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Design Guide for Bridges for Service Life (2013)

Chapter: 11 Life-Cycle Cost Analysis

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Suggested Citation:"11 Life-Cycle Cost Analysis." National Academies of Sciences, Engineering, and Medicine. 2013. Design Guide for Bridges for Service Life. Washington, DC: The National Academies Press. doi: 10.17226/22617.
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502 11.1 introduction This chapter introduces life-cycle cost analysis (LCCA) and its use in the decision- making process for selecting optimum cost-effective bridge systems, subsystems, and elements that can achieve long-term service life. It includes general guidelines and best practices for application of LCCA, outlines the steps in the process, and briefly dis- cusses the economic principles involved. References to available models are made without recommending the use of a specific software or model. LCCA, in lieu of purely initial construction cost evaluation, is essential in evaluat- ing the long-term benefit of many strategies that can achieve extended service life (in excess of 100 years) yet require additional and sometimes considerable initial invest- ment. LCCA can assist agencies with investment decisions by considering the initial costs and relevant future costs associated with required inspection, maintenance, reha- bilitation, and possible component replacement, including associated demolition, dis- posal, and user costs. In its broadest form, LCCA can be used in the evaluation of alternative bridge systems. In its more simplified forms, it aids in evaluating alternatives for bridge com- ponents, such as decks, superstructures, and substructures; or more specialized bridge element applications, such as comparing alternatives for deck joints or bearings. This chapter is intended only as a brief discussion of the benefits, principles, and methodologies involved in LCCA. Additional detail on this entire process and its application are provided in the attached references, primarily in the Life-Cycle Cost Analysis Primer (FHWA 2002a) and in NCHRP Report 483: Bridge Life-Cycle Cost Analysis (Hawk 2003). 11 LiFE-CyCLE COST ANALySiS

503 Chapter 11. LiFE-CyCLE COST ANALySiS 11.2 LccA deFined LCCA is an analysis methodology that assists in comparing and choosing alternative strategies for achieving long-term service life for bridge systems, subsystems, or ele- ments. It considers not only the initial construction cost, but also all of the costs that are expected to occur over the entire service life of the bridge, typically maintenance, major rehabilitation, component or element replacement (including relevant demoli- tion and disposal costs), and user costs. Economic methods are used to convert antici- pated future costs to present dollar values so that lifetime costs of various alternatives can be directly compared. 11.2.1 Steps in LCCA The five basic steps in the LCCA process are described in the following sections (FHWA 2002b). Step 1. Establish Design Alternatives Step 1 involves establishing the elements of initial design and identifying the associated activities that will be required throughout the structure’s service life for maintenance, rehabilitation, or element replacement within a system or subsystem for each alterna- tive being considered. Step 2. Determine Activity Timing The timing of associated activities throughout the period of comparison must be determined as part of the identification process. Estimating when and how often cer- tain activities must be performed is important in making realistic comparisons. This process might involve identifying certain required maintenance on a yearly basis, or certain levels of potential rehabilitation due to expected wear after a specified period of time, or when individual components or elements such as decks or bearings may have to be replaced. Agency data are important in establishing when various levels of maintenance, rehabilitation, or replacement may be required. In the absence of data, expert opinion can be used. Step 3. Estimate Costs This step involves estimating the initial construction cost associated with each design alternative and the costs associated with the various identified future maintenance, rehabilitation, and replacement activities. Costs are computed on the basis of current cost data. It is recommended as a best practice that costs include both agency costs and user costs. This practice is discussed further in Section 11.2.2. Step 4. Compute Life-Cycle Costs Step 4 involves computing the present value of all costs identified for a given alterna- tive. The concepts of present value are further discussed in Section 11.3.1. As part of this computational process, two approaches, either deterministic or stochastic (prob- abilistic), address the variability and uncertainty associated with input factors. The

