Modelling Known Unknowns
A Case Study for Private Sewers
Contents
• Background
• Problems Faced
• Modelling the Solution
• Including Uncertainty
English & Welsh Wastewater Companies
What are Private Sewers?
Any Sewer that…
• Not owned by a
wastewater company
AND
• Serves more than one
property
OR
• On someone else's land
What’s out there?
• Miles of sewers
– In gardens
– Under drives
– Under roads
Is it just pipes?
• Manholes & Covers
• Interceptors
– U bends
• Pumping Stations
How do they come about?
• Current definition of owners responsibility
• Developer build sewers that do not meet wastewater
companies Requirement
– Wastewater company declines to adopt them
• Built with no intention of being adopted
– Often to save money
What’s the problem?
Sewers
• Pitch Fibre pipes
– Collapse lots
Manholes & Covers
• Often cheaper covers
used
– At the end of their life
• Health & Safety
• On peoples property
– Hard to access
– More expensive to repair
What’s the problem?
Interceptors
• Fails lots
• Need removing
– No longer necessary
Pumping Stations
• Many not to standard
– Electrics
– Health and Safety
• Poor access
– Hard to maintain
• Will need to move/rebuild
many
So why adopt them?
The UK government says so!
• Complications on who is
responsible for problems
• Spread the costs over more
people
• Better service in the long term
What’s the wastewater company’s problem?
• How to adopt these assets?
• How to look after the assets?
• How much will it cost?
How much will it cost?
Bills
Investment
How much will it cost?
£
Requested
£ Allowed
£ Spend
What’s the wastewater company’s problem?
• How many are there?
• What are they?
– Age
– Material
– Quality
• How many failures?
• What impact on service?
What do the companies need to know?
• Assets
– How many things are
there?
• Service
– How will customers be
affected?
• Risk
– Financial value of lack
of service
• Cost
– How much will need to
be invested?
Modelling
Deterioration
Regulation
Assets
Configured
Requirement
Failures
Proactive Plan
Lack of Service
Reactive Plan
Cost
Risk
Private Sewer Model
Model Process
Number
of Assets
Types of
Asset
Portfolio of
Assets
Failure
Rates
Investment
Plan
Failures
Consequence of
Failure
Cost of
Plan
Service
Valuation
of
Service
Risk
Cost
Matrix Multiplication
Number
of Assets
N *
Portfolio
of Assets
Types of
Asset
T
=
Failure
Rates
Consequence of
Failure
Failures
Service
Valuation
of
Service
Risk
A1
A1 * R(age) = F1
F1
*
C
= S1
S1 * V
Investment
Plan
A2=(A1-F1)*Ps+F1*Rs
= R1
Matrix Multiplication
1,057
532
*
* Illustrative Values
Sewer
Chamber
Consequence of
Failure
Service
External Flooding
Internal Flooding
Chamber Block
Sewer Block
Failures
5%
50%
2%
90%
= Internal
External
63.49
1,007.3
BUT WHAT ABOUT THE
UNKNOWN?
Including Uncertainty
Model Process
Number
of Assets
Types of
Asset
Portfolio
of Assets
Failure
Rates
Investment
Plan
Failures
Consequence of
Failure
Cost of
Plan
Service
Valuation
of
Service
Risk
Cost
Sewer Block
Chamber Block
External Flooding
Internal Flooding
Model Process
Consequence of
Failure
5%
50%
RiskTriang(0%,5%,10%)
RiskTriang(40%,50%,90%)
2%
90%
RiskTriang(0%,2%,6%)
RiskTriang(80%,90%,99%)
* Illustrative Values
Model Process
Number
of Assets
Types of
Asset
Portfolio
of Assets
Failure
Rates
Strategy
Failures
Consequence of
Failure
Cost of
Strategy
Service
Valuation
of
Service
Risk
Cost
Uncertain Outputs
£160k
£140k
£120k
Risk
£100k
£80k
£60k
£40k
Cost
£20k
2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021
* Illustrative Values
Uncertain Outputs
2015 Cost
• Average
– £65k
• Percentiles
– 90th £69k
• Confidence Range
– (£61k, £71k)
* Illustrative Values
Sensitivity
• Used sensitivity
analysis
• Identified inputs that
most influence output
• Concentrate investment
here
Benefits of Using @Risk
• Takes account of the many unknowns
• Add Confidence Intervals to Outputs
• Identifies key input uncertainties
• Easy to use
• Ability to ‘swap in’ functions
– Output viewable without @Risk
• VBA framework
– Automate procedures to be more user friendly
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