« maintenance · risk-based maintenance (rbm) • basic idea: risk is the criterion for the basis...
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« Maintenance »
expertise
UPSTREAM ACTIVITIES- Management
- Programs, Preparation
- Logistics support management
- Organisation, tasks monitoring
- Budgetary control
- Administration
DOWNSTREAM
ACTIVITIES- Experience follow-up
- Indicators
- Diagnostic maintenance
- Benchmarking
- Improvement process
- …
RoboticsSurveillance
and control
approaches
RealizationMaintenance
CorrectivePreventive
Scheduled On Condition
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]
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Strategy setting
• Maintenance Management Process
Strategy Definitionconditions the success of maintenance in an organization,
determines the effectiveness of the subsequent implementation
Strategy Implementationallow us to minimize the maintenance direct cost,
determines the efficiency of our management
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Strategy setting
• Maintenance Management Process
Strategy Definitionconditions the success of maintenance in an organization,
determines the effectiveness of the subsequent implementation
Strategy Implementationallow us to minimize the maintenance direct cost,
determines the efficiency of our management
“…doing the right thing”
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Strategy setting
• Maintenance Management Process
Strategy Definitionconditions the success of maintenance in an organization,
determines the effectiveness of the subsequent implementation
Strategy Implementationallow us to minimize the maintenance direct cost,
determines the efficiency of our management
“…doing the right thing”
“…doing the (right) thing right”
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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 toits characteristics and to the consequences of its failure.
• A decision must be taken on the maintenance strategy, which defines thecomponents of a system that will have a corrective, scheduled or condition-based maintenance and will further specify the details of each of this type ofapproaches
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What to take into account, for every component?
LegislationCompany’s
quality policy
Manufacturer
indications
Maintenance
experience
Job priority
analysis
Criticality
analysis
Mathematical
models
Component
Work instruction description
Required disciplines
Required working hours and spare list
Eventual priorities
Unplanned
Periodic
Condition-based
Predictive
…
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Maintenance Strategy
• Reliability-Centred Maintenance (RCM)
• Risk-Based Maintenance (RBM)
Two common approaches for defining a maintenance strategy
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Maintenance Strategy
Two common approaches for defining a maintenance strategy
• Reliability-Centred Maintenance (RCM)
• Risk-Based Maintenance (RBM)
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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.
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The Concept of Risk
Hazard
Environment
People
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The Concept of Risk
Hazard
Safeguards
Environment
People
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The Concept of Risk
Hazard
Safeguards
Environment
People
UNCERTAINTY
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Risk Analysis: scenario
Accident
Scenarios
Identification
QualitativeRAM
analyses
1. What undesired conditions may occur? Accident Scenario, S
Hazard Analysis
Hazop
FMEA
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1. What undesired conditions may occur? Accident Scenario, S
2. With what probability do they occur? Probability, p
Failure
Probabilty
Assessment
FTA
ETA
Markov Models
Hazard Analysis
Hazop
Accident
Scenarios
IdentificationFMEA
QuantitativeRAM
analyses
QualitativeRAM
analyses
Petri Net
Bayesian Networks
Risk Analysis: probability
Uncertainty Representation: (probabilistic & non-probabilistic frameworks)
Uncertainty Propagation (advanced and hybrid MC methods)
Multi-state degradation modelsDynamic behaviors
Influencing Factors
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1. What undesired conditions may occur? Accident Scenario, S
2. With what probability do they occur? Probability, p
3. What damage do they cause? Consequence, x
Failure
Probabilty
Assessment
FTA
ETA
Markov Models
Hazard Analysis
Hazop
Accident
Scenarios
IdentificationFMEA
QuantitativeRAM
analyses
QualitativeRAM
analyses
Petri Net
Bayesian Networks Evaluation of
the
consequences
International Standards
Best Practices & Lessons Learnt
Transport Model
Resilience and Vulnerability analysis
Risk Analysis: consequence
Fire& Explosion models
ABM for Emergent phenomena
Uncertainty Representation: (probabilistic & non-probabilistic frameworks)
Uncertainty Propagation (advanced and hybrid MC methods)
Multi-state degradation modelsDynamic behaviors
Influencing Factors
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Failure
Probabilty
Assessment
FTA
ETA
Markov Models
Hazard Analysis
Hazop
Accident
Scenarios
IdentificationFMEA
QuantitativeRAM
analyses
QualitativeRAM
