Performance Measures and LCCA

1. Performance Measures and LCCA

2. Performance Measures • Performance is the “degree to which a facility serves its users and fulfills the purpose for which it was built or acquired as measured by accumulated quality and length of service it provides to users” (Hudson et al., 1997) • Ability to give satisfactory service

3. Needs of Performance Measures • Performance measures used as tools to: • Support management decisions • Diagnose, rank, and monitor potential problems • Signal suppliers and users • Allocate resources • Track data in information systems • Needs/expectations change over time; therefore, we need a framework for consistency • Different parties have different views; thus they care about different indicators

4. Limitations in Assembling Performance Information • Data are collected by multiple/different agencies • Data that are collected tend to differ in collection method and context • Type of data • Reliability/Precision • Spatial/temporal frequency • Consistency is variable

5. Approaches to Performance • Condition Assessment • Condition Indices • Reliability Theory • Multi-dimensional Measures

6. Condition Assessment • Measure type, severity, extent of deterioration • Specific examples or indicators of deterioration used • Subjective ratings • Visual evaluation • Destructive and non-destructive testing • Direct measurement

7. Examples • Pavement - total length of cracks per lane mile, roughness, deflection • Bridge decks - chloride content • Pipeline - breaks per mile • Roof - square feet of wet insulation

8. Subjective Ratings • Predefined, arbitrary scale • Requires training to minimize errors and discrepancies across inspectors • Ex: Present Serviceability Rating (PSR) AASHO Road Test: Bad = 0, Good = 5 AASHO: American Association of State Highway Officials

9. Example of Deterioration Curves (LCCA primer, 2002)

10. Inspection Data Collection Example: Bridge Maintenance Management Condition Assessment (Deterioration Level) Condition Prediction Model Long-term Maintenance Planning Maintenance Action Decisions Itoh, Y., Hammad, A., and Liu, C. (1997). Network-Level Bridge Lifecycle Management System. Journal of Infrastructure Engineering, ASCE, Vol. 3, No. 1, pp.31-39.

11. Inspection Data Condition Assessment (Deterioration Degree) Like new 0.0-0.2 Condition Assessment of RC Bridge Decks Minor deterioration 0.2-0.4 Cracks in one direction Aggravating deterioration 0.4-0.6 Cracks in two directions Obvious deterioration 0.6-0.8 Honeycomb cracks Potentially hazardous 0.8-1.0 Concrete spalling

12. Routine Maintenance Replacement Rehabilitation Repair Routine Maintenance Replacement Repair Rehabilitation Deterioration Degree 1 Selecting Maintenance Methods Deterioration curve 0.8 0.6 0.4 0.2 0 Service Age

13. Initial deterioration degree Piecewise linear deterioration model Maintenance Plan Maintenance actions Maintenance cost Deterioration degree Objective function Penalty cost Optimal maintenance plan

14. 25 30 35 40 45 1.0 0.8 0.6 0.8 0.4 0.2 0.0 0 5 10 15 20 25 0 5 10 15 20 25 Routine maintenance Repair Rehabilitation Optimization results (25 years) 1st ($ 47 m) Replacement Comparing Three Budget Policies at the Bridge Level Optimization results (5 cycles of 5 years) Service Age 2st ($ 54 m) 3st ($ 75 m) Conventional strategy Deterioration Degree Planning Year Planning Year

15. 1.0 0.8 0.6 0.4 0.8 0.2 0.0 0 5 10 15 20 25 0 5 10 15 20 25 Optimization results (25 years) Average Deterioration Degree 1st ($ 47 m) Comparing Three Budget Policies at the Network Level Optimization results (5 cycles of 5 years) 2st ($ 54 m) 3st ($ 75 m) Conventional strategy Planning Year Planning Year

16. Testing • Destructive: Requires actual invasive test (or removal) of infrastructure to be compared with reference samples • E.g. cores for density, chemical content • Bending/Breaking trusses • Non-Destructive Testing (NDT): uses technology and sensors to give similar results (e.g. Ground-penetrating radar to detect cracks/defects)

17. Condition Indices • Developed to address multitude of condition measures • Based on amount of distress or damage, results from non-destructive tests, relationships between use conditions • Condenses ‘vector’ of data into one ‘scalar’ value

