adding quantitative risk analysis your swiss army knife
TRANSCRIPT
©Square Peg Consulting, 2010, all rights reserved
Adding Quantitative Risk Analysis
to your
“Swiss Army knife”
John C. Goodpasture
Managing PrincipalSquare Peg Consulting
©Square Peg Consulting, 2010, all rights reserved
Schedule: Your “Swiss Army Knife”
�Calendar
�Deliverables
�Tasks
�Work Breakdown of scope
�Project Logic
�Resource plan
�Margin of Risk [slack]
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What’s missing?
�Not much
�Quantitative risk analysis
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Project Context
�Projects are the result of business
investment decisions
�Investors seek returns
commensurate with risk and
resources committed
�Public sector, private sector, non-
profits
�Monetary or mission-success returns
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Project Manager’s mission: “Deliver the
scope, taking measured risks to do so”
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Balancing the Project
� Investor
� Business driven
outcomes
� Deterministic, limited,
resources
� Risk proportional to
expected reward
� Unknowing of
implementation
details
�Project Manager
� Charter specified
outcomes
� Resources estimates
with variation
� Risk driven by internal
& external events and
conditions
� Details drive risk
assessments and
resource estimates
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Project Equation:
Resources committed =
Resources Estimated + Project Risks
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Project Value from
the Top Down
Project Estimate from
the Bottom Up
Investor’s
Resource
Commitment
Management’s Expected
Return on Investment
Risk
Scope
Time
Resources
Project’s Employment
of Investment
Risk balances Value with Capacity
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Managing risk
�All plans have uncertainties, and
thus outcomes are at risk
�Probabilities and statistics are
important data to understand and
deal with uncertainties
�Information provides insight for
problem avoidance
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Why apply risk analysis to schedules?
�Determine the likelihood of overrunning
the schedule
�Find architectural weakness in the
schedule
�Estimate risk needed to balance
investor commitment
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Quantitative Methods
�Statistics and Probabilities are the main
tools
�Important equations and most useful
distributions are found in the PMBOK
� Triangular & Beta distributions simulate
many project situations
�Asymmetry is key to “real world” estimates
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The Math of Distributions
�Averages of independent distributions
can be added
�Variances of independent distributions
can be added
�Most Likely’s can not be added
�CPM dates are deterministic, but if taken
from distributions, they should not be
“most likely’s”
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�Activity
duration risk
�Path duration
risk
�Parallel Paths:
convergence risk
Three Basic Components of Schedules
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Managing “Long Task Duration”Risk
Path 1.0: 60 work days
1/1
2/121/21 3/25
3/151.1
1.2
1.3
1.4
CPM Date
1/13/25
Baseline
Long task
Replanned
short task
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Work Breakdown
Structure of
Scheduled
Activities in Days
Minimum
[-10% ]
Most
Likely
Maximum
[+30% ] Average
Variance
(Days-
squared)
Standard
Deviation
(Days)
WBS Activity 1.0
(Baseline) 54 60 78 64.00 26.00 5.10
WBS Activity 1.1 13.5 15 19.5 16.00 1.63 1.27
WBS Activity 1.2 13.5 15 19.5 16.00 1.63 1.27
WBS Activity 1.3 18 20 26 21.33 2.89 1.70
WBS Activity 1.4 9 10 13 10.67 0.72 0.85
WBS Activity 1.0
Summary (New
Baseline) 64.00 6.86 2.62
Managing Duration Risk
Distribution Unknown
Triangle Probability Distribution of Duration
Baseline restructured into four subtasks and a summary task
No
change
from
Baseline
74%
improved
from
Baseline
49%
improved
from
Baseline
Average = [min + max + most likely]/3
Variance = [[max-min][max-min] +
[most likely - min][most likely - max]]/18
Standard Deviation = sq root [Variance]
Variance improved by 1/N
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Applying the Math
�Average may not improve with task
subdivision
�Sum of the Averages, 64 days, is the average
of the Summary task
�Variance is reduced by subdividing tasks
into independent sub-tasks
�Variances of independent tasks add
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Monte Carlo Simulation
�Automates the tedium of calculations
�“Runs” the project schedule many
times, independently
�Each “run” uses the probability distribution
to determine a duration for each task, run-
by-run
�Result is a distribution of outcomes
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Monte Carlo Simulation proves the calculations
Sam
ple
Count
17
34
51
68
85
102
119
136
153
170
Cum
ula
tive P
robabili
ty
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date
3/23/99 3/31/99 4/9/99
Date: 3/9/99 10:30:27 PMNumber of Samples: 1000Unique ID: 6Name: Task 1.4
Completion Std Deviation: 2.4d95% Confidence Interval: 0.1dEach bar represents 1d.
