adding quantitative risk analysis your swiss army knife

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

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

�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

�Parallel Paths:

convergence risk

Three Basic Components of Schedules

Managing “Long Task Duration”Risk

Path 1.0: 60 work days

2/121/21 3/25

3/151.1

CPM Date

1/13/25

Baseline

Long task

Replanned

short task

Work Breakdown

Structure of

Scheduled

Activities in Days

Minimum

[-10% ]

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

change

Baseline

improved

Baseline

improved

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

tive P

robabili

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

2/121/21 3/25

60 work days1.1

σ results

Calculated 2.62,

Simulation 2.4

3/25 is 5% probable

tive P

robabili

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

2/121/21 3/25

60 work days1.1

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

Task 2

Joining tasks have Merge Bias

P3=P1*P2

Task 1 & 2 at

Date D1 with

probability P3

Task 1 & 2

Task 1& 2 at Date D2

with cum probability

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

tive P

robabili

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

2/121/21 3/25

60 work days1.1

Probability of 3/30 =

0.5 or less

lative

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

Parallel Paths cause “shift right” bias

Probability of 3/30 = 0.5 * 0.5 = 0.25 or

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

info@sqpegconsulting.com

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