analyses
Petri Net
Bayesian Networks Evaluation of
the
consequences
RISK = {Si, pi, xi}
4
3
2
1
p/x A B C D
Risk Analysis: evaluation
International Standards
Best Practices & Lessons Learnt
Transport Model
Resilience and Vulnerability analysis
Fire& Explosion models
ABM for Emergent phenomena
Uncertainty Representation: (probabilistic & non-probabilistic frameworks)
Uncertainty Propagation (advanced and hybrid MC methods)
Multi-state degradation modelsDynamic behaviors
Influencing Factors
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Failure
Probabilty
Assessment
FTA
ETA
Markov Models
Hazard Analysis
Hazop
Accident
Scenarios
IdentificationFMEA
QuantitativeRAM
analyses
QualitativeRAM
analyses
Petri Net
Bayesian Networks Evaluation of
the
consequences
Risk Analysis: evaluation
International Standards
Best Practices & Lessons Learnt
Transport Model
Resilience and Vulnerability analysis
Fire& Explosion models
ABM for Emergent phenomena
Risk mitigationMa
inte
nan
ce
De
sig
n
PHM
Inspections
FRACAS/RCA
Redundancies
Reliable components
Uncertainty Representation: (probabilistic & non-probabilistic frameworks)
Uncertainty Propagation (advanced and hybrid MC methods)
Multi-state degradation modelsDynamic behaviors
Influencing Factors
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Failure
Probabilty
Assessment
FTA
ETA
Markov Models
Hazard Analysis
Hazop
Accident
Scenarios
IdentificationFMEA
QuantitativeRAM
analyses
QualitativeRAM
analyses
Petri Net
Bayesian Networks Evaluation of
the
consequences
Risk Analysis: evaluation
International Standards
Best Practices & Lessons Learnt
Transport Model
Resilience and Vulnerability analysis
Fire& Explosion models
ABM for Emergent phenomena
Uncertainty Representation: (probabilistic & non-probabilistic frameworks)
Uncertainty Propagation (advanced and hybrid MC methods)
Multi-state degradation modelsDynamic behaviors
Influencing Factors
Risk mitigationMa
inte
nan
ce
De
sig
n
PHM
Inspections
FRACAS/RCA
Redundancies
Reliable components
How to cost-effectively
reduce the asset risk?
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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 topevent (failure scenario) such to satisfy the acceptable risk criterion; compute thecorresponding new probabilities of the basic events (failure modes) and fromthese infer the corresponding maintenance intervals;
- the Analytic Hierarchy Process (AHP): identify the risk factors affecting thefailure scenario; pairwise compare their importance in contributing to the failurescenario; derive the risk factors likelihoods; combine the risk factors likelihoods tocompute the probability of failure; prioritize components and plan maintenanceinterventions based on the risk factors likelihood contributions and relatedinsights.
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Reverse Fault Tree Analysis
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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.
Basic Failure Events ID Code
1Pressure equalizer valve
failureV1
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.
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Fault Tree Model
Objective: Reduce the Top Event probability to make the risk acceptable
Decision Problem: how?
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 2011.
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‘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
𝑅𝑅𝑊𝐷𝑜𝑜𝑟 =𝑃(𝐴𝑖𝑟 𝐿𝑜𝑐𝑘 𝐹𝑎𝑖𝑙𝑢𝑟𝑒)
𝑃(𝐴𝑖𝑟 𝐿𝑜𝑐𝑘 𝑓𝑎𝑖𝑙𝑢𝑟𝑒|𝐷𝑜𝑜𝑟 𝑤𝑜𝑟𝑘𝑖𝑛𝑔)
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‘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):
Rank component importance values
Calculate component RRW values
Apply one of the possible actions on the most important basic
event
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‘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):
Rank component importance values
Calculate component RRW values
Apply one of the possible actions on the most important basic
event
Drawback:the procedure does not
necessarily lead to the global
optimal solution
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• 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
Portfolio Optimization for RBM
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Methodology steps:
1. Failure scenario modeling
2. Definition of failure probabilities
3. Specification of actions
4. Optimization model
Our methodology
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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. 46-53 (2013).
To analyze the failure
scenarios, the Fault Tree is
mapped into a Bayesian Belief
Network.
Step 1: Failure scenario modeling
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Step 1: Airlock system failure modeling
Multi-state description
of pipe leakage event
Advantages of BBN
Multi-state modeling
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Step 1: Airlock system failure modeling
Advantages of BBN
Multi-state modeling
Extension of concepts of AND/OR gates
Example: AND gate
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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.
Step 2: Definition of failure probabilities
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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.