Completion Probability Table
Prob Date0.05 3/25/990.10 3/25/990.15 3/26/990.20 3/26/990.25 3/29/990.30 3/29/990.35 3/29/990.40 3/30/990.45 3/30/990.50 3/30/99
Prob Date0.55 3/31/990.60 3/31/990.65 4/1/990.70 4/1/990.75 4/1/990.80 4/2/990.85 4/2/990.90 4/5/990.95 4/6/991.00 4/9/99
1/1
2/121/21 3/25
3/15
60 work days1.1
1.2
1.3
1.4
σ results
Calculated 2.62,
Simulation 2.4
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3/25 is 5% probable
Sam
ple
Count
17
34
51
68
85
102
119
136
153
170
Cum
ula
tive P
robabili
ty
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date
3/23/99 3/31/99 4/9/99
Date: 3/9/99 10:30:27 PMNumber of Samples: 1000Unique ID: 6Name: Task 1.4
Completion Std Deviation: 2.4d95% Confidence Interval: 0.1dEach bar represents 1d.
Completion Probability Table
Prob Date0.05 3/25/990.10 3/25/990.15 3/26/990.20 3/26/990.25 3/29/990.30 3/29/990.35 3/29/990.40 3/30/990.45 3/30/990.50 3/30/99
Prob Date0.55 3/31/990.60 3/31/990.65 4/1/990.70 4/1/990.75 4/1/990.80 4/2/990.85 4/2/990.90 4/5/990.95 4/6/991.00 4/9/99
1/1
2/121/21 3/25
3/15
60 work days1.1
1.2
1.3
1.4
Probability of 3/25 =
0.1 or less
Cumulative
Probability
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More Schedule Math
�“Joint Probabilities” describes the probability
of occurrence two or more independent events
� Joint Probability is the product of the individual
probabilities
� Important tool for schedule analysis of joining or
merging tasks
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Task 1
Cumulative Probability
Date
P1
D1
Task 2
P2
Joining tasks have Merge Bias
P3=P1*P2
Task 1 & 2 at
Date D1 with
cum
probability P3
Task 1 & 2
Task 1& 2 at Date D2
with cum probability
P2
D2
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3/30 is the 50% probable date for the milestone
Sam
ple
Count
17
34
51
68
85
102
119
136
153
170
Cum
ula
tive P
robabili
ty
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date
3/23/99 3/31/99 4/9/99
Date: 3/9/99 10:30:27 PMNumber of Samples: 1000Unique ID: 6Name: Task 1.4
Completion Std Deviation: 2.4d95% Confidence Interval: 0.1dEach bar represents 1d.
Completion Probability Table
Prob Date0.05 3/25/990.10 3/25/990.15 3/26/990.20 3/26/990.25 3/29/990.30 3/29/990.35 3/29/990.40 3/30/990.45 3/30/990.50 3/30/99
Prob Date0.55 3/31/990.60 3/31/990.65 4/1/990.70 4/1/990.75 4/1/990.80 4/2/990.85 4/2/990.90 4/5/990.95 4/6/991.00 4/9/99
1/1
2/121/21 3/25
3/15
60 work days1.1
1.2
1.3
1.4
Probability of 3/30 =
0.5 or less
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Sa
mp
le C
ou
nt
38
76
114
152
190
228
266
304
342
380
Cu
mu
lative
Pro
ba
bili
ty
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date
3/24/99 4/1/99 4/12/99
Date: 3/8/99 9:31:06 PM
Number of Samples: 2000
Unique ID: 12
Name: Finish Milestone
Completion Std Deviation: 2.0d
95% Confidence Interval: 0.1d
Each bar represents 1d.
Completion Probability Table
Prob Date
0.05 3/29/99
0.10 3/29/99
0.15 3/30/99
0.20 3/30/99
0.25 3/30/99
0.30 3/31/99
0.35 3/31/99
0.40 3/31/99
0.45 3/31/99
0.50 4/1/99
Prob Date
0.55 4/1/99
0.60 4/1/99
0.65 4/2/99
0.70 4/2/99
0.75 4/2/99
0.80 4/2/99
0.85 4/5/99
0.90 4/5/99
0.95 4/6/99
1.00 4/12/99
Project 2: 60 work days
2 parallel 4-task paths
2/121/21
3/25
3/15
1/1
2/121/21
3/25
3/15
Parallel Paths cause “shift right” bias
Probability of 3/30 = 0.5 * 0.5 = 0.25 or
less
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What’s been learned?
�Quantitative analysis can determine the
likelihood of overrunning the schedule
�Architectural weaknesses in the schedule are
revealed and quantified
�Risks needed to balance investor commitment
can be estimated
©Square Peg Consulting, 2010, all rights reserved
Questions?
John GoodpastureSquare Peg Consulting