504 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE deterministic approach (most used) uses fixed discreet values. The stochastic approach defines input variables by a probability distribution. These computational approaches are further discussed in Section 11.3.4. Step 5. Analyze Results The final step involves comparing the initial and life-cycle costs associated with the various alternatives and determining the optimal cost-effective solution. If the alter- natives provide different levels of service, then the alternatives that provide the best overall long-term benefit can also be compared. 11.2.2 LCCA Cost types 11.2.2.1 Agency Costs Agency costs include all the costs borne by the agency or owner of the bridge (includ- ing design, initial construction, inspection, maintenance, rehabilitation, and element replacement) and have been the primary elements for consideration in LCCA. Some costs, such as initial construction, rehabilitation, and replacement, are more easily estimated on the basis of current industry cost data. Other costs, such as maintenance, are more difficult and rely on the existence and accuracy of agency historical cost data. In the absence of these data, expert opinion can be used. 11.2.2.2 User Costs User costs are primarily associated with reduced traffic capacity in work zones and involve costs to the users because of delays, vehicle operating costs, and accidents. Estimating these costs may be the greatest challenge to LCCA implementation. Many agencies have been reluctant to incorporate user costs into LCCA because of the dif- ficulty and uncertainty in assigning value to user delay time, or because user costs are not factored into agency budgets. These issues have led many agencies to give lesser credence to user costs in evaluating overall lowest-cost solutions; however, minimizing user impacts and associated costs is a major concern today, especially with implementa- tion of accelerated bridge construction. A recent pooled-fund study led by the Oregon Department of Transportation (DOT) (Doolen et al. 2011) developed a set of decision- making tools to determine if accelerated bridge construction techniques are more ef- fective than traditional construction for a given bridge replacement or rehabili tation project. These tools incorporate quantified user costs as part of an LCCA evaluation. User costs can play an important factor in evaluating various options for long- term service life. Section 11.3.3 further discusses the approach for estimating user costs based on traffic volumes and user delays. 11.2.2.3 Vulnerability Costs Vulnerability costs are associated with extraordinary circumstances and risks, such as overload, collision, blast, fire, floods, scour, or earthquake, and typically would not be included in an LCCA for comparison of service life strategies. They are useful,

505 Chapter 11. LiFE-CyCLE COST ANALySiS however, in evaluating vulnerability of existing bridges that might have a high prob- ability for one or more of these extreme events. 11.2.3 LCCA Versus Benefit–Cost Analysis LCCA is a subset of benefit–cost analysis, which compares benefits, as well as costs, in selecting optimal alternatives. Benefit–cost analysis is useful in comparing alternatives that do not achieve the same level of service or benefit. For example, benefit–cost anal- ysis can be useful in comparing bridge replacement options that provide either three or four lanes of traffic with corresponding different levels of service. Clearly there are both cost and benefit variations between each option. LCCA is typically considered alone for service life evaluation of various alternatives that can ultimately provide the same level of service. 11.3 eLementS oF LccA This section discusses methodologies for determining net present value (NPV) and discount rates. It further discusses other elements considered in LCCA such as activity timing and service life, user costs, computational approaches, and analysis tools. 11.3.1 net Present Value The NPV concept in LCCA is an economic method for combining initial costs and present dollar values of future expected costs so that lifetime costs for various alter- natives can be directly compared. Dollars spent at different times within a structures life have different present values, so the projected activity costs for an alternative can- not simply be added together to calculate the total life-cycle cost for that alternative. Accord ing to TRB’s Transportation Economic Committee (2013), A dollar today is worth more than a dollar five years from now, even if there is no inflation, because today’s dollar can be used productively in the ensuing five years, yielding a value greater than the initial dollar. Future benefits and costs are discounted to reflect this fact. The purpose of discounting is to put all present and future costs into a common metric, their net present value [NPV]. The formula to convert the sum of the initial cost and the present value of future repair and renewal costs into NPV is given by Equation 11.1: ∑ ( ) = + +        = r k NPV initial cost rehab cost 1 1 k k N n 1 (11.1) where r = real discount rate, k = order number of a rehabilitation activity undertaken in the future, N = total number of rehabilitation activities, and nk = year in the future when the cost will be incurred.

