Maintenance: definition

Transcription

1

2 Maintenance: definition Group of technical, administrative and managerial actions during one component s life cycle, intended to keep or re-establish it into a state which allows it to carry out the required functions [EN13306] Robotics Realization Preventive Maintenance Corrective Surveillance and control approaches Scheduled On Condition UPSTREAM ACTIVITIES - Management - Programs, Preparation - Logistics support management - Organisation, tasks monitoring - Budgetary control - Administration «Maintenance» expertise DOWNSTREAM ACTIVITIES - Experience follow-up - Indicators - Diagnostic maintenance - Benchmarking - Improvement process -

3 Strategy setting Maintenance Management Process Strategy Definition conditions the success of maintenance in an organization, determines the effectiveness of the subsequent implementation Strategy Implementation allow us to minimize the maintenance direct cost, determines the efficiency of our management

4 Strategy setting Maintenance Management Process Strategy Definition conditions the success of maintenance in an organization, determines the effectiveness of the subsequent implementation doing the right thing Strategy Implementation allow us to minimize the maintenance direct cost, determines the efficiency of our management

5 Strategy setting Maintenance Management Process Strategy Definition conditions the success of maintenance in an organization, determines the effectiveness of the subsequent implementation doing the right thing Strategy Implementation allow us to minimize the maintenance direct cost, determines the efficiency of our management doing the (right) thing right

6 Maintenance Decision-Making Strategies: the issue Industrial systems are made up of various components, equipment and structures characterized by: different reliability different failure mechanisms different impacts on the cost of operation different impacts on the safety of the equipment, operators and public Each equipment needs to have a maintenance approach that is appropriate to its characteristics and to the consequences of its failure. A decision must be taken on the maintenance strategy, which defines the components of a system that will have a corrective, scheduled or conditionbased maintenance and will further specify the details of each of this type of approaches

7 What to take into account, for every component? Component Legislation Company s quality policy Manufacturer indications Maintenance experience Job priority analysis Criticality analysis Mathematical models Work instruction description Required disciplines Required working hours and spare list Eventual priorities Unplanned Periodic Condition-based Predictive

8 Maintenance Strategy Two common approaches for defining a maintenance strategy Reliability-Centred Maintenance (RCM) Risk-Based Maintenance (RBM)

9 Maintenance Strategy Two common approaches for defining a maintenance strategy Reliability-Centred Maintenance (RCM) Risk-Based Maintenance (RBM)

10 Risk-Based Maintenance (RBM) BASIC IDEA: Risk is the criterion for the basis of maintenance planning. OBJECTIVE: reduce the overall risk that may result as the consequence of unexpected failures of operating facilities. METHOD: Identify all the failure scenarios Determine the associated risk Prioritize the failure scenarios according to the associated risk Develop a maintenance strategy that minimizes the occurrence of the high-risk failure scenarios: EXPECTED RESULTS: high-risk components will be inspected with greater frequency and maintained in a more thorough manner, so that the overall operation of the system achieves tolerable risk criteria.

11 The Concept of Risk Environment Hazard People

12 The Concept of Risk Safeguards Environment Hazard People

13 The Concept of Risk UNCERTAINTY Safeguards Environment Hazard People

14 Risk Analysis: scenario Hazard Analysis Hazop FMEA Qualitative RAM analyses Accident Scenarios Identification 1. What undesired conditions may occur? Accident Scenario, S

15 Risk Analysis: probability Uncertainty Representation: (probabilistic & nonprobabilistic frameworks) Uncertainty Propagation (advanced and hybrid MC methods) Multi-state degradation models Dynamic behaviors Influencing Factors Hazard Analysis Hazop FMEA FTA ETA Markov Models Petri Net Bayesian Networks Qualitative RAM analyses Quantitative RAM analyses Accident Scenarios Identification Failure Probabilty Assessment 1. What undesired conditions may occur? Accident Scenario, S 2. With what probability do they occur? Probability, p

