State of Good Repair: Prioritizing the Rehabilitation and Replacement of Existing Capital Assets and Evaluating the Implications for Transit (2012)

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111 Analytical Approach Details This appendix provides additional details concerning the analytical approach discussed in Section 5, including the formu- lae behind the approach. Section E.1 describes the prioritization model. Section E.2 details the vehicle model, while Sections E.3 and E.4 detailed the age-based and condition-based models, respectively. E.1 Prioritization Model As described in Section 5, the basic problem an agency faces in allocating a fixed budget to a set of capital projects is termed the Capital Budgeting Problem (1), though with an objective of maximizing utility rather than net present value. Utility may be equal to economic benefit, or it may include additional non-economic factors, as described in Section 4. Regardless of the specific factors included in a utility function, it may be expressed generically as a weighted sum of the utility from different aspects or objectives of the alternative as follows: U x u xi i i ( ) = ( )∑β ( )1 where U(x) is the utility for some alternative x, ui(x) is the utility corresponding to objective i, and bi is the weight on objective i. Obtaining an exact solution to the Capital Budgeting Prob- lem requires formulating the problem as an integer program. However, this implies that the solution time for the problem increases exponentially as the problem size increases, mean- ing it can be time consuming to obtain an exact solution even for a seemingly modest-sized problem. Thus, various heuris- tic approaches are commonly used in the interest of reducing solution time. One such approach is to formulate the problem as a linear program, then round off the solution if it results in recommending fractional parts of a project. Easier still, if solv- ing the problem for a single period and a single budget con- straint, and if projects are independent of one another, then the optimal solution can be approximated by ranking proj- ects in decreasing order of their utility-cost ratio and selecting projects until the budget is expended. This is the approach described in Section 5. An appealing aspect of the heuristic approach outlined above is that it introduces a metric that can be used for pri- oritization, termed the prioritization index (PI) in Section 5. However, once additional constraints are introduced into the Capital Budgeting Problem, simply selecting projects in rank order may not yield an optimal solution. Below is a form- ulation of the problem adapted from Louch et al. (2) that includes constraints by type of work and work phase that one can use to obtain an optimal solution: max ( ), 1 1 2 +  ∑ ∑i Ut t i t i i δ such that ∀ ∀ = {i t i tδ , ( )01 3 ∀ ≤∑i i t t δ , ( )1 4 ∀ ≤∑∑ ∑∑l i t ti i j k l t kj lC Mδ , , , , , ( )5 ∀ ∀ ≤∑∑ ∑j l i t ti i j k l t k j lC Jδ , , , , , , ( )6 ∀ ∀ ≤∑∑ ∑k l i t ti i j k l t j k lC Kδ , , , , , , ( )7 where di,t = 1 if alternative i is programmed beginning in period t, 0 otherwise Ui = utility obtained from performing alternative i Ci,j,k,l = cost of performing alternative i beginning in period t for investment type j and work phase k, period l A P P E N D I X E

112 Ml = maximum budget for period l Jj,l = maximum budget for investment type j, period l Kk,l = maximum budget for work phase k, period l Solving for this problem yields a recommended set of proj- ect alternatives to fund that maximizes utility. Equations 3 and 4 specify that each alternative can be chosen once and only once. Equations 5, 6 and 7 are constraints on the over- all budget, the budget by investment type (e.g., bus, rail), and by phase of work (e.g., design and construction), respectively. The formulation allows for different constraints, and different costs in each period. This approach can be easily extended to include additional constraints, such as bundling constraints that specify two alternatives must be selected together or not at all. Also, the integer constraint can be relaxed for projects that can be subdivided. Given this model, the proposed approach to project priori- tization can be summarized as follows: • For each project alternative, the utility of the project should be calculated, and the rank of the project should be approx- imated using the utility/cost ratio (also termed PI). • For alternative testing, or for cases where an agency has only an overall budget constraint approach the recommended approach to prioritization is to allocate funds in rank order until the budget is expended as described in Section 5. • For prioritizing projects considering multiple periods and constraints, it is not recommended that ranks be used directly. Instead, the prioritization problem should be formulated as described in Equations 2 to 7 and solved either as an integer program, or one should approximate the solution by solving the problem as a linear program. • If it is unfeasible to solve the prioritization problem as an optimization problem, then ranks can be used to develop an approximate solution, with projects selected in rank order within groups defined based on any constraints defined by the agency. • In all cases, automated approaches should be used to pro- vide insight into prioritization, but the final decision on project priorities