Download - Your schedule as a Swiss Army knife
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Adding Quantitative Risk Analysis
to your
Swiss Army knifeJohn C. Goodpasture
Managing Principal
Square Peg Consulting
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Schedule: Your Swiss ArmyKnife
CalendarDeliverables
Tasks
Work Breakdown of scope
Project Logic
Resource plan
Margin of Risk [slack]
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Whats missing?
Not muchQuantitative risk analysis
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Project Context
Projects are the result of businessinvestment decisions
Investors seek returns
commensurate with risk andresources committed
Public sector, private sector, non-
profitsMonetary or mission-success returns
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Project Managers mission: Deliver thescope, 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
Investors
ResourceCommitment
Managements Expected
Return on Investment
Risk
Scope
Time
ResourcesProjects Employment
of Investment
Risk balances Value with Capacity
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Managing risk
All plans have uncertainties, andthus outcomes are at risk
Probabilities and statistics are
important data to understand anddeal with uncertainties
Information provides insight forproblem avoidance
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Why apply risk analysis toschedules?
Determine the likelihood of overrunningthe schedule
Find architectural weakness in the
scheduleEstimate risk needed to balance
investor commitment
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Quantitative Methods
Statistics and Probabilities are the maintools
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 distributionscan be added
Variances of independent distributions
can be addedMost Likelys can not be added
CPM dates are deterministic, but if taken
from distributions, they should not bemost likelys
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Activityduration risk
Path duration
risk
Parallel Paths:convergence risk
Three Basic Components ofSchedules
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Managing Long Task DurationRisk
Path 1.0: 60 work days
1/1
2/121/21 3/25
3/15
1.1
1.2
1.3
1.4
CPM Date
1/13/25
BaselineLong task
Replanned
short task
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Work Breakdown
Structure ofScheduled
Activities in Days
Minimum
[-10% ]
Most
Likely
Maximum
[+30% ] Average
Variance(Days-
squared)
StandardDeviation
(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 + m ax + m ost 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 tasksubdivision
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 distributionto 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
Sa
mpleCount
17
34
51
68
85
102
119
136
153
170
Cum
ulativeProbability
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 3/30/99
0.45 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 4/5/99
0.95 4/6/991.00 4/9/99
1/1
2/12
1/21 3/25
3/15
60 work days1.1
1.2
1.3
1.4
results
Calculated 2.62,
Simulation 2.4
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3/25 is 5% probable
Sa
mpleCount
17
34
51
68
85
102
119
136
153
170
Cum
ulativeProbability
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 3/30/99
0.45 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 4/5/99
0.95 4/6/991.00 4/9/99
1/1
2/12
1/21 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 theproductof the individual
probabilities
Important tool for schedule analysis of joining or
merging tasks
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Task 1
Cumula
tiveProb
ability
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
Sa
mpleCount
17
34
51
68
85
102
119
136
153
170
Cum
ulativeProbability
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 3/30/99
0.45 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 4/5/99
0.95 4/6/991.00 4/9/99
1/1
2/12
1/21 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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S
ampleCount
38
76
114
152
190
228
266
304
342
380
Cumu
lativeProbability
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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Whats 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 commitmentcan be estimated
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Questions?
John GoodpastureSquare Peg Consulting