16 Risk Analysis: consequence Uncertainty Representation: (probabilistic & nonprobabilistic frameworks) Uncertainty Propagation (advanced and hybrid MC methods) Multi-state degradation models Dynamic behaviors Influencing Factors Hazard Analysis Hazop FMEA FTA ETA Markov Models Petri Net Bayesian Networks Qualitative RAM analyses Quantitative RAM analyses Accident Scenarios Identification International Standards Transport Model Fire& Explosion models ABM for Emergent phenomena Best Practices & Lessons Learnt Resilience and Vulnerability analysis Failure Probabilty Assessment 1. What undesired conditions may occur? Accident Scenario, S 2. With what probability do they occur? Probability, p Evaluation of the consequences 3. What damage do they cause? Consequence, x

17 Risk Analysis: evaluation Uncertainty Representation: (probabilistic & nonprobabilistic frameworks) Uncertainty Propagation (advanced and hybrid MC methods) Multi-state degradation models Dynamic behaviors Influencing Factors Hazard Analysis Hazop FMEA FTA ETA Markov Models Petri Net Bayesian Networks Qualitative RAM analyses Quantitative RAM analyses Accident Scenarios Identification International Standards Transport Model Fire& Explosion models ABM for Emergent phenomena Best Practices & Lessons Learnt Resilience and Vulnerability analysis RISK = {S i, p i, x i } Failure Probabilty Assessment p/x A B C D Evaluation of the consequences

18 Maintenance Design Risk Analysis: evaluation Uncertainty Representation: (probabilistic & nonprobabilistic frameworks) Uncertainty Propagation (advanced and hybrid MC methods) Multi-state degradation models Dynamic behaviors Influencing Factors Hazard Analysis Hazop FMEA FTA ETA Markov Models Petri Net Bayesian Networks Qualitative RAM analyses Quantitative RAM analyses Accident Scenarios Identification International Standards Transport Model Fire& Explosion models ABM for Emergent phenomena Best Practices & Lessons Learnt Resilience and Vulnerability analysis Failure Probabilty Assessment Evaluation of the consequences PHM Inspections FRACAS/RCA Risk mitigation Redundancies Reliable components

19 Maintenance Design Risk Analysis: evaluation Uncertainty Representation: (probabilistic & nonprobabilistic frameworks) Uncertainty Propagation (advanced and hybrid MC methods) Multi-state degradation models Dynamic behaviors Influencing Factors Hazard Analysis Hazop FMEA FTA ETA Markov Models Petri Net Bayesian Networks Qualitative RAM analyses Quantitative RAM analyses Accident Scenarios Identification International Standards Transport Model Fire& Explosion models ABM for Emergent phenomena Best Practices & Lessons Learnt Resilience and Vulnerability analysis Failure Probabilty Assessment Evaluation of the consequences PHM How to cost-effectively reduce the asset risk? Inspections FRACAS/RCA Risk mitigation Redundancies Reliable components

20 Risk-Based Maintenance: techniques 1. Risk Assessment 2. Maintenance planning based on risk: Maintenance should be planned so as to lower the risk to meet the acceptable criterion by reducing the probability of failures and their consequences Typical approaches for decision-making used are: - the Reverse Fault Tree Analysis (RFTA): assign the desired probability of the top event (failure scenario) such to satisfy the acceptable risk criterion; compute the corresponding new probabilities of the basic events (failure modes) and from these infer the corresponding maintenance intervals; - the Analytic Hierarchy Process (AHP): identify the risk factors affecting the failure scenario; pairwise compare their importance in contributing to the failure scenario; derive the risk factors likelihoods; combine the risk factors likelihoods to compute the probability of failure; prioritize components and plan maintenance interventions based on the risk factors likelihood contributions and related insights.

21 Reverse Fault Tree Analysis 21

22 Example: CANDU airlock system The Airlock System (AS) prevents the dispersion of contaminants by keeping the pressure of the inside of the reactor vault lower than the outside pressure. 1 Basic Failure Events Pressure equalizer valve failure ID Code V1 2 Doors failure D1 3 Seal failure S1 4 Gearbox failure G1 5 Minor pipe leakages P1 6 Major pipe leakages P2 7 Exhaust pipe failure E1 8 Empty tank T1 9 Tank failure T2 Lee A., Lu L., Petri Net Modeling for Probabilistic Safety Assessment and its Application in the Air Lock System of a CANDU Nuclear Power Plant, Procedia Engineering, 2012 International Symposium on Safety Science and Technology, Volume 25, pp.11-20, 2012.