should be left to decision makers. Even the most well-conceived model makes simplifying assump- tions, and may omit key constraints and other information needed to make the best decision. Thus, automated priori- tization approaches are best suited for tasks such as provid- ing an initial solution for review by a decision maker, testing different strategies, or “filling in the blanks” to approximate what projects might be selected in the future given a set of known priorities. • Once a set of projects has been selected or simulated as being selected, the resulting performance obtained from the set can be calculated. Determining the budget required to achieve a given performance target requires solving the problem for different budget levels, observing at each level what performance results from the specified budget. E.2 Vehicle Model As described in Section 5, the life cycle cost of a vehicle depends on its purchase cost, the costs of rehabilitation, energy (fuel, in the case of buses), maintenance and delay from road calls or failures. This cost may be expressed as follows: LCC CP CMR CME CMM CMD AM i t t t t t t A = + + + +( ) +( )=∑ 1 80 ( ) where LCC = life cycle cost CP = vehicle purchase cost A = age in years at which a vehicle is assumed to be replaced CMRt = rehabilitation cost per vehicle mile at time t CMEt = energy (fuel) cost per vehicle mile at time t CMMt = maintenance cost per vehicle mile at time t CMDt = delay cost per vehicle mile at time t AM = annual vehicle mileage i = discount rate The equation above predicts based on accumulated mileage, but there are other variables that can influence the decision making process on when to rehabilitate and/or replace buses, including geography, weather, type of service operated and roadway congestion. The calculations described here should be performed at a fleet level, ideally with all vehicles exposed to the same set of environmental and operating conditions to control for these factors. Ideally, the cost of rehabilitation per mile, CMRt would be determined based on an agency’s data. However, often it may be difficult to derive this cost based on available data. For buses a relationship between rehabilitation cost per vehicle mile and lifetime mileage was developed using data on the expected lives and replacement costs for individual bus components detailed in Useful Life of Transit Buses and Vans (3). Specifically, data were taken from Table F-2 for operators that carry out their major component replacements on a continuous, as-needed basis (rather than following a fixed schedule for major mid-life overhauls). Rather than assume that the lives of components are exactly equal to their expected lives, probability distributions were used to account for the possibility that the actual lives of indi- vidual components may be much longer or shorter than their expected lives, particularly when rehabilitation is carried out on an as-needed basis. Figure E-1 shows the resulting relation- ship between rehabilitation cost per mile and lifetime mileage. The cost for a particular time t can be approximated using the accumulated mileage up to the corresponding year.

113 The following equation is used to estimate energy costs per vehicle mile as a function of lifetime mileage: CME LM k ee ke LM( ) = 2 1 9 ( ) where LM = lifetime mileage ke1 = a constant reflecting the sensitivity of energy cost to lifetime mileage ke2 = a constant set to match base year energy cost And the following equation is used to estimate maintenance costs per vehicle mile as a function of lifetime mileage: CMM LM k em km LM( ) = 2 1 10 ( ) where km1 = a constant reflecting the sensitivity of maintenance cost to lifetime mileage km2 = a constant set to match base year maintenance cost For buses the values for the constants ke1 and km1 were derived based on regression analyses of fuel cost per mile, maintenance cost per mile, lifetime mileage, and average speed using data from the 2009 NTD normalized to 2010 dollars. A value of 6.27E-07 was derived for ke1 and 1.26E-06 was derived for km1. NTD data were used to derive constants for these values for rail, as well. The research team identified instances where rail fleets did not change from one year to the next (except, naturally, that they were one year older and had more lifetime mileage). For these fleets, energy consumption (measured in kilowatt hours) and vehicle maintenance costs were analyzed to determine how they increased from one year to the next. Regarding energy consumption, the analysis indicated that consumption increased by 2.1% per year for heavy rail and 1.6% per year for light rail. Using annual mileages per vehicle of 58,000 for heavy rail and 42,000 for light rail (per the NTD) the estimated value for ke1 is 4E-07 for light rail or heavy rail. Regarding maintenance costs, the analysis indicated that maintenance costs increased by 2.2% per year for heavy rail and 2.1% per year for light rail. Using the NTD mileages this equates to values for km1 of 4E-07 for heavy rail and 5E-07 for light rail. The constants ke2 and km2 should be set to reproduce base year values. This process is demonstrated in the supporting spreadsheet tool described in Section 5. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 Lifetime Mileag e R eh ab ili ta tio n Co st P er B us M ile (2 01 0$ ) Figure E-1. Predicted bus rehabilitation cost per mile.