𝑠
𝑃𝑖(s)
𝑠
𝑃𝑎𝑖(s)
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Step 2 and 3: Definition of failure probabilities
Action RRR
Calibration test 𝑎1 10−1
Sensor 𝑎2 10−2
Valve failure
𝑃𝑎12 𝑠 = 1 = 10−4 ∙ 10−1
𝑃𝑎22 𝑠 = 1 = 10−4 ∙ 10−2
Risk Reduction Rate
(RRR)
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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
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Action Parameters
Synergic
effect:
selection of
both
actions
cost saving
and risk
reduction
extra-benefit
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Actions Parameters
Synergic
effect: if we
act on both
seal and pipe,
we gain a cost
saving
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Step 4: Optimization model
Risk
acceptability
Sele
ct th
e o
ptim
al a
ctio
n p
ortfo
lio
Action portfolio #2
Action portfolio #3
Action portfolio #4
Action portfolio #5
Action portfolio #9
Budget
constraints
Action
feasibility
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.
Action portfolio #6
Action portfolio #7
Action portfolio #8
Action portfolio #10
Action portfolio #11
Action portfolio #12
Action portfolio #1
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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.
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Step 4: Optimization model results
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Step 4: Optimization model results
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Step 4: Optimization model results
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Step 4: Optimization model results
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Application of RRW approach
The application of this approach leads to the following issues
Iteration Most risky event Issue
𝑡 = 1 Valve failureThere are two possible actions, so which one
should the experts select?
𝑡 = 2 Tank failureThe only applicable action is very expensive, could it be that many inexpensive actions have a higher
impact on risk reduction?
𝑡 = 3Valve failureDoor failure
In case of a limited budget, which componentshould be improved first?
𝑡 = 4 Valve failureIf the experts apply a second action, do the joined
actions have the same characteristics as two separate actions?
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• If we are given Budget B=350K€, then we getthe following results:
Final Comparison
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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 multi-objective failure scenarios they account for a unique critical event.
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Application of AHP to RBM
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• A multiple criteria decision-making technique, which allows toreduce complex decisions to a series of simple comparisonsand rankings
• It is used in RBM applications to prioritize components andplan maintenance interventions based on the risk factorslikelihood and consequence contributions, and relatedinsights
AHP: What is it?
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• Phase 1: formulate the decision problem in the form of ahierarchical structure. The decomposition of the decisioncriteria 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
AHP: Method
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• 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.
Example
P.K. Dey, A risk-based maintenance model for inspection and maintenance of cross-country petroleum pipeline, J.
Qual. Maint. Eng. 7 (1) (2001), 25–41.
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• Phase 1: formulate the decision problem in the form of ahierarchical structure. The decomposition of the decisioncriteria 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.
AHP: Method
how many times more
important or dominant an
element is over another
Intensity of
Importance
Definition Explanation
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.
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• 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.
Example
Slightly favours of Corrosion over external interference
Dominance of corrosion over Acts of God
demonstrated in practice
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• Phase 1: formulate the decision problem in the form of ahierarchical structure. The decomposition of the decisioncriteria proceeds until further refinements are not needed.
• Phase 2: determine the relative importance of the elements ineach level of the hierarchy through a pair-wise comparison.Each element in an upper level of the hierarchical tree is usedas criterion to compare the elements in the level immediatelybelow.
• Phase 3: compute the relative weights of the factors(mathematical procedure based on eigenvectorscomputation)
AHP: Method
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Example
Preference
Weight
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• Phase 1: formulate the decision problem in the form of ahierarchical structure. The decomposition of the decisioncriteria proceeds until further refinements are not needed.
• Phase 2: determine the relative importance of the elements ineach level of the hierarchy through a pair-wise comparison.Each element in an upper level of the hierarchical tree is usedas criterion to compare the elements in the level immediatelybelow.
• Phase 3: compute the relative weights of the factors(mathematical procedure based on eigenvectorscomputation)
• Phase 4: compute the relative weights of the alternatives withrespect to the leaves of the tree
• Phase 5: find the composite weights of the decisionalternatives by aggregating the weights through hierarchy.
