adding quantitative risk analysis your swiss army knife

©Square Peg Consulting, 2010, all rights reserved

Adding Quantitative Risk Analysis

to your

“Swiss Army knife”

John C. Goodpasture

Managing PrincipalSquare Peg Consulting


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

� 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


Project Equation:

Resources committed =

Resources Estimated + Project Risks


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


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”


�Activity

duration risk

�Path duration

risk

�Parallel Paths:

convergence risk

Three Basic Components of Schedules


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


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


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


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


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




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


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


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


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




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


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.


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


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 GoodpastureSquare Peg Consulting

[email protected]

adding quantitative risk analysis your swiss army knife

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