114 To predict delay costs it is necessary to first predict road calls or failures per vehicle mileage, and then relate road calls or failures to delay. The following equation is used to predict road calls or failures per vehicle mile as a function of lifetime mileage: RM LM k er kr LM( ) = 2 1 11 ( ) where RM = road calls or failures per vehicle mile kr1 = a constant reflecting the sensitivity of road calls or failures to lifetime mileage kr2 = a constant set to match base year road calls or fail- ures For buses the value for kr1 was estimated as 1.98E-06 using data on the relationship between road calls per mile and vehicle age based on data provided in Useful Life of Transit Buses and Vans (3). Vehicle age was converted to lifetime mileage assum- ing annual mileage of 35,000 miles. Rail analysis was performed of NTD data as described above. The analysis indicated that, on average, failures per mile increased by about 4% from one year to the next for both heavy rail and light rail. Based on the analysis values for kr1 were estimated to be 7E-07 for heavy rail and 1E-06 for light rail. As for fuel and maintenance costs, the constant kr2 should be set to reproduce base year values. For buses, passengers delayed by a road call include those who were already on the bus at the time it went out of ser- vice and those who are waiting for the bus (up to the time when normal service is restored). Assuming that those on the bus when the road call occurs will be picked up by the next bus after the road call bus, their delay is equal to the schedule headway time. Up to the time when a replacement bus takes over the slot occupied by the road call bus, those passengers who were going to board the road call bus also are assumed to board the next bus, so their delay is also equal to the schedule headway. The average number of passengers on the bus when the road call occurs can be estimated as passenger miles divided by revenue bus miles. We estimate the number of passengers delayed waiting for the road call bus as the product of average boardings per revenue bus hour and the recovery time, which we define as the time until a replacement bus takes over the place that should have been occupied by road call bus. Putting this all together: PDR H VC PM VM RT PT VH = +    ( )12 where PDR = passenger delay per road call or failure H = headway VC = vehicles per consist (1 for buses) PM = passenger miles VM = revenue vehicle miles RT = recovery time PT = passenger trips VH = revenue vehicle hours As an example, assume the following for a typical bus system: • Schedule headway (H) of 0.5 hours • Vehicles per consist of 1 • 10 passenger miles per revenue vehicle mile (PM/VM) • Recovery time (RT) of one hour • 30 passenger trips per revenue vehicle hour (PT/VH) With these assumptions, passenger delay per road call is 20 hours, calculated as 0.5 p ( 10.0 + 1.0 p 30.0 ) = 20.0. Explicitly modeling added delay to passenger on trains behind temporarily immobilized or slowed trains is very complicated, since this delay is very sensitive to the following: • The fraction of rail car failures that result in immobilized or slowed trains • The length of time the train is immobilized and the speed reduction for slowed trains • Whether or not the train is immobilized at a location where it can be bypassed • The time of day (with peak periods being the worst due to the shorter headways and higher passenger load factors) Instead, we recommend that the analyst make an upward adjustment to the number of cars per train (VC) to account for this possibility. For example, if the analysis thinks that about 20% of total passenger delays due to rail car failures are experienced by passengers on trains behind an immobilized or slowed train, then a 25% upward adjustment in the num- ber of cars per train would be appropriate. The 25% upward adjustment is calculated as 20/(100-20). Combining Equations 11 and 12, and incorporating con- sideration of passenger value of time, the delay cost per vehi- cle mile can be calculated as a function of lifetime mileage as follows: CMD LM V H VC PM VM RT PT VH k er kr LM( ) = +    2 1 13( ) where V is the passenger value of time per hour. Concern- ing the value of time, U.S. DOT recommends that local travel time be valued at $11.20 per person-hour (in 2000 dollars) for the purpose of conducting benefit-cost analyses (4). This cor- responds to $12.10 in 2010 dollars. However, unanticipated delays are much more onerous to travelers than recurring delays. Specifically, the literature on valuation of travel time variability suggests that, on a per hour basis, unanticipated

115 delay is typically valued at two to six times recurring delay by travelers (5). Using the middle of this range, we assume that passenger hours of delay due to road calls or failures are valued at four time $1.10 or $48.40 per passenger hour. An important consideration in the model is the appropri- ate point for replacing a bus, specified as LM in the equations above. Ideally one should set LM to minimize the annual cost, which may be calculated by multiplying the life cycle cost by an annualization factor as follows: AC LCC i i A = − +( )    −1 1 14( ) where AC is the annual cost. For example, with an asset life (A) of 10 years and discount rate (i) of 7%, the annualization factor is 0.1424. This means that paying a life cycle cost (LCC) of $100 now is equal in value to paying $14.24 (AC) at the end of each of the next 10 years. The model can also be used to estimate the benefits of replacing vehicles older than age A. Specifically, the net ben- efit of replacing a vehicle relative to deferring the replacement can be approximated as the difference between the cost C of keeping the vehicle in operation an additional year and the annualized life cycle cost of a new vehicle AC. This difference represents the net increase in agency and user costs that would be incurred by deferring a recommended vehicle replacement for one year. Generally, if selecting vehicles to replace, one can maximize benefits (minimize costs) by replacing vehicle when the net benefit is greater than 0. The value C – AC represents the dif- ference between the future cost streams generated by two com- peting alternatives: one in which the asset is replaced now and one in which the asset is replaced at the end of this year. For the “Replace Now” alternative, the future stream of costs is equiv- alent to a cost of AC in each future year (if we assume that the replacement asset is again replaced at the end of its useful life and so on off into the