Transcript Cost Risk Analysis `Back Allocation.`

Cost Risk Analysis:
Back Allocation Among
the Elements
Presented by
Marc Rose, MCR Federal, LLC
[email protected]
SCEA National Conference
Manhattan Beach, CA
15 June, 2004
Developed under the FAA SETA II Contract
P.O. B
Chantilly, Virg
(703
Fax: (703
www
Agenda
 Overview
– Brief description of Cost Risk Analysis




Various Allocation Methods
Why Worry About Allocation?
Proposed Methodology
Conclusions
2
Overview
 What is Cost Risk Analysis
– Sum of cost elements (Ci) each with an associated
probability distribution
C1 = Triangular Distribution
C2 = Normal Distribution
Cost = C1+C2+…
– Determine High Confidence Cost (e.g., 80th Percentile)
usually via Monte-Carlo simulation
(e.g.,
Crystal Ball ™)
– Then Allocate the “Risk” dollars among the elements
3
Various Allocation
Methods
 First Order Methods – Scaling with:
– Mode or Point Estimate (most common)
– Mean, Median
 Second Order Methods
– Mean & Standard Deviation
– Mean & Variance
– 80th Percentile & Point Estimate
 Proposed Methodology
– Median with High Confidence Value (e.g., 80th)
4
Allocating Risk Dollars
Why Do We Care – an example
 Example – 2 Elements with triangular distributions
– Capital (10, 20, 100)
– Operations (10, 20, 30)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
120
5
Why We Care – Continued
 Solving for the High Confidence Value
– High Confidence (80th) Cost = $83.0
 Apply Mode (Most Likely) Scaling
– Capital = $41.5, Ops = $41.5
 Operations is given more than it can spend
– Result is outside the distribution range (non-viable)
 Capital has only a 50% chance of success
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Proposed Methodology(Median_P)
 Use the selected confidence level with the median:
( Pi th  50 thi )
Ei  50 
( P th   50 thj )
th
th
j
 ( Pj  50 j )
th
i
j
th
where Pi is the value of the ith cost element at the chosen percentile
50thi is the median value of the ith cost element, and
P th is the value of the Total Cost with risk at the chosen percentile
 From the previous example using the 80th percentile*
– Operations = 20+(23.675-20)/(3.675+22.05)*(83-60)= $23.3
– Capital = 40+(62.05-40)/(3.675+22.05)*(83-60) =
$59.7
 This corresponds to a 77.5% probability of success for
each element and an overall confidence of 80%
* Scale with median directly if 50% is chosen confidence level
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Risk Allocation Summary
 There is no correct allocation
– This is a statistical process, it is not possible to know
which elements will go well, which bad
– Often additional information will result in modifications
(e.g., knowledge of the budget)
 There are incorrect allocations
– Allocations with results outside of the viable range of
values
8
Risk Allocation Summary
 The Median_P methodology is guaranteed to
produce viable results
– Has to fall between the selected confidence level and the
median
– Results are consistently close to providing the same
probability of success among the cost elements
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