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OCR for page 33
33 DECREASING RELATIONSHIP Do-nothing area UBC = Upper benefit cutoff value Condition Indicator Decreasing AREABENEFIT() LBC = Lower benefit cutoff value Age, years INCREASING RELATIONSHIP Do-nothing area UBC = Upper benefit cutoff value Condition Indicator Increasing AREABENEFIT(+) LBC = Lower benefit cutoff value Age, years Figure 9. Illustration of the benefit area (AREABENEFIT) for a single decreasing or increasing individual post-treatment condition indicator. nance scenario. First, the present worth (at year zero) of each EUACi = Computed equivalent uniform annual cost asso- included treatment, rehabilitation, user-delay, or routine main- ciated with the ith timing scenario. tenance cost is determined using equation 7. PW$i = Sum of present worth values of all agency main- tenance or rehabilitation costs included in the cost PW$ = C (1 + d ) - n (Eq. 7) stream associated with the ith timing scenario. d = Discount rate expressed as a percentage (e.g., a where: discount rate of 4 percent translates to d = 0.04 in the equation). PW$ = Present worth value of an included cost (in year i = Index associated with the current timing scenario. zero dollars). pi = Analysis period associated with the ith timing C = Individual maintenance or rehabilitation cost (in scenario (time from construction until year at actual dollars). which the first included condition indicator per- d = Discount rate expressed as a percentage (e.g., a formance curve reaches the benefit cutoff value discount rate of 4 percent translates to d = 0.04). [from step 5]). n = Year (since construction) in which the individual cost is realized. Step 10: Determining the Most Cost-Effective Second, the computed total present worth cost is converted Timing Scenario into an equivalent uniform annual cost (EUAC) using equa- tion 8. The final step of the analysis procedure is to analyze the benefits and costs computed for each application age to deter- d (1 + d ) pi EUAC i = PW$i (1 + d ) p - 1 (Eq. 8) mine the timing scenario that provides the largest B/C ratio. i To normalize these computed B/C ratios, EIs are computed for each timing scenario by dividing each individual B/C ratio where: by the largest observed B/C ratio from all the different timing

OCR for page 33
34 Upper benefit cutoff value Friction number Overall post-treatment analysis life of 20 years Lower benefit AREABENEFIT(FRICTION) cutoff value 5 10 15 20 25 Age, years Upper benefit cutoff value Rutting AREABENEFIT(RUTTING) Overall post-treatment analysis life of 20 years (associated with friction) Lower benefit cutoff value set to zero 5 10 15 20 25 Age, years Upper benefit cutoff value International Roughness Index (IRI) AREABENEFIT(ROUGHNESS) Overall post-treatment analysis life of 20 years (associated with friction) Lower benefit cutoff value 5 10 15 20 25 Age, years Figure 10. Illustration of benefit areas associated with individual post-treatment condition indicators (applicable for investigating multiple condition indicators). scenarios investigated. The most cost-effective timing scenario observed B/C ratio (i.e., 0.01123 computed for an application is that with the largest B/C ratio (i.e., that associated with an EI age of 4 years after construction). Thus, the EI for applica- of 100). This process is best illustrated using an example. tion age 1, for example, is 0.00527/0.01123 100 = 47). The For an analysis to investigate six timing scenarios for a treat- EI results for this example are illustrated in Figure 11. ment applied on an HMA pavement 1, 2, 3, 4, 5, and 6 years These results indicate that the optimal time to apply this after construction, benefit, cost, and B/C ratios are com- preventive maintenance treatment is in year 4, although an puted for each scenario using the previously outlined pro- application in year 3 produces very similar results. In such cedures. The computed values for this example are presented cases, other output results such as total benefit, EUAC, or in Table 20. These values show that timing scenario 4 (i.e., extension of life may help identity the most appropriate tim- application age at 4 years) provides the largest B/C ratio. ing scenario. Using equation 1, EIs are computed for each scenario by Although the optimal timing methodology is based on dividing each individually computed B/C ratio by the largest comparing B/C ratios, an agency may select treatment based