indefinite future). This is because AC is, by definition, the annualized cost of the replacement asset. For the “Replace Next Year” alternative, the future stream of costs is C for this year and then AC for each subsequent year. Hence, the only difference between the two alternatives is their first year cost: C for the “Replace Next Year” alternative and AC for the “Replace Now” alternative. In estimating the values of C and AC for an asset, the ana- lyst should attempt to include all costs that are significantly affected by asset age and condition, including not only agency costs but also costs to passengers and others. Further, while there is much room for analyst discretion in selecting the cost models to be used, it is important that internally consistent procedures be used for estimating C and AC, since priorities for an asset replacement project are assigned based on their difference. Special treatment is required when the annual cost of keeping an asset in place decreases over time. This is rare for operating, maintenance, and passenger costs. It can, however, occur for rehabilitation costs if a costly rehabilitation is required next year to keep the asset in place. In such cases, the cost of keeping the asset in place for an additional year (C in the above equation) should be replaced by the average cost for keeping the asset in place over the next N years, where N is selected to mini- mize the value of C. For example, if the costs required to keep the asset in place over the next five years are $20,000, $5,000, $7,000, $9,000, and $11,000 respectively, the value of C is mini- mized when N equals four years. In this case, C is $10,250. Note that C would be higher for N equals three or N equals five. E.3 Age-Based Model As discussed in Section 5, for the age-based model the likelihood of asset failure is modeled using a Weibull distri- bution. This distribution is commonly used for applications such as survival analysis, and its use is described in textbooks on applied statistics and related topics, such as (6). The math- ematical formula for the cumulative probability function of this distribution is as follows: f t e t k( ) = − −( )1 15λ ( ) where: f(t) = cumulative probability of asset failure; t = asset age (in year, miles, or other units); k = shape parameter; and l = scale parameter. Figure E-2 shows sample survival curves developed using Weibull distributions. These show the probability of failure on the vertical axis and asset age on the horizontal axis. The left panel shows the probability of asset failure at a given age, and the right panel shows the cumulative probability of asset failure for a given age or less. The Weibull distribution is described by the parameters k and l, which describe its shape and scale (characteristic age), respectively. The shape parameter is particularly important for determining when to replace an asset. As k increases the distri- bution shown in the left panel becomes more pronounced and failure becomes more likely over time, which tends to increase the relative benefit of replacing the asset before it reaches a specified threshold. But if k<1 then proactive replacement of the asset may not be justified, as the asset actually improves with age and it becomes increasingly less likely that the asset will fail as it continues to survive. The scale parameter indicates the age by which 63.2% of a population of assets is expected to fail. The shape and scale parameter were then calculated using this information and Equation 15.

116 for an asset such as an escalator, a failure would be an inter- ruption in service that is severe enough to trigger overhaul of the escalator. However, a minor interruption in service requiring maintenance work would not be considered a failure in this context. • The next step is to calculate the transit agency and user costs of asset failure. Typically the cost of a failure is at least as great as the recommended action to avert failure – or if it is not then the optimal policy is to replace the asset only upon failure. The cost may include emergency costs to mobilize equipment and personnel to address the failure in the short term, and may include costs of user delay, such as to detour around a facility or asset that is out of service. • Once asset failure and its costs have been characterized, then a survival curve should be developed for the asset. Weibull curves such as those shown in Figure 5-2, are com- monly used for this application, and can be fit to data using various statistical packages. • After a Weibull curve has been developed one can then establish the policy for replacing the asset, selecting the replacement age A that minimizes the annual cost AC. The tool described in Section 5.3 illustrates use of Monte Carlo simulation to determine these values. As in the case of the vehicle model, the marginal benefit of replacing an asset relative to deferring the replacement can be approximated as the difference between the cost of maintaining the asset an additional year and the annualized cost of a new asset Note that if k = 1 then failure is equally likely at any time. For such assets, the determination of the optimal policy may be better determined based on the condition of the asset using a Markov Decision Process than using survival analysis, as described in the next subsection. This approach is often used for complex assets, such as bridges and facilities that have many elements or components and multiple failure modes. A useful property of the Weibull distribution is that it can be used to predict the conditional probability of failure in time t + 1 given an asset has survived until time t. This conditional probability is calculated as follows: P t t e e t k t k +( ) = − − +  −   1 1 16 1 λ λ ( ) The following approach to modeling rehabilitation and replacement analysis is recommended for assets (other than vehicles) in cases in which age is the best predictor of rehabili- tation and replacement need: • First, it is important to define what constitutes asset failure. The discussion here assumes that failure does not necessar- ily imply catastrophic failure of the asset, but does result in the asset’s being effectively removed from service, trigger- ing a failure cost (which may include agency and user cost components) to restore the asset to service. For instance, Cumulative Distribution Function Age C um ul at iv e P ro ba bi lit y of F ai lu re k=1 k=3 k=5 Probability Distribution Function Age P ro ba bi lit y of F ai lu re k=1 k=3 k=5 Figure E-2. Typical asset survival curves.