23 Fault Tree Model Top event = AS fails to maintain the pressure boundary. FT developed for analyzing a scenario of a Design Basis Accident occurred in the AS of a CANDU Nuclear Power Plant in Objective: Reduce the Top Event probability to make the risk acceptable Decision Problem: how?

24 Traditional RFTA Approach Application of Risk Importance Measures (RIMs), which aim at quantifying the contribution of components or basic events to the system risk Example: Risk Reduction Worth (RRW) is the maximum decrease in risk consequent to an improvement of the component associated with the basic failure event considered RRW Door = P(Air Lock Failure) P(Air Lock failure Door working)

25 Traditional RFTA Approach Application of Risk Importance Measures (RIMs), which aim at quantifying the contribution of components or basic events to the system risk Example: Risk Reduction Worth (RRW) is the maximum decrease in risk consequent to an improvement of the component associated with the basic failure event considered Approach (Iterative): Calculate component RRW values Rank component importance values Apply one of the possible actions on the most important basic event

26 Traditional RFTA Approach Application of Risk Importance Measures (RIMs), which aim at quantifying the contribution of components or basic events to the system risk Example: Risk Reduction Worth (RRW) is the maximum decrease in risk consequent to an improvement of the component associated with the basic failure event considered Approach (Iterative): Calculate component RRW values Rank component importance values Drawback: the procedure does not necessarily lead to the global optimal solution Apply one of the possible actions on the most important basic event

27 Portfolio Optimization for RBM Objectives Develop methods for identifying combinations (portfolios) of risk management actions to minimize residual risks at different cost levels of risk management cost Account for risk, cost of risk management and resource constraints simultaneously Apply and evaluate methods to nuclear and other safety critical systems Challenges Develop computationally tractable approaches for large systems Using incomplete information when reliable parameter estimates are not available 27

28 Our methodology Methodology steps: 1. Failure scenario modeling 2. Definition of failure probabilities 3. Specification of actions 4. Optimization model 28

29 Step 1: Failure scenario modeling To analyze the failure scenarios, the Fault Tree is mapped into a Bayesian Belief Network. Reference: Khakzad N., Khan F., Amyotte P., Dynamic safety analysis of process systems by mapping bow-tie into Bayesian network, Process Safety and Environmental Protection 91 (1-2), pp (2013). 29

30 Step 1: Airlock system failure modeling Advantages of BBN Multi-state modeling Multi-state description of pipe leakage event 30

31 Step 1: Airlock system failure modeling Advantages of BBN Multi-state modeling Extension of concepts of AND/OR gates Example: AND gate

32 Step 2: Definition of failure probabilities Information sources Information provided by AND/OR gates in FT Statistical analyses Expert elicitation The probability of occurrence of the events is defined according to their role in the failure scenarios. Specifically: Initiating events failure probabilities of system components; Intermediate and top events conditional probability tables. 32

33 Step 3: Specification of actions Action characteristics: Impact on the prior and conditional probabilities; Action a modify the probability of occurrence of the states s of event i. P i (s) P a i (s) s s

34 Step 2 and 3: Definition of failure probabilities Valve failure Action RRR Calibration test a Sensor a P 2 a1 s = 1 = P 2 a2 s = 1 = Risk Reduction Rate (RRR)

35 Step 3: Specification of actions Action characteristics: Impact on the prior and conditional probabilities; Entail a cost (capital investment costs and ordinary periodic expenses over the life-time). To consider this, we relay on the annualized cost at year Λ (time horizon): r= discounted rate, λ=year number

36 Action Parameters Synergic effect: selection of both actions cost saving and risk reduction extra-benefit 36

37 Actions Parameters Synergic effect: if we act on both seal and pipe, we gain a cost saving 37

38 Step 4: Optimization model Implicit enumeration algorithm to identify the optimal portfolios of safety actions. The resulting portfolios are globally optimal in the sense that minimize the failure risk of critical events, instead of selecting actions that target the riskiness of the single events. Risk acceptability Budget constraints Action feasibility Action portfolio #1 Action portfolio #2 Action portfolio #3 Action portfolio #4 Action portfolio #5 Action portfolio #6 Action portfolio #7 Action portfolio #8 Action portfolio #9 Action portfolio #10 Action portfolio #11 Action portfolio #12 Select the optimal action portfolio

39 Step 4: Optimization model results Airlock failure probability for the optimal portfolio of actions for different budget levels. Greater budget more effective actions lower residual risk of failure of the airlock system.