506 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE The term r k 1 1 n( )+         is called the discount factor. Input factors in computing NPV are the initial cost (usually the cost of planning, design and construction of a new structure), the cost and timing of rehabilitation activ- ities, and the real discount rate. Discounting is a method of considering the opportunity cost of money as it applies to current versus future funds. It can be thought of in terms of the alternative economic return that could be gained on funds such as earning interest. The computed potential amount of interest is based on what is referred to as the discount rate, which is gener- ally described as having three components: 1. The real opportunity cost of capital to account for productive value of funds; 2. The premium to account for financial risk (i.e., that the loan will not be repaid); and 3. The anticipated rate of inflation. According to TRB’s Transportation Economic Committee, Life-cycle analyses typically ignore inflation because the prediction of future prices introduces unnecessary uncertainty into the analysis. Therefore, dis- count rates are typically based on interest rates for government borrowing, which have little risk, with the inflation component removed, yielding the “real” interest rate. This rate is typically calculated by subtracting the rate of inflation (consumer price index) from the interest rate of an investment such as a 10-year U.S. Treasury bill. For example, if the interest on a 10-year Trea- sury bill is 5.5% and the inflation rate is 3%, then the discount rate would be 2.5%. Circular No. A94 (OMB 1992) provides general guidance for conducting cost- effectiveness analyses and provides specific guidance on the discount rates to be used in evaluating programs whose benefits and costs are distributed over time. It also provides standard criteria for deciding whether programs can be justified on economic principles. The OMB publishes real interest rates for NPV analyses on its website. As Figure 11.1 shows, the discount rate can have a significant impact on the analy- sis. A low discount rate favors projects with long-term benefits and near-term costs. When evaluating alternative projects, a sensitivity analysis using a range of discount rates can be used to determine the importance or impact of the discount rate in the relative project performance. Even with a low discount rate, values far in the future have a relatively low present value.

507 Chapter 11. LiFE-CyCLE COST ANALySiS Figure 11.1. Effect of discount rates on present value. Increasing Rate Figure 11.1. Effect of discount rates on present value. 11.3.2 Activity timing, Service Life, and Life Cycle 11.3.2.1 Deterioration Models Deterioration models describe the relationship between the condition of the bridge (or its element) and time, showing how the bridge deteriorates. The model assumes that no replacements or major repairs are made, but it usually implies that scheduled main- tenance actions are performed as planned. The basic model applies either to a bridge as a whole, or to any of its elements (e.g., deck, substructure, bearings, columns). The shape of a deterioration curve depends on the type of the element and the definitions of condition states. Figure 11.2 shows a deterioration curve. If the bridge is placed in service at time T0, its condition gradually declines, and the deterioration curve represents its condi- tion over time. Initially the condition is good, but after a period of wear and aging, it eventually (at time Tf) reaches an unacceptably low condition (Cf). The period between T0 and Tf is called the service life of the bridge. In practice, however, realistic deterioration models that are based on actual physi- cal and chemical deterioration processes are generally not available to accurately pre- dict service life. The most acceptable deterioration model is in the form of the solution to Fick’s second law, used to predict the rate of chloride ingress through concrete cover. This model, including its limitations, is described in Chapter 5 of the Guide. It is expected that with time additional deterioration models will become available that

508 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE Bridge Deterioration Service Life T 0 Cf Tf Condition Time of Use Figure 11.2. Bridge deterioration curve. will greatly enhance quantification of the service life of bridge elements, components, subsystems, and systems. Developing deterioration models is a data-intensive procedure that is complicated by the lack of knowledge of the underlying processes that foster deterioration, as well as by data availability. In lieu of deterioration models based on actual physical and chemical deterioration processes, other approximate methods must be used. Bridge management software programs such as Pontis and BRIDGIT, which are used in nearly all 50 states, have deterioration models contained within them that are typically based on expert opinion and analysis of available historical data. Recent studies by the New York State DOT (Agrawal et al. 2009) and the Florida DOT (Sobanjo 2011) have further attempted to develop bridge element deteriora- tion models on the basis of state DOT bridge inspection databases along with expert opinion. The New York State DOT study applied computerized statistical methods to develop deterioration curves using inspection data going back to 1981. The study included the influence of various factors such as average daily truck traffic and climate. The New York State DOT study implemented a stochastic approach to account for the uncertainty and randomness of factors affecting the deterioration process. In the stochastic approach, the ratings of bridge elements (reflective of their condition at a particular time) and the durations that elements will stay at a particular rating were assumed to be random variables and were modeled by probability distributions. The study developed and compared deterioration curves using both Markov chain– and Weibull distribution–based stochastic models. Markov chain, the most commonly used model for developing deterioration rates for infrastructure facilities, is used in advanced bridge management systems such as Pontis and BRIDGIT. It models the deterioration process by considering the probability of transition from one condition state to another in a discrete time, and it accounts for the current element condition in predicting the future condition. A Weibull-based model considers the probability of how long a bridge element will remain at a particular state, and it also considers past conditions. The New York State DOT study found that the Weibull-based models gen- erally provided the best overall fit with historical bridge inspection data.

