This document provides an overview of programmatic risk management. It discusses: 1. The importance of managing risk to cost, schedule, and technical performance for project success. 2. How single point estimates are not sufficient and statistical estimates are needed to build a credible cost and schedule model given the uncertainty inherent in projects. 3. The key aspects of risk management including identifying risk, analyzing risk probability and impact, and communicating risk as an ongoing process for decision making.

1. Programmatic Risk Management Work (Handbook)
Programmatic Risk Management:
A “not so simple” introduction to the
complex but critical process of building a
“credible” schedule
Program Planning and Controls Workshop, Denver, Colorado
October 6th and October 14th 2008

2. Agenda
Duration Topic
20 Minutes Risk Management in Five Easy Pieces
15 Minutes Basic Statistics for programmatic risk management
15 Minutes Monte Carlo Simulation (MCS) theory
20 Minutes Mechanics of MSFT Project and Risk+
15 Minutes Programmatic Risk Ranking
15 Minutes Building a Credible schedule
20 Minutes Conclusion
120 Minutes

3. When we say “Risk Management”
What do we really mean?

4. Five Easy Pieces†:
The Essentials of
Managing
Programmatic Risk
Managing the risk to cost, schedule, and technical performance is the
basis of a successful project management method.
† With apologies to Carole Eastman and Bob Rafelson for their 1970 film staring Jack Nicholson
Risk in Five Easy Pieces

5. Hope is Not a Strategy
When General Custer was completely surrounded,
his chief scout asked, “General what's our strategy?”
Custer replied, “The first thing we need to do is
make a note to ourselves – never get in this situation
again.”
Hope is not a strategy!
A Strategy is the plan to successfully complete the project
If the project’s success factors, the processes that deliver them,
the alternatives when they fail, and the measurement of this
success are not defined in meaningful ways for both the
customer and managers of the project – Hope is the only
strategy left.
Risk in Five Easy Pieces

6. No Single Point Estimate can be correct without
knowing the variance
When estimating
 Single Point Estimates use sample data to
cost and duration calculate a single value (a statistic) that serves as
for planning a "best guess" for an unknown (fixed or random)
purposes using population parameter
Point Estimates  Bayesian Inference is a statistical inference
results in the where evidence or observations are used to infer
least likely result. the probability that a hypothesis may be true
A result with a
 Identifying underlying statistical behavior of the
50/50 chance of
being true.
cost and schedule parameters of the project is the
first step in forecasting future behavior
 Without this information and the model in which it
is used any statements about cost, schedule and
completion dates are a 50/50 guesses
Risk in Five Easy Pieces

7. Without Integrating $, Time, and TPM
you’re driving in the rearview mirror
Technical
Performance (TPM)
Addressing customer satisfaction means incorporating
product requirements and planned quality into the
Performance Measurement Baseline to assure the true
performance of the project is made visible.
Risk in Five Easy Pieces

8. Without a model for risk management, you’re driving in the dark with
the headlights turn off
The Risk
Management
process to the
right is used by
the US DOD and
differs from the
PMI approach in
how the
processes areas
are arranged.
The key is to
understand the
relationships
between these
areas. Risk Management means using a proven risk management
process, adapting this to the project environment, and using this
process for everyday decision making.
Risk in Five Easy Pieces

9. Risk Communication is …
An interactive process of exchange of
information and opinion among
individuals, groups, and institutions;
often involving multiple messages about
the nature of risk or expressing
concerns, opinions, or reactions to risk
messages or to legal or institutional
arrangements for risk management.
Bad news is not wine. It does not improve with age
— Colin Powell
Risk in Five Easy Pieces

10. Basic Statistics for Programmatic
Risk Management
Since all point estimates are wrong, statistical estimates will be needed
to construct a credible cost and schedule model
Basic Statistics