40 Step 4: Optimization model results

41 Step 4: Optimization model results

42 Step 4: Optimization model results

43 Step 4: Optimization model results

44 Application of RRW approach The application of this approach leads to the following issues Iteration Most risky event Issue t = 1 t = 2 Valve failure Tank failure There are two possible actions, so which one should the experts select? The only applicable action is very expensive, could it be that many inexpensive actions have a higher impact on risk reduction? t = 3 Valve failure Door failure In case of a limited budget, which component should be improved first? t = 4 Valve failure If the experts apply a second action, do the joined actions have the same characteristics as two separate actions?

45 Final Comparison If we are given Budget B=350K, then we get the following results: 45

46 Application of Risk Importance Measures (RIMs) Limitations of using RIM for RFTA in RBM: Actions can be applied to initiating events only not accounting for synergies of joined actions. They do not account for feasibility and budget constraints. They do not necessarily lead to the global optimal portfolio of actions because the procedure implies assumptions and expert opinions which strongly affect the decisions at the following iterations. They cannot be applied in case of multi-state and multiobjective failure scenarios they account for a unique critical event.

47 Application of AHP to RBM 47

48 AHP: What is it? A multiple criteria decision-making technique, which allows to reduce complex decisions to a series of simple comparisons and rankings It is used in RBM applications to prioritize components and plan maintenance interventions based on the risk factors likelihood and consequence contributions, and related insights 48

49 AHP: Method Phase 1: formulate the decision problem in the form of a hierarchical structure. The decomposition of the decision criteria proceeds until further refinements are not needed. Top level: overall objective of the decision problem Intermediate levels: elements affecting the decision Lowest level: decision options 49

50 Example Crude oil pipeline (1500 km) in the western part of India. The entire pipeline is classified into a few (in this case 5) stretches (i.e., pipeline sections in between two stations). A risk structure model is built in the Analytic Hierarchy Process (AHP) framework. P.K. Dey, A risk-based maintenance model for inspection and maintenance of cross-country petroleum pipeline, J. Qual. Maint. Eng. 7 (1) (2001),

51 AHP: Method Phase 1: formulate the decision problem in the form of a hierarchical structure. The decomposition of the decision criteria proceeds until further refinements are not needed. Phase 2: determine the relative importance of the elements in each level of the hierarchy through a pair-wise comparison. Each element in an upper level of the hierarchical tree is used as criterion to compare the elements in the level immediately below. Intensity of Importance Definition Explanation how many times more important or dominant an element is over another 1 Equal Importance Two activities contribute equally to the objective 3 Moderate importance Experience and judgment slightly favor one activity over another 5 Strong importance Experience and judgment strongly favor one activity over another 7 Very strong or demonstrated importance An activity is favored very strongly over another; its dominance demonstrated in practice 9 Extreme importance The evidence favoring one activity over another is of the highest possible order of affirmation 2,4,6,8 For compromise between the above values Sometimes one needs to interpolate a compromise judgment numerically because there is no good word to describe it. 51

52 Example Pairwise comparisons of risk factors Each number represents the expert s view about the dominance of the element in the column on the left over the element in the row on top. Slightly favours of Corrosion over external interference Dominance of corrosion over Acts of God demonstrated in practice 52

53 AHP: Method Phase 1: formulate the decision problem in the form of a hierarchical structure. The decomposition of the decision criteria proceeds until further refinements are not needed. Phase 2: determine the relative importance of the elements in each level of the hierarchy through a pair-wise comparison. Each element in an upper level of the hierarchical tree is used as criterion to compare the elements in the level immediately below. Phase 3: compute the relative weights of the factors (mathematical procedure based on eigenvectors computation) 53

