Your schedule as a Swiss Army knife

8/4/2019 Your schedule as a Swiss Army knife

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Square Peg Consulting,2010, all rights reserved

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




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




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.


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

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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

[email protected]

Your schedule as a Swiss Army knife

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