117 AC. The benefit of taking action relative to deferral is rep- resented below. B P t t CF CP P t t CM AC= −( ) −( )+ − −( )( ) −1 1 1 17  ( ) where: B = benefit of taking action relative to deferral CF = failure cost CM = annual maintenance cost CP = purchase/replacement cost The age-based modeling tool described in Section 5 is pre- populated with deterioration curves for common transit assets other than vehicles. Deterioration data from TERM Lite were used to develop these curves. To define the Weibull distribu- tion corresponding to a TERM model, the TERM model was used to predict the age at which the predicted condition was 2.5 (assumed to be the point at which 50% of a population of assets would fail) and the age at which the predicted condition was 1.5 (assumed to be the point at which 75% of a popula- tion of assets would fail). Table E-1 details the results of this exercise, listing the asset name, corresponding ID in the TERM Lite database, and resulting shape and scale parameters for the asset’s survival curve. E.4 Condition-Based Model The approach of using a Markov Decision Process to develop a policy for maintaining an asset is described in oper- ations research texts (7), and has been used in asset manage- ment systems such as the FHWA National Bridge Investment Analysis System (8). The reader is referred to these resources for additional information on this approach. In formulating the problem it is necessary to describe the optimal stationary policy for the asset—that is, the optimal set of actions to take in each condition state—using Bellman’s optimality equation: LCC x C i P LCC y a x a x y a y  ( ) = + + ( )  ∑min (, , 1 1 18) where LCCp(x) = minimum life cycle cost for asset in state x a = optimal action to perform in state x Cx,a = cost of taking action a in state x Pax,y = probability of transition from state x to state y given action a is performed Although Equation 18 is a dynamic equation, it can be formulated and solved as a linear program. Once the optimal policy has been determined, the life cycle cost for an asset in state x given action a is performed in the next period can be specified as follows: LCC x a C i P LCC yx a x ya y ( ) = + + ( )∑, , ( )1 1 19 Note this equation assumes that following the next period, the optimal policy is followed. Thus, the difference between LCC(x|a) and LCCp(x) represents the additional cost incurred if action a is followed rather than the optimal action. Likewise, the benefit B of performing an action relative to deferring action for one decision period (typically one year) is the dif- ference between the life cycle costs for the do-minimum action and the selected action. Below are additional notes on applying this approach to transit assets: • The approach can be easily applied to assets inspected using the five-point scale described in TERM. For complex assets, such as structures, it is generally necessary to represent the asset using subcomponents or elements, with each having its own model. • Typically an additional “failed” state is defined, for which only one action is available. The cost of this action is the failure cost. The existence of a failure cost, if it is sufficiently high, serves to force selection of actions to avert asset failure. • Applications of the approach typically consider agency costs only, and assume asset failure can occur only from the worst condition state. However, these assumptions tend to result in a solution in which action is deferred until an asset reaches its worst condition. Thus, if there is a probability of asset failure from states other than the worst condition, and/or if there are additional costs associated with declining condition, these should be incorporated in the model. The condition-based modeling tool described in Section 5 is pre-populated with deterioration curves for common transit assets other than vehicles. Deterioration data from TERM Lite were used to develop these curves. The following approach was used to determine a set of transition