AHP: Method
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Example
Final weights
Final ranking
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• 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
Methodology drawback
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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
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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
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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
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Multi Attribute Value Theory
Likelihood
Pipe Features
Material Pipe Age Diameter
Past Events
Blockages Flushing
Local Circumstances
Soil Traffic Load
Step 1: Value treeOperational
losses
Item repair cost
Cost to externals
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Multi Attribute Value Theory
Step 1: Value tree
Step 2: Score elicitation for leaf attributes (SWING Method)
Likelihood
Pipe Features
Material Pipe Age Diameter
Past Events
Blockages Flushing
Local Circumstances
Soil Traffic Load
൧𝑣𝑖 𝑥𝑖𝑗
= [𝑣𝑖 𝑥𝑖𝑗; 𝑣𝑖(𝑥𝑖
𝑗)
𝑖=leaf attribute
𝑥𝑖𝑗=score of pipe 𝑗 with respect to attribute 𝑖
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Example
0
20
40
60
80
100
120
1940 1960 1980 2000 2020
Sco
re
Pipe age
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»
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Multi Attribute Value Theory
Likelihood
Pipe Features
Material Pipe Age Diameter
Past Events
Blockages Flushing
Local Circumstances
Soil Traffic Load
Step 1: Value tree
Step 2: Score elicitation for leaf attributes (SWING Method)
Step 3: Criteria relative importance (PAIRS Method)
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Example
«With resepect to 𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒, attribute 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 is more important than attribute 𝐴𝑔𝑒 which in turn is more important than attribute 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟».
𝑤𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 ≥ 𝑤𝐴𝑔𝑒 ≥ 𝑤𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
𝑤𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 + 𝑤𝐴𝑔𝑒 + 𝑤𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 1
Diameter
Age
Material
Feasible
region
𝑣𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑥𝑗 = min[
𝑖
𝑤𝑖 𝑣𝑖 𝑥𝑖𝑗]
𝑣𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑥𝑗 = max[
𝑖
𝑤𝑖 𝑣𝑖(𝑥𝑖𝑗)]
Under mild assumptions, the
maximum and minimum values are
attained at the extreme points of the
weight feasible region (i.e.,
1 0 0 ;1
2
1
20 ; (
1
3
1
3
1
3))
𝑣𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒 𝑥𝑗 = min[1 ∙ 𝑣𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑥𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑗
,1
2𝑣𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑥𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙
𝑗+1
2𝑣𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑥𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
𝑗,1
3𝑣𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑥𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙
𝑗+1
3𝑣𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑥𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
𝑗+1
3𝑣𝐴𝑔𝑒 𝑥𝐴𝑔𝑒
𝑗]
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𝑙=first level attribute
Back-propagation of uncertainty
𝑤𝑝𝑖𝑝𝑒 𝑓𝑒𝑎𝑡𝑢𝑟𝑒𝑠 ≥ 𝑤𝑙𝑜𝑐𝑎𝑙 𝑐𝑖𝑟𝑐𝑢𝑚𝑠𝑡𝑎𝑛𝑐𝑒𝑠
𝑤𝑝𝑎𝑠𝑡 𝑒𝑣𝑒𝑛𝑡𝑠 ≥ 𝑤𝑙𝑜𝑐𝑎𝑙 𝑐𝑖𝑟𝑐𝑢𝑚𝑠𝑡𝑎𝑛𝑐𝑒𝑠Pipe Features
Past events
Local Circumstances
Feasible
region
Example: Elicited Expert Preferences
«Local circumstances is the least important criterion in defining pipe failure
likelihood»
• 𝑣𝐿 𝑥𝑗 = min[σ𝑙𝑤𝑖 𝑣𝑖 𝑥𝑖𝑗]
• 𝑣𝐿 𝑥𝑗 = max[σ𝑙𝑤𝑖 𝑣𝑖(𝑥𝑖𝑗)]
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Multi Attribute Value Theory
Likelihood
Pipe Features
Material Pipe Age Diameter
Past Events
Blockages Flushing
Local Circumstances
Soil Traffic Load
Step 1: Value tree
Step 2: Criteria relative importance
Step 3: Score elitation for leaf attributes
Step 4: Value computation
Material Pipe Age Diameter Blockages Flushings Soil Traffic Load Likelihood
Pipe ID1 [30 40] [10 20] [100 100] [40 60] [50 60] [20 40] [30 50] [40 60 ]
Pipe ID2 … …. …
….
