost Analysis = $21,275 per crash
A sample benefit-cost analytical procedure is presented here:
The total savings per year is the product of the aver-
a) Estimate the relative injury cost (RIC) for all two- age cost of a crash and the expected crash reduction
lane roadways (or a large sample) in the jurisdiction: per year:
wfat (Fat) + winj (Inj) + (PDO) Crash savings benefit
RIC = (6-6)
(Fat) + (Inj) + (PDO) per year = $21,275 * 0.841 (6-9)
= $17,892 per mile-year
Where
c) Determine an annual cost of installing and maintain-
Fat = Number of fatal injury crashes,
Inj = Number of nonfatal injury crashes, ing PRPMs. Each jurisdiction should obtain its own
PDO = Number of property-damage-only crashes, annual cost estimate for the installation and mainte-
wfat = Weighting factor for fatal injury crashes, nance of PRPMs at the study locations.
and The annual cost estimate will consist of three
winj = Weighting factor for nonfatal injury crashes. components:
1. Indirect installation cost. This includes the cost
The weighting factor for fatal injury crashes (wfat) of providing work zone signs, attenuation vehi-
is the ratio of the cost of a fatal injury crash to the cles, special law enforcement, and so forth to
cost of a PDO crash. The weighting factor for non- implement PRPMs. This cost is incurred at each
fatal injury crashes is the ratio of the cost of a non- site where PRPM lenses are replaced or PRPMs
fatal injury crash to the cost of a PDO crash. The two are installed. The indirect cost per PRPM can be
most commonly used accident cost figures are those determined by dividing the total indirect cost by
contained in the AASHTO Roadside Design Guide the total number of PRPMs to be installed during
(50) and the FHWA comprehensive cost figures the contract. The following equation can be used
based on the willingness-to-pay concept. Users to determine the annual indirect cost, A:
should choose the set of accident cost figures that
best suits their particular study. Table 6-7 shows the COST i(1 + i ) n
crash costs used by the FHWA (51) updated to 2002 A= (6-10)
(1 + i ) n - 1
dollars and the RIC values estimated from these
crash cost values.
Assume that on all two-lane roadways within this Where
jurisdiction, the average number of crashes per year COST = Indirect cost of installation per PRPM,
i = Annual discount rate, and
TABLE 6-7 Crash costs n = Number of years in lens replacement
and relative injury cost values cycle.
Crash severity Cost (2002) RIC
Fatal $3,000,000 1304.3 If the indirect cost of implementing 500 PRPMs
is $5,000, then the indirect cost per PRPM =
Injury $63,000 27.4
$5,000/500 = $10. Assuming a discount rate
PDO $2,300 1.0
of 5 percent, the annual cost = 10 × 0.05 ×

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(1.05)3/[(1.05)3 - 1] = $3.67 per PRPM for a 3-year discount rate of 5 percent, the annual cost equals
lens replacement cycle. 6.20 × 0.05 × (1.05)3/[(1.05)3 - 1] = $2.28 per
2. Direct installation cost. This refers to the actual PRPM is estimated for a 3-year lens replacement
cost of installing or replacing the PRPM and cycle. If justified by jurisdictional procedures,
includes the cost of material, equipment, and labor. any annual costs incurred by lens replacement
Equation 6-10 can be used to calculate the annual outside the typical cycle should be included in the
direct installation cost, in which case n is equal to overall maintenance costs. The total annual cost
the number of years in the PRPM replacement per PRPM is the sum of these three cost compo-
cycle. For example, in Missouri (52), the cost of nents: $3.67 + $5.50 + $2.28 = $11.45. Based on
installing one PRPM is about $42.50, and PRPMs this assumed cost, the cost per mile (1 mile =
are replaced every 10 years. Assuming a discount 5,280 ft) for 40 ft and 80 ft PRPM spacings are
rate of 5 percent, the annual cost equals 42.50 × $1,511 and $756, respectively. For the example
0.05 × (1.05)10/[(1.05)10 - 1] = $5.50 per PRPM for illustrated here, if PRPMs are implemented at a
a 10-year PRPM replacement cycle. 40-ft (12-m) spacing (at curves) for 80 percent of
3. Maintenance cost. This refers to the average the length of the 1-mile-long section and at 80-ft
annual cost of replacing the lens according to the (24-m) spacing for the remainder of the length,
replacement cycle and includes the cost of mate- the annual PRPM implementation and mainte-
rials, equipment, and labor. Equation 6-10 can be nance cost will be 0.8($1,511) + 0.2($756) =
used to calculate the annual maintenance cost, in $1,360 for a 1-mile-long, two-lane roadway
which case n is equal to the number of years in the section.
lens replacement cycle. For example, Missouri d) Determine benefit-cost ratio. The benefit-cost ratio
DOT replaces the lens every 3 years at a cost of equals the present value of crash savings divided by
approximately $6.20 per lens (52). Assuming a the implementation cost ($17,892/$1,360 = 13.16).