Adding quantitative risk analysis your Swiss Army Knife

Adding Quantitative Risk Analysis
to your
“Swiss Army knife”
John C. Goodpasture
Managing Principal
Square 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]


What’s missing?

Not much
Quantitative risk analysis


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


Project Manager’s mission: “Deliver the
scope, taking measured risks to do so”


Balancing the Project

Investor Project Manager
Business driven Charter specified
outcomes outcomes
Deterministic, limited, Resources estimates
resources with variation
Risk proportional to Risk driven by internal
expected reward & external events and
Unknowing of conditions
implementation Details drive risk
details assessments and
resource estimates


Project Equation:
Resources committed =
Resources Estimated + Project Risks

Risk balances Value with Capacity
Project Value from Project Estimate from
the Top Down the Bottom Up

Risk
Investor’s
Resource
Commitment Scope
Time
Resources
Management’s Expected Project’s Employment
Return on Investment of Investment


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


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


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


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”


Three Basic Components of
Schedules
Activity Parallel Paths:
duration risk convergence risk

Path duration
risk


Managing “Long Task Duration”
Risk
Path 1.0: 60 work days
Baseline 1/1
Long task 3/25

Replanned CPM Date
1.1
short task 1/1 1.2 3/15
1.3
1/21 3/25
2/12 1.4


Variance improved by 1/N
Managing D uration Risk

Work Breakdow n
Triangle Probability Distribution of Duration
Structure of Variance Standard
Scheduled Minimum Most Maximum (Days- Deviation
Activities in Days [-10% ] Likely [+30% ] Average squared) (D ays)
WBS Activity 1.0
(Baseline) 54 60 78 64.00 26.00 5.10
Baseline restructured into four subtasks and a summ ary task

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 Distribution Unknown
B aseline) 64.00 6.86 2.62
Average = [min + m ax + most likely]/3 No 74% 49%
Variance = [[max-m in][max-min] + change improved improved
[most likely - min][most likely - max]]/18 from from from
Standard Deviation = sq root [Variance] Baseline Baseline Baseline


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


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


1/1 60 work days
1.1
1.2 3/15
1.3
1/21 1.4
3/25
2/12

Date: 3/9/99 10:30:27 PM Completion Std Deviation: 2.4d
σ results
Number of Samples: 1000
Unique ID: 6
95% Confidence Interval: 0.1d
Each bar represents 1d. Calculated 2.62,
Name: Task 1.4
170 1.0
Simulation 2.4
Completion Probability Table
153 0.9 Prob Date Prob Date

Cumulative Probability
136 0.8 0.05 3/25/99 0.55 3/31/99
119 0.7 0.10 3/25/99 0.60 3/31/99
0.15 3/26/99 0.65 4/1/99
102 0.6
Sample Count

0.20 3/26/99 0.70 4/1/99
85 0.5 0.25 3/29/99 0.75 4/1/99
68 0.4 0.30 3/29/99 0.80 4/2/99
0.35 3/29/99 0.85 4/2/99
51 0.3
0.40 3/30/99 0.90 4/5/99
34 0.2 0.45 3/30/99 0.95 4/6/99
17 0.1 0.50 3/30/99 1.00 4/9/99

3/23/99 3/31/99 4/9/99
Completion Date

Monte Carlo Simulation proves the calculations

1/1 60 work days
1.1
1.2 3/15
1.3
1/21 1.4
3/25
2/12

Cumulative
Number of Samples: 1000 Probability of 3/25 =
Unique ID: 6 Each bar represents 1d.
Probability
Name: Task 1.4 0.1 or less
170 1.0 Completion Probability Table

136 0.8 0.05 3/25/99 0.55 3/31/99
119 0.7 0.10 3/25/99 0.60 3/31/99
0.15 3/26/99 0.65 4/1/99
102 0.6
Sample Count

0.20 3/26/99 0.70 4/1/99
85 0.5 0.25 3/29/99 0.75 4/1/99
68 0.4 0.30 3/29/99 0.80 4/2/99
0.35 3/29/99 0.85 4/2/99
51 0.3
0.40 3/30/99 0.90 4/5/99
34 0.2 0.45 3/30/99 0.95 4/6/99
17 0.1 0.50 3/30/99 1.00 4/9/99

3/23/99 3/31/99 4/9/99
Completion Date

3/25 is 5% probable

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


Joining tasks have Merge Bias

P1 Task 1 Task 2

Task 1 & 2
P2
P3=P1*P2

D1 D2
Date Task 1 & 2 at Task 1& 2 at Date D2
Date D1 with with cum probability
cum P2
probability P3

1/1 60 work days
1.1
1.2 3/15
1.3
1/21 1.4
3/25
2/12

Number of Samples: 1000 Probability of 3/30 =
Name: Task 1.4 0.5 or less

136 0.8 0.05 3/25/99 0.55 3/31/99
119 0.7 0.10 3/25/99 0.60 3/31/99
0.15 3/26/99 0.65 4/1/99
102 0.6
Sample Count

0.20 3/26/99 0.70 4/1/99
85 0.5 0.25 3/29/99 0.75 4/1/99
68 0.4 0.30 3/29/99 0.80 4/2/99
0.35 3/29/99 0.85 4/2/99
51 0.3
0.40 3/30/99 0.90 4/5/99
34 0.2 0.45 3/30/99 0.95 4/6/99
17 0.1 0.50 3/30/99 1.00 4/9/99

3/23/99 3/31/99 4/9/99
Completion Date

3/30 is the 50% probable date for the milestone

1/21 3/15
1/1 2/12 3/25
Project 2: 60 work days
3/15
1/21 2 parallel 4-task paths
2/12 3/25

Number of Samples: 2000 ProbabilityInterval: 0.1d = 0.5 * 0.5 = 0.25 or
95% Confidence of 3/30
Name: Finish Milestone less
304 0.8 0.05 3/29/99 0.55 4/1/99

266 0.7 0.10 3/29/99 0.60 4/1/99
Sample Count

0.15 3/30/99 0.65 4/2/99
228 0.6
0.20 3/30/99 0.70 4/2/99
190 0.5 0.25 3/30/99 0.75 4/2/99
152 0.4 0.30 3/31/99 0.80 4/2/99
0.35 3/31/99 0.85 4/5/99
114 0.3
0.40 3/31/99 0.90 4/5/99
76 0.2 0.45 3/31/99 0.95 4/6/99
38 0.1 0.50 4/1/99 1.00 4/12/99

3/24/99 4/1/99 4/12/99
Completion Date

Parallel Paths cause “shift right” bias

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


Questions?

John Goodpasture
Square Peg Consulting

info@sqpegconsulting.com


Adding quantitative risk analysis your Swiss Army Knife

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