509 Chapter 11. LiFE-CyCLE COST ANALySiS Methods that use historical data to develop long-term bridge element deteriora- tion models have certain limitations. Aside from not considering the actual physical deterioration process, older historical data do not consider more recent improvements in construction materials or methods, which can greatly affect future service life. Fur- ther, there is some uncertainty about extrapolating the data beyond the duration for which the data were collected. 11.3.2.2 Expenditure Stream As shown in Figure 11.3, a bridge will deteriorate over the period of its service life if left unattended. However, in most cases a bridge is not left to follow the basic dete- rioration path and reach an unacceptable condition without interruption. The agency responsible for the bridge will, from time to time, undertake repairs, rehabilitations, and renewals that return conditions to higher levels and extend its service life. The sequence of events and actions that determine the bridge condition through- out its life cycle is called a life-cycle activity profile. Actions are usually associated with expenditures that have to be incurred when repair, rehabilitation, and renewal activi- ties occur. These expenditures may be plotted on a separate diagram that represents the stream of expenditures associated with construction and repair activities. Such a diagram is sometimes called a cash flow diagram. An example of such diagram is shown in Figure 11.4. In cash flow diagrams, all resource flows are usually attributed either to the begin- ning or the end of the time period in which they actually occur. In cases in which a resource flow is extended over several periods, the expenses are represented as a series of lines. Cash flow diagram expenses are shown as lines graphed in the positive domain; revenues and other returns (e.g., the terminal value of the bridge) are shown as negative values. For simplicity, only agency costs have been plotted on the example cash flow diagram shown in Figure 11.4. When other types of costs (e.g., user costs and vulnerability costs) are included, the cash flow diagram serves as a graphic repre- sentation of the NPV computation. Bridge Condition Service Life T 0 Cf Time of use Condition Tf Figure 11.3. Bridge condition life cycle.

510 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE 11.3.3 Estimating User Costs Work zone user costs are the increased vehicle operating costs, delay, and crash costs incurred by highway users as a result of construction, maintenance, or rehabilitation work zones. User costs may represent the greatest data challenge for consideration in an LCCA. When calculated, user costs are often so large that they may substantially exceed agency costs, particularly for transportation investments being considered for high-traffic areas. Congestion statistics and cost can be obtained from the Annual Urban Mobility Report prepared by the Texas Transportation Institute (Schrank et al. 2011). FHWA’s Life-Cycle Cost Analysis in Pavement Design (Walls and Smith 1998) includes a rational step-by-step procedure for determining user costs associated with work zones: Work zone is defined in the Highway Capacity Manual (2010) as an area of a highway where maintenance and construction operations impinge on the number of lanes available to traffic or affect the operational characteristics of traffic flowing through the area. . . . In order to analyze work zone user costs, work zone characteristics associated with alternative designs and supporting maintenance and rehabilitation strategies must be defined as part of the devel- opment of alternative [designs]. Figure 11.4. Cash flow diagram.