18. Index Requirements • Completeness - covers all aspects of deterioration • Measurable - to ensure consistency and repeatability • Relevance - provides rational quantification of condition • Example: Building Condition Index BCI = Total Deferred Maintenance / Replacement Value • Excellent: BCI < 2% • Good: 2% < BCI < 5% • Adequate: 5%< BCI < 10% • … • Fail BCI > 60%

19. Condition Index Limitations • Tries to make performance into one value • Hard to choose right aggregation • May be hard to integrate technology • Anything outside index not included

20. Reliability Theory • Based on probability of failure • Widely used in high tech industries • Can minimize costs while maximizing reliability

21. Reliability-Based Management • From Frangopol (2001) paper * • Funds are scarce, therefore, there is a need for a better method • Have been focused on “condition-based” • Unclear which method might be cheaper • Bridge failure led to condition assessment/NBI methods • Which emphasized need for 4R’s ** • Eventually money got more scarce • Bridge Management Systems (BMS) born • PONTIS, BRIDGIT, etc. • Use deterioration and performance as inputs into economic efficiency measures * Frangopol et al. (2001). Reliability-Based Life-Cycle Management of Highway Bridges, Journal of Computing in Civil Engineering, Vol. 15, No. 1, January 2001, pp. 27-34. ** Repair, rehabilitation, replacement, reconstruction

22. Current BMS Features • Elements characterized by discrete condition states noting deterioration • Markov model predicts probability of state transitions (e.g. good-bad-poor) • Deterioration is a single step function • Transition probabilities are not time variant

23. Reliability Assessment • Decisions are made with uncertainty • Should be part of the decision model • Uses consideration of states, distribution functions, Monte Carlo simulation to track life-cycle safety and reliability for infrastructure projects • Reliability index b used to measure safety • Excellent: State 5, b >= 9, etc. • No guarantee that new bridge is in State 5! • In absence of maintenance, just a linear, decreasing function

24. Reliability-Based Life-Cycle Management of Highway Bridges Uncertainties during lifecycle processes Bridge reliability profile without maintenance and reliability states Frangopol et al. (2001)

25. Reliability (cont.) • Variables are all given probability distribution functions, e.g. • Initial performance, time to damage, deterioration rate without maintenance, time of first rehabilitation, improvement due to maintenance, etc. • Uses Monte Carlo simulation and existing bridge data to estimate effects • Reliability-based method could have significant effect on LCC (savings).

26. Markov Processes • Markov chain - a stochastic process with what is called the Markov property • Discrete and continuous versions • Discrete: consists of sequence X1,X2,X3,.... of random variables in a "state space", with Xn being "the state of the system at time n". • Markov property - conditional distribution of the "future" Xn+1, Xn+2, Xn+3, .... given the "past” (X1,X2,X3,...Xn), depends on the past only through Xn. • i.e. ‘no memory’ of how Xn was reached

27. Markov Processes (cont.) • i.e., knowledge of the most recent past state of the system renders knowledge of less recent history irrelevant. • Markov chain may be identified with its matrix of "transition probabilities", often called the transition matrix (T) . • Entries in T given by pij =P(Xn+1 = j | Xn = i ) • pij : probability that system in state j "tomorrow" given that it is in state i "today". • ij entry in the k th power of the matrix of transition probabilities is the conditional probability that k "days" in the future the system will be in state j, given that it is in state i "today".

28. Example: Predicting the weather • The probabilities of weather conditions, given the weather on the preceding day, can be represented by a transition matrix: • The matrix P represents the weather model in which a sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. The columns can be labeled "sunny" and "rainy" respectively, and the rows can be labeled in the same order. • (P)i j is the probability that, if a given day is of type i, it will be followed by a day of type j. • Notice that the rows of P sum to 1 • The weather on day 0 is known to be sunny. This is represented by a vector in which the "sunny" entry is 100%, and the "rainy" entry is 0%: • The weather on day 1 can be predicted by: • Thus, there is an 90% chance that day 1 will also be sunny. • The weather on day 2 can be predicted in the same way: • Or • General rules for day n are: http://en.wikipedia.org/wiki/Examples_of_Markov_chains

29. Sample Transition Matrix ] [ • pii suggests probability of staying in same state, 1- pii probability of getting worse • Could ‘simplify’ this type of model by just describing vector P of pii probabilities • (1 - pii) values are easily calculated from P • Condition distribution of bridge originally in state i after M transitions is CiTM T =

30. Infrastructure Application • Used to predict/estimate transitions in states, e.g. for bridge conditions • Used by Bridge Management Systems, e.g. PONTIS, to help see ‘portfolio effects’ of assets under control • Helps plan expenditures/effort/etc. • Need empirical studies to derive parameters * Chase and Gaspar, Journal of Bridge Engineering, November 2000.