probabilities correspond- ing to a given TERM model: • An initial set of transition probabilities was defined for the “do minimum” action for condition states 2 to 5 using the TERM condition state definitions. In each state the asset could either remain in the same state or deteriorate. For States 3 to 5 it was assumed that if an asset deterio- rated it would deteriorate to the next worst state (from State 5 to 4, etc . . . ). For State 2 it was assumed that it was equally likely that the asset would deteriorate to State 1 or fail. The probability of deterioration for State 1 was set to be equal to that determined for State 2. • The average condition was predicted for asset ages from 1 to 100 years using an asset starting at State 5 in Year 1. • The Excel Solver was used to determine the set of prob- abilities that minimized the sum of the squares of the dif- ference between the average condition predicted by the

118 TERM model and the average calculated using the transi- tion probabilities. The result of this process was a set of four transition prob- abilities for each TERM model, describing the probability of an asset remaining in State 2-5 from one year to the next. Table E-1 details the results of this exercise, listing the asset name, corresponding ID in the TERM Lite database, transi- tion probabilities used in the condition-based model (for the “do-minimum” action). Asset TERM ID Age-Based Model Parameters Condition Based Model – One-Year Probability of Remaining in Same State Shape Scale 5 4 3 2 Guideway-At Grade Ballasted or Expressway 10111 2.70 95.54 98.4% 96.2% 93.3% 89.0% Guideway-Grade Crossing 10210 3.48 20.38 90.2% 83.8% 74.4% 60.1% Guideway-Elevated Structure 10310 2.42 100.24 98.5% 96.4% 94.1% 60.2% Guideway-Steel Viaduct 10320 2.42 100.19 98.5% 96.4% 94.1% 60.2% Guideway-Bridge 10330 2.70 95.54 98.4% 96.2% 93.3% 89.0% Guideway-Foot Walk 10340 3.71 107.12 99.1% 96.9% 94.1% 90.1% Guideway-Elevated Fill 10400 2.72 129.80 99.3% 97.1% 94.2% 90.2% Guideway-Tunnel 10510 2.72 129.80 99.3% 97.1% 94.2% 90.2% Guideway-Retained Cut 10600 2.72 129.80 99.3% 97.1% 94.2% 90.2% Guideway-Tangent Direct Fixation Track 11101 3.94 48.89 96.0% 93.2% 89.2% 83.1% Guideway-Curved Direct Fixation Track 11102 3.12 31.80 93.6% 89.4% 83.2% 73.8% Guideway-Guarded Direct Fixation Track 11103 3.21 34.61 94.1% 90.2% 84.6% 75.9% Guideway-Direct Fixation Tangent Platform Track 11104 2.70 39.29 94.6% 91.2% 86.1% 78.3% Guideway-Direct Fixation Curved Platform Track 11105 2.38 29.29 92.5% 88.0% 81.3% 71.0% Guideway-Guarded Curved Direct Fixation Track 11106 2.37 32.31 93.2% 89.1% 83.0% 73.6% Guideway-Tangent Ballasted Track 11201 3.68 44.63 95.6% 92.5% 88.1% 81.4% Guideway-Curved Ballasted Track 11202 3.37 37.64 94.6% 91.1% 85.9% 77.9% Guideway-Guarded Ballasted Track 11203 3.42 40.35 95.0% 91.7% 86.8% 79.4% Guideway-Ballasted Tangent Platform Track 11204 3.10 39.00 94.7% 91.3% 86.2% 78.5% Guideway-Ballasted Curved Platform Track 11205 3.10 33.01 93.8% 89.7% 83.8% 74.7% Guideway-Guarded Platform Ballasted Track 11206 4.44 63.61 97.2% 94.9% 91.6% 86.7% Guideway-Tangent Embedded Track 11301 3.94 48.89 96.0% 93.2% 89.2% 83.1% Guideway-Curved Embedded Track 11302 3.12 31.80 93.6% 89.4% 83.2% 73.8% Guideway-At-Grade Crossing 11303 3.12 31.80 93.6% 89.4% 83.2% 73.8% Guideway-Special Track Work 11400 3.33 38.03 94.7% 91.2% 86.0% 78.1% Guideway-Direct Fixation Diamond Crossover 11402 3.16 36.09 94.3% 90.6% 85.2% 76.8% Guideway-Direct Fixation or Ballasted Turnout 11407 3.81 46.73 95.8% 92.9% 88.7% 82.3% Guideway-Turntable 11410 3.42 40.35 95.0% 91.7% 86.8% 79.4% Guideway-Yard Track 11500 3.53 40.22 95.0% 91.7% 86.8% 79.4% Guideway-Wood Tie 11601 3.48 20.38 90.2% 83.8% 74.4% 60.1% Guideway-Concrete Tie 11602 3.48 20.38 90.2% 83.8% 74.4% 60.1% Guideway-Retaining Wall 12200 1.85 49.65 95.1% 92.8% 89.1% 83.3% Guideway-At Grade Bus 13100 3.48 30.57 98.1% 95.9% 92.9% 88.5% Guideway-Bus Turnaround 13200 3.48 81.53 98.1% 95.9% 92.9% 88.5% Table E-1. Deterioration models derived from TERM data.