511 Chapter 11. LiFE-CyCLE COST ANALySiS Work zone characteristics of concern include such factors as work zone length, number and capacity of lanes open, duration of lane closures, timing (e.g., hours of the day, days of the week, season of the year) of lane closures, posted speed, and the availability of and the physical and traffic characteristics of alternative routes. The strategy for maintaining traffic should include any anticipated restrictions on the contractor’s or maintenance force’s hours of operation or ability to establish lane closures. Specific details in an LCCA should include 1. Projected year work zones occur (Years 5, 8, 12, and so forth); 2. Number of days the work zone will be in place (construction period); 3. Specific hours of each day, as well as the days of the week the work zone will be in place; and 4. Work zone length and posted speed. The duration of a work zone (the overall length of time a facility or por- tion of a facility is out of service or traffic is restricted) can range from sporadic daily lane closures for maintenance to several months for bridge-deck replace- ments. [In many cases,] the differential routine maintenance cost between [al- ternatives] tends to be insignificant when compared with initial construction and rehabilitation costs. To a great extent, the same is true of user costs result- ing from routine reactive-type maintenance activities. Routine maintenance work zones tend to be relatively infrequent, of short duration, and outside of peak traffic flow periods. As such, analysts should focus attention on user costs associated with major work zones. User costs are directly dependent on the volume and operating character- istics of the traffic on the facility. Each construction, maintenance, and reha- bilitation activity generally involves some temporary effect on traffic using the facility. The effect can vary from insignificant for minor work zone restrictions on low-volume facilities to highly significant for major lane closures on high- volume facilities. The major traffic characteristics of interest for each year a work zone will be established include 1. The overall projected average annual daily traffic volumes on both the facility and possible alternate routes; 2. The associated 24-hour directional hourly demand distributions; and 3. The vehicle classification distribution of the projected traffic streams.

512 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE On high-volume routes, distinctions between weekday and weekend traffic demand and hourly distributions become important. Seasonal average annual daily traffic distribution also becomes important when work zones are proposed on recreational routes during seasonal peak periods. . . . Once the individual work zones have been identified, each is evaluated separately. This is the point at which individual user cost components are quantified and converted to dollar cost values. A detailed example of the user cost calculation is given in Life-Cycle Cost Analysis in Pavement Design (Walls and Smith 1998). As mentioned in Section 11.2.2.2, the recent pooled-fund study led by the Oregon DOT (Doolen et al. 2011) developed a set of decision-making tools to evaluate the cost- effectiveness of using accelerated bridge construction techniques versus conventional construction. This study incorporated user costs as part of the LCCA comparison. The tools also incorporated an analytical hierarchy process, which is a technique that aids decision makers in prioritizing multiple criteria by using a multilevel hierarchical structure of objectives, criteria, and alternatives. This process considers both quantita- tive and qualitative criteria and quantifies the qualitative trade-offs and relationships between criteria by using a hierarchy of criteria. This analysis of trade-offs was impor- tant for accelerated bridge construction because it quantified various qualitative fac- tors contributing to user costs, such as user delay from a long detour, and could show the economic benefit resulting from reduced construction duration. 11.3.4 Computational Approaches The two approaches used in preparing an LCCA differ dramatically in how they ad- dress the variability and uncertainty associated with various input factors and with the risk associated with the various uncertainties. Often there is some level of possible variability and uncertainty in regard to the values identified for each input parameter. This possible variation can often have significant effects on the LCCA outcome. 11.3.4.1 Deterministic Approach Traditionally in the deterministic approach, input variables are treated as fixed values, as if those values were certain. This approach assigns each LCCA input variable with a fixed (base case) value based on statistics and nonlinear regression of actually occur- ring data or professional judgment. This method does not specifically address the degree of variability or uncertainty with input values. In order to incorporate uncertainty about input values into the analysis, a sensitivity analysis can be performed to see the effect of variation on any one parameter. However, the deterministic approach combined with the sensitivity analysis has two drawbacks. First, it can only be applied to input variables one by one, when the real question of interest is how the variation in several variables simultane- ously can affect the result. Even more importantly, sensitivity analysis alone does not provide any information on the relative likelihood of different outcomes. For example, the sensitivity analysis may suggest that if the initial construction cost is 10% higher