Feasible criteria weights
Back-p
ropagaio
no
f
uncerta
inty
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Risk Assessment
Dominance Non Dominance
Item 𝒙𝒕
Material: concrete
Pipe Age: 10 years
…
Likelihood score: [20 40]
Severity score: [30 60]
Item 𝒙𝒋
Material: PVC
Pipe Age: 40 years
…
Likelihood score: [60 90]
Severity score: [80 100]
Item 𝒙𝒌
Material: cast iron
Pipe Age: 30 years
…
Likelihood score: [40 70]
Severity score: [30 60]
𝒙𝒕
𝒙𝒋 𝒙𝒋
𝒙𝒌
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Risk Assessment: Output
Pareto front of most
critical maintenance items
Item 3
Item 56
Item 72
Item 101
…
…
…
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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
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Decision Tree Analysis
The benefit of performing maintenance depends on the item degradation state
These can be uncertain
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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
𝑝𝑠𝑑 𝑝𝑠
𝑑
𝑠 = 1 0 0.3
𝑠 = 2 0.3 0.5
𝑠 = 3 0.4 0.6
𝑠 = 4 0.5 0.7
𝑠 = 5 0.6 0.8
𝑠 = 6 0.7 0.9
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Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
We estimate the interval-valued costs of inspection, renovation and disruption
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Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
Lower bound cost of renovation 𝐶renj
(𝑠) = 𝑐𝑗𝑑 ∙ 𝑝1
𝑑 + 𝑐𝑗𝑠
Upper bound cost of renovation 𝐶renj
(𝑠) = ҧ𝑐𝑗𝑑 ∙ 𝑝
1𝑑+ ҧ𝑐𝑗
𝑠
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Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
Lower bound cost of no renovation 𝐶NOrenj
(𝑠) = 𝑐𝑗𝑑 ∙ 𝑝𝑠
𝑑
Upper bound cost of no renovation 𝐶NOrenj
(𝑠) = ҧ𝑐𝑗𝑑 ∙ 𝑝
𝑠𝑑
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Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
We will decide to renovate pipe 𝑗 only if 𝐶renj
𝑠 < 𝐶NOrenj
(𝑠)
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77
Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
The benefit of inspetion is related to the reduction of expected disruption cost
𝐵𝑗𝑠 =
0 if optimal decision is NO ren
𝐶NOrenj
(𝑠) − 𝐶renj
(s) otherwise
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78
Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
The benefit of inspetion is related to the reduction of expected disruption cost
ത𝐵𝑗𝑠 =
0 if optimal decision is NO ren
ҧ𝐶NOrenj
(𝑠) − 𝐶renj
(s) otherwise
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79
Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
Expected Benefit 𝐵𝑗 =
𝑠∈𝑆
𝑝𝑗𝑠 ∙ 𝐵𝑗
𝑠 ത𝐵𝑗 =
𝑠∈𝑆
𝑝𝑗𝑠 ∙ ത𝐵𝑗
𝑠
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80
Decision Tree Analysis
൧𝑐𝑗𝑡 = [𝑐𝑗
𝑡; ҧ𝑐𝑗𝑡
𝑐𝑗𝑠; ҧ𝑐𝑗
𝑠
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
𝑐𝑗𝑑; ҧ𝑐𝑗
𝑑
The decision for every pipe has to pursue two ojectives:
[𝐵𝑗 , ത𝐵𝑗]Maximize benefit
Minimize cost ൧[𝑐𝑗𝑡; ҧ𝑐𝑗
𝑡
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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
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Risk Assessment: Output
Pareto front of most
critical maintenance items
Item 3
Item 56
Item 72
Item 101
…
…
…
Yes
No
Yes
Yes
No
No
Yes
…
How to select maintenance
porfolios?
Example of
portfolio of actions
2𝑁possible
binary
portfolios of
actions !
Benefit
Cost
Benefit
Cost
Benefit
Cost
Benefit
Cost
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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
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Application
• Large sewerage network in Espoo,
Finland
• More than 33000 sewer pipes, for a
total length of about 900 km.
• Analysis of a subset of 6103
selected pipes, whose past
inspection outcomes are recorded.
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Results: Step 1
First Pareto frontier:
2079 pipes
Failure SeverityClass 1
Class 2
Class 3
Pipe 3
Pipe 56
Pipe 72
Pipe 101
Pipe 235
Pipe 367
Pipe 461
…
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Results: Step 2
NUMBER OF
PORTFOLIOS
RUNNING TIME
(MINUTES)
RPM 2000 30
Need for reducing the
uncertainty in expert
estimations
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•A risk-based approach has been developed to optimize pipeinspection campaigns on large underground networks in thepresence of imprecise knowledge.
•The division of the methodology into three steps allowsreducing the computational effort to select efficient inspectionportfolios.
•The integrated methodologies allow rigorously accommodatingimprecise expert statements.
•Espoo water system case study shows the feasibility of theapproach.
Conclusions