31. Superstructure Condition • NBI instructions: • Code 9 = Excellent • Code 0 = Failed/out of service • If we assume no rehab/repair effects, then bridges ‘only get worse over time’ • Thus transitions only go from Code i to Code i-1 • Need 10x10 matrix T • Just an extension of the 5x5 example above

32. Empirical Results • P = [0.66, 0.71, 0.95, 0.96, 0.97, 0.97, 0.97, 0.93, 0.86, 1] • Could use this kind of probabilistic model result to estimate actual transitions

33. Life Cycle Costing Analysis (LCCA) • Is a tool to assist decision makers in managing ‘total costs’ of projects • Includes design, construction, 4R’s (repair, rehabilitation, replacement, reconstruction), user costs, disposal • Converted into ‘present value’ costs • Generally an “economic-only” (costs only) framework

34. LCCA Background • ISTEA (1991) suggested LCCA for pavement, bridge, tunnel projects • FHWA in 1996 linked funds availability to use of LCC in major projects • Different from Benefit-Cost Analysis ISTEA: Intermodal Surface Transportation Efficiency Act

35. Initial Costs • Usually site preparation and construction • Should consider ‘user costs’ (traffic, etc) • Where to get data: • From current/completed projects similar in design/scope

36. 4R’s and Salvage Costs • Are dependent on technology and materials choices • E.g. depth of pavement affects useful life • Should not exclude costs that seem ‘too small’ • Salvage - potential value of materials at end-of-life (e.g. scrap steel, asphalt, etc.)

37. Examples (No User Costs) Discount rate: r=4% Project B: • Construction $350k • Prevent. Maint. @ Yr 8 $40k • Major Rehab @ Yr 15 $300k • Prevent. Maint. @ Yr 20 $40k • Prevent. Maint. @ Yr 25 $60k • Salvage@ 30 -$105k • PV $554k • Project A: • Construction $500k • Prevent. Maint. @ Yr 15 $40k • Major Rehab @ Yr 20 $300k • Salvage@ 30 -$150k • PV $612k

38. User (Delay) Costs • Consideration of opportunity cost of time for drivers when inconvenienced due to infrastructure downtime • E.g. congestion, re-routing around road • Should also consider vehicle operating delay cost (fuel, etc). • A cost/vehicle-hour estimate used • $12/ $25 for cars/big trucks

39. Developing Guidelines User Costs are calculated through a capacity analysis. • Traffic grows over time • Queuing cost • Hourly distributions • $ Value of time has a major influence • VOC (Vehicle Operating Cost) between alternatives negligible

40. Developing Guidelines Passenger Vehicle $10 - $13 Single Unit Truck $17 - $19 Combo Truck $21 - $24 Value of Time Recommendations: 1996 Dollars

41. FHWA LCCA Methodology • Steps • Establish Design Alternatives • Determine Activity Timing • Estimate Agency and User Costs • Compute Life-Cycle Costs • Analyze the Results

42. EXPENDITURE STREAM DIAGRAM, SHOWING ACTIVITIES, COSTS, AND TIMING

43. Example of Deterministic LCCA

44. Probabilistic Approach - Captures the uncertainty in the inputs - Carries that uncertainty through the computation process to generate probability distribution of result (a range of possible outcomes along with their likelihood of occurrence).

45. Results Net Present Value $ % Simulation Modeling Inputs M O D E L

46. LCCA Results • Deterministic Approach Project cost estimate is $12 million • Probabilistic Approach • 75 % chance the project will cost less than $12M

47. Role of Probability in LCCA • Accounting for variability in inputs: • Activity timing, costs, discount rate • Quantitatively determines risk in alternative strategy selection • Elevates the decision from questioning the inputs to discussing the merits of each alternative

48. Agency PV B Frequency A Present Value

49. Advantages of Probabilistic Approach • More Informed Decisions • Evaluate all possible outcomes • Expose areas of uncertainty (Quantify risk) • Determine significance of difference between alternatives • Examine influence of underlying variables on final results • Provide those vested with appropriate authority the opportunity to make decisions about risk taking