54 Example Preference Weight 54

55 AHP: Method Phase 1: formulate the decision problem in the form of a hierarchical structure. The decomposition of the decision criteria proceeds until further refinements are not needed. Phase 2: determine the relative importance of the elements in each level of the hierarchy through a pair-wise comparison. Each element in an upper level of the hierarchical tree is used as criterion to compare the elements in the level immediately below. Phase 3: compute the relative weights of the factors (mathematical procedure based on eigenvectors computation) Phase 4: compute the relative weights of the alternatives with respect to the leaves of the tree Phase 5: find the composite weights of the decision alternatives by aggregating the weights through hierarchy. 55

56 Example Final weights Final ranking 56

57 Methodology drawback AHP limitations: the rank reversal phenomenon (i.e., the relative ranking of two alternatives may change when a new alternative is introduced) Shortcomings of the 1-9 ratio scale Pitfalls in quantification of qualitatively stated pairwise comparisons Not applicable in case of a large number of alternatives Uncertainty is not accounted The AHP-based RBM methodology does not tackle the problem of how to optimize the inspection campaign 57

58 The objective Develop a methodology to select portfolios of maintenance inspections to optimally allocate resources to minimize costs and maximize the benefit of maintenance on risk reduction Accomodate imprecision of expert judgments 58

59 Proposed method Failure likelihood and severity assessment criticality ranking of items Item-specific maintenance optimization item s condition-specific rule to select maintenance option Maintenance portfolio optimization proposal for maintenance resources allocation 59

60 Proposed method Failure likelihood and severity assessment criticality ranking of items Item-specific maintenance optimization item s condition-specific rule to select maintenance option Maintenance portfolio optimization proposal for maintenance resources allocation 60

61 Multi Attribute Value Theory Likelihood Pipe Features Past Events Local Circumstances Material Pipe Age Diameter Step 1: Value tree Blockages Flushing Soil Traffic Load Operational losses Item repair cost Cost to externals 61

62 Multi Attribute Value Theory Likelihood Pipe Features Past Events Local Circumstances Material Pipe Age Diameter Blockages Flushing Soil Traffic Load Step 1: Value tree Step 2: Score elicitation for leaf attributes (SWING Method) v i x i j = [v i x j i ; v i (x j i ) ൧ i=leaf attribute x i j =score of pipe j with respect to attribute i 62

63 Score Example Elicited Expert Preferences «The installation year before 1955 has the maximum influence on Pipe features» «If the installation year is 1985, its influence on Pipe Features is between 40 and 80% of that of 1955» Pipe age 63

64 Multi Attribute Value Theory Likelihood Pipe Features Past Events Local Circumstances Material Pipe Age Diameter Blockages Flushing Soil Traffic Load Step 1: Value tree Step 2: Score elicitation for leaf attributes (SWING Method) Step 3: Criteria relative importance (PAIRS Method) 64

65 Example «With resepect to pipe feature, attribute Material is more important than attribute Age which in turn is more important than attribute Diameter». Age w Material w Age w Diameter w Material + w Age + w Diameter = 1 Feasible region Diameter Material v pipe feature x j = min[ w i v i x j i ] v pipe feature x j = max[ w i v i (x j i )] i i Under mild assumptions, the maximum and minimum values are attained at the extreme points of the weight feasible region (i.e., ; ; ( )) 1 2 v j Material x Material v pipe feature x j j = min[1 v Material x Material v j Diameter x Diameter, 1 3 v j Material x Material, v j Diameter x Diameter v j Age x Age ] 65

66 Back-propagation of uncertainty Example: Elicited Expert Preferences «Local circumstances is the least important criterion in defining pipe failure likelihood» Past events w pipe features w local circumstances w past events w local circumstances Feasible region Local Circumstances Pipe Features v L x j = min[σ l w i v i x i j ] v L x j = max[σ l w i v i (x i j )] l=first level attribute 66

67 Multi Attribute Value Theory Pipe Features Material Pipe Age Diameter Likelihood Blockages Past Events Flushing Local Circumstances Step 1: Value tree Step 2: Criteria relative importance Step 3: Score elitation for leaf attributes Step 4: Value computation Soil Traffic Load Back-propagaion of uncertainty Feasible criteria weights Material Pipe Age Diameter Blockages Flushings Soil Traffic Load Likelihood Pipe ID1 [30 40] [10 20] [ ] [40 60] [50 60] [20 40] [30 50] [40 60 ] Pipe ID2.. 67