513 Chapter 11. LiFE-CyCLE COST ANALySiS than is assumed in the base case, the corresponding NPV of all costs would be 7% higher than in the base case. However, it will provide no information on whether this scenario is likely to occur. In order to characterize the relative likelihood of various potential outcomes, a stochastic approach should be adopted. 11.3.4.2 Stochastic Approach A stochastic approach (sometimes referred to as a probabilistic approach or risk analy- sis approach) defines the value of input variables by a frequency (probability) distri- bution. For a given project alternative, the uncertain input parameters are identified. Then, for each uncertain parameter, a sampling distribution of possible values is de- veloped. Simulation programming randomly draws values from the stochastic descrip- tion of each input variable and uses these values to compute a forecasted NPV. This sampling process is repeated through thousands of iterations, and through the process, an entire probability distribution of NPVs is generated for the project alternative along with the mean or average NPV for that alternative. The resulting NPV distribution can then be compared with the projected NPVs for alternatives, and the most economical option for implementing the project can be determined for any given risk level. The concept of risk arises from the uncertainty associated with future events and the inability to know what outcomes will result from particular actions taken today. Risk can be objective or subjective. Subjective risk is a person’s perception of the likeli- hood of a particular event; this perception of risk may include the ability to avoid the risk and an assessment of the consequences of a particular outcome. Objective risk, on the other hand, incorporates theory, experiments, observation, and other unbiased information. Ultimately, decision makers who are characterized by different degrees of risk tolerance and whose perception of risk is intrinsically subjective make the deci- sions. However, the goal of risk analysis is to provide the best-unbiased risk estimates to arm the decision makers with the most accurate representation of objective risk. Figure 11.5 depicts the stochastic approach as a whole. Stated succinctly, it reflects uncertainty in input factors (e.g., construction and repair costs and the timing of those activities) in the probability distribution of the results. A description of the specific steps involved in the stochastic approach is provided. 11.3.4.2.1 Develop Structure and Layout of Problem The first step in conducting risk analysis consists of reducing the problem to its most basic elements and describing it in the form of an analytical model. The models for LCCA problems typically include NPV computation, definition of cost categories, and determination of other functional relationships, such as bridge condition curves. Project alternatives are also identified and described. Cash flow diagrams and life-cycle curves are convenient tools to clearly present the project details and the features of alternative implementations. Once the structure of the problem is fully determined, a list of inputs can be devel- oped. An example of input variables for an LCCA project is presented in Table 11.1. For each of the input variables, the general basis used to determine their values is

514 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE established, and a subset of input variables for which a stochastic distribution will be used is specified. 11.3.4.2.2 Develop Input Data The second step in conducting an LCCA is developing probability distributions for the uncertain variables identified in the next step. A probability distribution describes the complete range of values that a variable may assume and weighs the likelihood of its occurrence. Figure 11.6 illustrates some of the most common probability distributions shown in a histogram format: uniform, triangular, and normal distributions. The hori- zontal axis provides a range of all possible values that the variable assumes, and the vertical axis shows the relative frequency weighting of the occurrence of any particular value. For the distributions in Figure 11.6, the probability of a range of values is equal to the area under the curve, and the total area under the curve is equal to one. The choice of a particular distribution depends on the type of input and the amount of data available. A triangular distribution (see Figure 11.6) is the most common dis- tribution used to represent various variables using expert elicitation. Expert opinions are used to determine the minimum, the maximum, and the most likely value, and the triangle is constructed using those three points. This method is most appropriate for modeling such input variables as service life, discount rate, work zone delay, and so forth. Normal distribution is the most common continuous distribution used to repre- sent random variables symmetrically distributed around the mean value. It is usually a good candidate to represent cost-like variables, such as construction cost and main- tenance cost. A normal distribution can either be used to represent the information Probability Distribution of NPV Uncertainty in Construction Costs Uncertainty in Timing Uncertainty in Repair Costs Figure 11.5. Stochastic approach to LCCA.

515 Chapter 11. LiFE-CyCLE COST ANALySiS tABLE 11.1. LccA inPut vAriAbLeS LCCA Component Input Variable Source Initial and future agency costs Preliminary engineering Estimate Construction management Estimate Construction Estimate Maintenance Assumption Timing of costs Bridge deterioration Projection User costs Current traffic Estimate Future traffic Projection Hourly demand Estimate Vehicle distributions Estimate Value of delay time Assumption Work zone configuration Assumption Work zone hours of operation Assumption Work zone duration Assumption Work zone activity years Projection Crash rates Estimate Crash cost rates Assumption Vulnerability costs Flood probability Estimate Flood damage distribution Estimate Earthquake probability Estimate Earthquake damage Estimate Load distribution probability Estimate Load-related structural damage Estimate Other parameters Discount rate Assumption Figure 11.6. Example probability distributions. Figure 11.6. Example probability distributions.