119 Asset TERM ID Age-Based Model Parameters Condition Based Model – One-Year Probability of Remaining in Same State Shape Scale 5 4 3 2 Facilities-Building Utilities- Elevators and Conveying Systems 21510 3.48 20.38 90.2% 83.8% 74.4% 60.1% Facilities-Building Utilities- Generator 21512 3.48 20.38 90.2% 83.8% 74.4% 60.1% Facilities-Storage Yard 22210 3.48 81.56 98.1% 95.9% 92.9% 88.5% Facilities-Storage Yard-Bus 22300 3.48 81.56 98.1% 95.9% 92.9% 88.5% Facilities-Bus Turnaround Facility 22400 2.74 40.03 94.7% 91.3% 86.4% 78.7% Facilities-Maintenance Equipment 23301 2.49 20.27 89.4% 82.9% 73.4% 58.7% Facilities-Pollution Treatment 23400 3.48 30.57 98.1% 95.9% 92.9% 88.5% Facilities-Bus Washer 23402 3.48 81.56 98.1% 95.9% 92.9% 88.5% Facilities-Train Washer 23403 2.74 40.03 94.7% 91.3% 86.4% 78.7% Facilities-Vehicle Paint Booth 23404 3.48 81.56 98.1% 95.9% 92.9% 88.5% Facilities-Fuel Island 23405 3.48 81.56 98.1% 95.9% 92.9% 88.5% Facilities-Dynamometer 23406 3.48 20.38 90.2% 83.8% 74.4% 60.1% Facilities-Portable Lift 23407 3.48 20.38 90.2% 83.8% 74.4% 60.1% Facilities-Fixed Lift 23408 3.48 81.56 98.1% 95.9% 92.9% 88.5% Facilities-Wheel Truing Machine 23409 3.42 40.35 95.0% 91.7% 86.8% 79.4% Facilities-Brake Lathe 23410 3.42 40.35 95.0% 91.7% 86.8% 79.4% Facilities-Major Rail Shop 24100 3.48 81.53 98.1% 95.9% 92.9% 88.5% Facilities-Major Bus Shop 24200 3.48 81.53 98.1% 95.9% 92.9% 88.5% Facilities-Train Control Center 25000 3.48 50.95 98.1% 95.9% 92.9% 88.5% Systems-Train Control, Electrification, Communications, Revenue Collection & Utilities 30001 2.80 37.00 94.3% 90.7% 85.3% 77.1% Systems-Train Control 31001 2.50 41.34 94.8% 91.5% 86.7% 79.3% Systems-Train Control 31101 2.74 40.03 94.7% 91.3% 86.4% 78.7% Systems-Signals & Train Stops 31111 2.73 40.27 94.8% 91.4% 86.4% 78.8% Systems-Train Control Cable 31121 2.77 38.75 94.6% 91.1% 85.9% 78.1% Systems-Signal Bridge 31122 3.48 241.13 99.9% 97.7% 95.3% 79.5% Systems-Centralized Train Control 31301 3.48 50.94 98.1% 95.9% 92.9% 88.5% Systems-Gates, Flashers, Crossings 31400 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Roadway Traffic Signals 31410 3.48 16.31 87.9% 79.9% 68.3% 50.6% Systems-Interlocking 31500 2.15 48.15 95.3% 92.5% 88.4% 82.1% Systems-Electrification 32001 2.95 41.31 95.0% 91.7% 86.9% 79.5% Guideway-Elevated-Bus 13300 3.48 50.95 98.1% 95.9% 92.9% 88.5% Guideway-Subway Bus 13500 3.48 50.95 98.1% 95.9% 92.9% 88.5% Facilities-Administrative Building 21100 2.52 103.12 98.6% 96.4% 93.5% 89.3% Facilities-Maintenance Building 21210 2.90 54.79 96.3% 93.7% 89.9% 84.1% Facilities-Passenger Building 21300 2.52 103.12 98.6% 96.4% 93.5% 89.3% Facilities-Building Utilities 21500 2.46 51.40 95.8% 93.1% 89.1% 83.0% Facilities-Access and Parking 21509 3.48 81.56 98.1% 95.9% 92.9% 88.5% Systems-Electrification Catenary/Pole 32100 3.04 43.95 95.3% 92.2% 87.7% 80.7% Table E-1. (Continued). (continued on next page)

120 Asset TERM ID Age-Based Model Parameters Condition Based Model – One-Year Probability of Remaining in Same State Shape Scale 5 4 3 2 Systems-Communications Cable 33100 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Communications 33102 2.49 20.27 89.4% 82.9% 73.4% 58.7% Systems-MIS/IT/Network System 33103 3.48 15.29 87.1% 78.6% 66.3% 47.5% Systems-Emergency Location System 33300 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-SCADA RTU 33815 3.48 5.10 74.5% 50.0% 25.0% 25.0% Systems-Communications Hut or Room 33850 3.04 43.95 95.3% 92.2% 87.7% 80.7% Systems-Bus On-Board Video System 33901 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Central Revenue Collection 34000 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Coin/Bill Counter 34100 3.48 5.10 74.5% 50.0% 25.0% 25.0% Systems-Revenue Collection System-Rail 35000 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Turnstile 35104 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-In Station Revenue Collection Equipment 35116 2.49 20.27 89.4% 82.9% 73.4% 58.7% Systems-Parking Meter 35117 3.48 15.29 87.1% 78.6% 66.3% 47.5% Systems-Change Machine 35118 3.48 15.29 87.1% 78.6% 66.3% 47.5% Systems-Passenger Counter-Rail 35130 