68 Risk Assessment Item x t Material: concrete Pipe Age: 10 years Likelihood score: [20 40] Severity score: [30 60] Item x j Material: PVC Pipe Age: 40 years Likelihood score: [60 90] Severity score: [80 100] Item x k Material: cast iron Pipe Age: 30 years Likelihood score: [40 70] Severity score: [30 60] Dominance x j Non Dominance x k x j x t 68

69 Risk Assessment: Output Pareto front of most critical maintenance items Item 3 Item 56 Item 72 Item

70 Proposed method Failure likelihood and severity assessment criticality ranking of items Item-specific maintenance optimization item s condition-specific rule to select maintenance option Maintenance portfolio optimization proposal for maintenance resources allocation 70

71 Decision Tree Analysis The benefit of performing maintenance depends on the item degradation state These can be uncertain 71

72 Decision Tree Analysis The benefit of performing maintenance depends on the item degradation state. The probability of being in state s depends on the pipe likelihood and is uncertain Degrad ation State d d p s p s s = s = s = s = s = s =

73 Decision Tree Analysis We estimate the interval-valued costs of inspection, renovation and disruption c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 73

74 Decision Tree Analysis j Lower bound cost of renovation C ren (s) = c d j p d s 1 + c j j Upper bound cost of renovation C ren (s) = c j ҧ d d p 1 + cjҧ s c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 74

75 Decision Tree Analysis j Lower bound cost of no renovation C NOren (s) = c d d j p s j Upper bound cost of no renovation C NOren (s) = c j ҧ d d p s c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 75

76 Decision Tree Analysis j We will decide to renovate pipe j only if C ren j s < C NOren (s) c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 76

77 Decision Tree Analysis The benefit of inspetion is related to the reduction of expected disruption cost B j s = j C NOren (s) C ren 0 if optimal decision isno ren j (s) otherwise c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 77

78 ҧ Decision Tree Analysis The benefit of inspetion is related to the reduction of expected disruption cost തB j s = j C NOren 0 if optimal decision isno ren (s) C ren (s) j otherwise c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 78

79 Decision Tree Analysis Expected Benefit B j = p s s j B j s S തB j = p s s j തB j s S c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 79

80 Decision Tree Analysis The decision for every pipe has to pursue two ojectives: Maximize benefit [B j, തB j ] Minimize cost [c t t j ; c j ҧ ൧ c s s j ; c j ҧ c d d j ; c j ҧ c j t = [c j t ; ҧ c j t ൧ c d d j ; c j ҧ c d d j ; c j ҧ 80

81 Proposed method Failure likelihood and severity assessment criticality ranking of items Item-specific maintenance optimization item s condition-specific rule to select maintenance option Maintenance portfolio optimization proposal for maintenance resources allocation 81

82 Risk Assessment: Output Pareto front of most critical maintenance items Example of portfolio of actions Item 3 Item 56 Item 72 Item 101 Benefit Cost Benefit Cost Benefit Cost Benefit Cost How to select maintenance porfolios? Yes No Yes Yes No No Yes 2 N possible binary portfolios of actions! 82

83 Portfolio Decision Analysis Objective: Identification of efficient inspection portfolios, i.e. a portfolio is efficient if no other feasible portfolio gives a higher overall benefit at a lower cost. RPM: linear programming optimization technique, handling interval-valued objective functions and alternative interdependencies 83

84 Application Large sewerage network in Espoo, Finland More than sewer pipes, for a total length of about 900 km. Analysis of a subset of 6103 selected pipes, whose past inspection outcomes are recorded. 84

85 Results: Step 1 First Pareto frontier: 2079 pipes Pipe 3 Pipe 56 Pipe 72 Pipe 101 Pipe 235 Pipe 367 Failure Severity Class 1 Class 2 Class 3 Pipe

86 Results: Step 2 NUMBER OF RUNNING TIME PORTFOLIOS (MINUTES) RPM Need for reducing the uncertainty in expert estimations 86

87 Conclusions A risk-based approach has been developed to optimize pipe inspection campaigns on large underground networks in the presence of imprecise knowledge. The division of the methodology into three steps allows reducing the computational effort to select efficient inspection portfolios. The integrated methodologies allow rigorously accommodating imprecise expert statements. Espoo water system case study shows the feasibility of the approach. 87