516 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE obtained from the expert elicitation or to use data collected from other sources when the amount of data is sufficiently large. If little information about the input variable is available, a uniform distribution might be used as a rough approximation. Uniform distribution assumes that outside of a certain range, the probability of outcomes drops to zero. Within the range, however, there is no information as to which outcomes are more likely, so it is assumed uniform over that range. Although normal and uniform distributions are symmetric around their mean values, the triangular distribution can be either symmetric or asymmetric. Other types of common asymmetric distributions are exponential and lognormal. When a large amount of hard data is available, the best distribution can be determined by using sta- tistical techniques to establish goodness of fit for each of them. However, when data availability is limited, a triangular distribution can be used as a rough estimate of the distribution shape. Figure 11.7 shows a cumulative probability distribution in ascending order that portrays a cumulative probability of a group of possible events. (Sometimes cumula- tive distributions are shown in descending order, and then the points on the curve show the probability of exceeding a particular value.) For example, there is an 80% probability that the project cost will not exceed $4 million. Each probability distribu- tion has a corresponding cumulative distribution. Cumulative distributions present the data in a form that is easy to interpret for the purposes of risk analysis. 11.3.4.2.3 Develop Probability Distributions When existing data are available, the standard method is to use the data to choose a functional form of a probability distribution that best fits the available data. Many statistical methods and software packages can be used to compare common distribu- tion types with the available data and to determine goodness of fit, that is, to indicate how well a particular probability distribution fits the data. Figure 11.7. Ascending cumulative probability distribution.

517 Chapter 11. LiFE-CyCLE COST ANALySiS However, when sufficient relevant data are not readily available, group inter- views are often used to develop probabilities of uncertain variables. Expert panels are convened to establish the boundaries and general shape of input distributions. The process of eliciting information from experts may include group meetings, individual interviews, and formal surveys and questionnaires. The goal of expert elicitation is to establish the general shape of the input distribution and to determine if there are any interdependencies among input variables. The process of expert elicitation is shown on Figure 11.8. 11.3.4.2.4 Perform Simulations The next step in the LCCA process involving risk analysis is to run a computer simu- lation of the model in order to obtain results. The process of using random numbers to sample from a probability distribution is known as Monte Carlo sampling. In the Monte Carlo simulation process, a series of random numbers is generated by the com- puter along the cumulative probability scale of input distribution (see Figure 11.7). Values corresponding to each random number are sampled along the x-scale. The sam- pled value for one input is then combined with sampled values for all other inputs to compute the single result. This process is repeated hundreds or thousands of times to generate a cumulative distribution of the outcomes. The stopping rule involves either a prespecified number of iterations or a convergence rule, which reflects the situation in which additional iterations do not significantly affect the distribution of the results. Monte Carlo simulations require a large number of iterations to assure that values with low probabilities are sufficiently sampled and represented in the results. Such sampling is especially important when the input distributions are highly unsymmetric. When the number of iterations is insufficient, the low-probability outcomes may be underepresented and not adequately accounted for in simulations. This is especially significant when a low-probability outcome can have a particularly strong effect on the results. To avoid such problems, different sampling methods can be employed. For example, Latin hypercube sampling uses special techniques to generate samples from all probability ranges with a relatively low total number of iterations. Expert Opinion Elicitation Fr eq ue nc y Model Parameter Figure 11.8. Using expert opinion to develop probability distributions. Figure 11.8. Using expert opinion to develop a probability distribution.

518 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE 11.3.4.2.5 Interpret Results The final step in the risk analysis is the interpretation of the results. If the analysis uses the traditional deterministic approach, the only data available to decision makers would be the means of the output distributions for the alternatives investigated. Based on the comparisons of the means (50% probability), the difference between Alterna- tive 1 and Alternative 2 in Figure 11.9 is small and may be assumed to be negligible. The risk analysis allows one to evaluate a much more nuanced picture. When inter- preting the risk profile in Figure 11.9, it is important to distinguish the upside risk from the downside risk. Downside risk for project costs implies a cost overrun, a chance that the costs will be much higher than anticipated. In contrast, the upside risk presents an opportunity for low cost, a cost underrun. From Figure 11.9, it can be seen that Alternative 1 has a greater upside risk than Alternative 2; in other words, it has a better chance that the cost will be very low. At the same time, Alternative 1 is a preferred choice because it reduces the downside risk of cost overruns. Another con- sideration is to compare the two alternatives at the 80% cumulative probability level. Alternative 1 is about $100,000, and Alternative 2 is $130,000. Although the means have a negligible risk difference, Alternative 1 exhibits a far smaller financial risk. As a part of the risk assessment, a sensitivity analysis of simulation results can be performed to identify the key input variables that have the most influence on the output distributions. Typically, this analysis is done by computing the degree of cor- relation between inputs and outputs: the higher the degree of correlation, the more significant a particular input variable is for determining the results. Figure 11.9. Cumulative risk profile of NPV for Alternatives 1 and 2. Alternative 1 Alternative 2