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-System Utilities 36000 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Lighting 36100 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Guideway Drainage 36200 2.32 48.52 95.8% 93.1% 89.1% 83.0% Systems-Pump Room 36202 3.48 30.57 98.1% 95.9% 92.9% 88.5% Systems-Deep Utility Well 36203 3.14 65.65 97.1% 94.7% 91.4% 86.4% Systems-Sump Pump/Discharge Pipes 36204 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Subway Ventilation 36301 2.32 48.52 95.8% 93.1% 89.1% 83.0% Systems-Fan Plant 36302 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Compressed Air Pipes 36303 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Air 36304 3.48 20.38 90.2% 83.8% 74.4% 60.1% Conditioning/HVAC- Subway Systems-Emergency Exit 36400 3.48 50.95 98.1% 95.9% 92.9% 88.5% Systems-Tunnel Handrail 36401 2.32 48.52 95.8% 93.1% 89.1% 83.0% Systems-ITS, APC, AVL, CAD, GPL 37000 2.49 20.27 89.4% 82.9% 73.4% 58.7% Systems-Electrification Substation 32200 3.04 43.95 95.3% 92.2% 87.7% 80.7% Systems-High Tension Towers 32213 3.48 81.56 98.1% 95.9% 92.9% 88.5% Systems-Electrification Substation Building Components 32214 2.46 51.40 95.8% 93.1% 89.1% 83.0% Systems-Electrification Breaker House 32300 2.17 43.94 94.8% 91.8% 87.4% 80.5% Systems-Electrification Contact Rail/Protection Boards 32400 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Heaters 32408 2.49 20.27 89.4% 82.9% 73.4% 58.7% Systems-Power Cable 32500 2.58 28.13 92.4% 87.7% 80.7% 69.9% Systems-Electrical Systems 32600 3.48 20.38 90.2% 83.8% 74.4% 60.1% Systems-Trolley Wire 32700 3.14 65.65 97.1% 94.7% 91.4% 86.4% Station-Building-Rail 41000 2.17 43.94 94.8% 91.8% 87.4% 80.5% Stations-Building-Subway 41250 2.72 129.80 99.3% 97.1% 94.2% 90.2% Table E-1. (Continued).

121 Asset TERM ID Age-Based Model Parameters Condition Based Model – One-Year Probability of Remaining in Same State Shape Scale 5 4 3 2 Stations-Bus Shelter 42207 3.48 20.38 90.2% 83.8% 74.4% 60.1% Stations-Station Canopy 42300 2.24 70.04 97.0% 94.8% 91.6% 86.7% Stations-Bus Station Platform 42800 2.22 71.23 97.1% 94.9% 91.7% 86.9% Stations-Signage & Graphics 42900 3.48 20.38 90.2% 83.8% 74.4% 60.1% Stations-Ferry Terminal Building/Dock 43010 2.24 70.04 97.0% 94.8% 91.6% 86.7% Stations-Elevator/Escalator 41400 3.48 30.57 98.1% 95.9% 92.9% 88.5% Stations-Parking Garage/Lot 41601 3.48 20.38 90.2% 83.8% 74.4% 60.1% Stations-Parking Equipment 41604 3.48 20.38 90.2% 83.8% 74.4% 60.1% Stations-Pedestrian Walkway/Elevated 41701 3.48 101.89 98.9% 96.7% 93.9% 89.7% Stations-Pedestrian Walkway/Subway 41702 3.48 101.90 98.9% 96.7% 93.9% 89.7% Stations-At-Grade Rail Platform 41801 2.22 71.25 97.1% 94.9% 91.7% 86.9% Stations-Elevated Rail Platform 41803 2.29 80.95 97.6% 95.5% 92.4% 87.9% Stations-Subway Rail Platform 41805 2.79 95.50 98.5% 96.3% 93.3% 89.1% Stations-Building/Ground Access-Bus 42201 2.46 51.40 95.8% 93.1% 89.1% 83.0% Stations-Shelter-Rail 41270 3.48 20.38 90.2% 83.8% 74.4% 60.1% Stations-Token Booth 41280 3.48 20.38 90.2% 83.8% 74.4% 60.1% E.5 Appendix E References (1) H. Weingartner, H. Mathematical Programming and the Analysis of Capital Budgeting Problems, Prentice Hall, 1963. (2) Louch, H, Robert, W, Gurenich, D. and Hoffman, J. Asset Manage- ment Implementation Strategy. Report NJ-2009-005 prepared for the New Jersey Department of Transportation (NJDOT). NJDOT, 2009. (3) Booz Allen Hamilton Inc. Useful Life of Transit Buses and Vans. Technical Report FTA VA-26-7229-07.1 prepared for FTA. FTA, 2007. (4) Frankel, E. “Revised Departmental Guidance: Valuation of Travel Time in Economic Analysis.” U.S. DOT, February 11, 2003. (5) Cohen, H and Southworth, F. “On the Measurement and Valuation of Travel Time Variability Due to Incidents on Freeways.” Journal of Transportation and Statistics, December 1999. (6) Levine, D., Ramsey, P. and Smidt, R. Applied Statistics for Engineers and Scientists, Prentice Hall, 2001. (7) Winston, W. Operations Research: Applications and Algorithms (Third Edition), Duxbury Press, 1994. (8) Cambridge Systematics, Inc. “NBIAS 3.3 Technical Manual.” Tech- nical Report prepared for FHWA, 2007. Table E-1. (Continued).