519 Chapter 11. LiFE-CyCLE COST ANALySiS From the perspective of most transportation agencies, the application of stochastic LCCA is relatively new. Stochastic LCCA has become more practical as a result of the dramatic increases in computer data-processing capabilities. Simulating and account- ing for simultaneous changes in LCCA input parameters can now be accomplished easily and quickly and provides invaluable information for making informed decisions. 11.3.5 LCCA Analysis tools 11.3.5.1 Simplified LCCA Applications Various tools and software are available for determining LCCA. All steps of a simpli- fied deterministic LCCA can be performed using generic spreadsheet software such as Microsoft Excel. Several commercial programs are available for conducting a stochastic or risk- based LCCA. These microcomputer-based risk and analysis software programs are either spreadsheet based or work as add-ons to other generic spreadsheet software. These tools incorporate Monte Carlo simulation capabilities for stochastic analyses. Two common applications are presented in Table 11.2. In using simple generic spreadsheets, the economic life-cycle analysis model has to be programmed into the spreadsheet, and other considerations such as incorporating user costs also must be computed separately. However, the user has much more control over the process and how data are used and presented. For simple applications, generic spreadsheet solutions are common and easily applied. 11.3.5.2 Comprehensive LCCA Applications Specialized comprehensive software tools for performing LCCAs have recently been developed by federal agencies and are available from government public websites. The available software tools described are capable of calculating comprehensive life-cycle costs including agency, user, operations and maintenance, disposal, and remaining ser- vice life costs. They are also capable of performing both deterministic and stochastic analyses. tABLE 11.2. riSk-bASed LccA SoFtwAre Software Name Producer @Risk Palisade Corporation www.palisade.com Oracle Crystal Ball Decisioneering Corporation www.decisioneering.com

520 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE 11.3.5.2.1 BridgeLCC Software from the National Institute of Standards and Technology BridgeLCC 2.0 is comprehensive LCCA software developed by the National Insti- tute of Standards and Technology (NIST) to help bridge designers determine the cost- effectiveness of alternative bridge designs, construction and repair strategies, and construction materials (Ehlen 2003). The software uses a life-cycle costing methodol- ogy based on the ASTM E917 standard practice for life-cycle costing and a cost classi- fication scheme developed by NIST (Ehlen 2003). This software is specifically tailored to highway bridges. BridgeLCC 2.0 can segregate costs by bearer (agency, user, and third party), by timing (initial construction; operations, maintenance, and repair; and disposal), and by component (deck, superstructure, substructure, other, nonelemental, and new technology introduction). The program also includes advanced features such as cal- culation of user delay and cost, has capabilities for both deterministic and stochastic analyses, and includes sensitivity analysis and risk analysis using Monte Carlo simula- tion (Ehlen 2003). 11.3.5.2.2 RealCost LCCA Software RealCost was developed by FHWA to support the application of LCCA in the pave- ment project-level decision-making process (FHWA 2004). RealCost automates FHWA’s LCCA methodology as it applies to pavements. Work is being considered to make it applicable to bridges, but currently, bridges have not been included in this document. The software calculates life-cycle values for both agency and user costs associated with construction and rehabilitation. The software can perform both deterministic and stochastic modeling (Monte Carlo simulation) and can also include user costs. Outputs are provided in tabular and graphic format. RealCost is an add-in for Microsoft Excel providing a graphical user interface that facilitates the creation of an Excel Workbook containing the input data and results of the LCCA. RealCost can only evaluate two alternatives at a time.

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TRB’s second Strategic Highway Research Program (SHRP 2) Report S2-R19A-RW-2: Design Guide for Bridges for Service Life provides information and defines procedures to systematically design new and existing bridges for service life and durability.

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