11. Uncertainty and Risk are not the same
thing – don’t confuse them
 Uncertainty stems from  Risk stems from known
unknown probability probability distributions
distributions – Cost estimating methodology risk
– Requirements change impacts resulting from improper models of
– Budget Perturbations cost
– Re–work, and re–test phenomena – Cost factors such as inflation,
labor rates, labor rate burdens,
– Contractual arrangements
etc
(contract type, prime/sub
relationships, etc) – Configuration risk (variation in the
technical inputs)
– Potential for disaster (labor
troubles, shuttle loss, satellite – Schedule and technical risk
“falls over”, war, hurricanes, etc.) coupling
– Probability that if a discrete event – Correlation between risk
occurs it will invoke a project distributions
delay
Basic Statistics

12. There are 2 types of Uncertainty
encountered in cost and schedule
 Static uncertainty is natural variation and
foreseen risks
– Uncertainty about the value of a parameter
 Dynamic uncertainty is unforeseen
uncertainty and “chaos”
– Stochastic changes in the underlying
environment
– System time delays, interactions between
the network elements, positive and negative
feedback loops
– Internal dependencies
Basic Statistics

13. The Multiple Sources of Schedule Uncertainty
and Sorting Them Out is the Role of Planning
 Unknown interactions drive
uncertainty
 Dynamic uncertainty can be
addressed by flexibility in the
schedule
– On ramps
– Off ramps
– Alternative paths
– Schedule “crashing” opportunities
 Modeling of this dynamic
uncertainty requires simulation
rather than static PERT based path
assessment
– Changes in critical path are
dependent on time and state of the
network
– The result is a stochastic network
Basic Statistics

14. Statistics at a Glance
 Probability distribution – A  Bias –The expected deviation of the
function that describes the expected value of a statistical
probabilities of possible outcomes estimate from the quantity it
in a "sample space.” estimates.
 Random variable – variable a  Correlation – A measure of the joint
function of the result of a impact of two variables upon each
statistical experiment in which other that reflects the simultaneous
each outcome has a definite variation of quantities.
probability of occurrence.  Percentile – A value on a scale of
 Determinism – a theory that 100 indicating the percent of a
phenomena are causally distribution that is equal to or
determined by preceding events or below it.
natural laws.  Monte Carlo sampling – A modeling
 Standard deviation (sigma value) – technique that employs random
An index that characterizes the sampling to simulate a population
dispersion among the values in a being studied.
population.
Basic Statistics

15. Statistics Versus Probability
 In building a risk tolerant
schedule, we’re interested in the
probability of a successful
outcome
– “What is the probability of making a
desired completion date?”
 But the underlying statistics of the
tasks influence this probability
 The statistics of the tasks, their
arrangement in a network of tasks
and correlation define how this
probability based estimated
developed.
Basic Statistics

16. Each path and each task along that path has a
probability distribution
 Any path could be critical depending on the convolution of the
underlying task completion time probability distribution functions
 The independence or
dependency of each task
with others in the network,
greatly influences the
outcome of the total project
duration
 Understanding this
dependence is critical to
assessing the credibility of
the plan as well as the total
completion time of that plan
Basic Statistics

17. Probability Distribution Functions are the Life
Blood of good planning
 Probability of
occurrence as a
function of the
number of
samples
 “The number of
times a task
duration appears
in a Monte Carlo
simulation”
Basic Statistics

18. Statistics of a Triangle Distribution
Triangle 50% of all possible values are under
distributions are this area of the curve. This is the
useful when there definition of the median
is limited
information about
the characteristics
of the random
variables are all
that is available.
This is common in
project cost and Minimum Maximum
schedule estimates. 1000 hrs 6830 hrs
Mode = 2000 hrs Mean = 3879 hrs
Median = 3415 hrs
Basic Statistics

19. Basics of Monte Carlo Simulation
Far better an approximate answer to the right question, which is often
vague, than an exact answer to the wrong question, which can always
be made precise. — John W. Tukey, 1962
Basics of Monte Carlo

20. Monte Carlo Simulation
 Yes Monte Carlo is named after the
country full of casinos located on
the French Rivera
 Advantages of Monte Carlo over
PERT is that Monte Carlo…
– Examines all paths, not just the critical
path
– Provides an accurate (true) estimate of
completion
• Overall duration distribution
• Confidence interval (accuracy range)
– Sensitivity analysis of interacting tasks
– Varied activity distribution types – not restricted to Beta
– Schedule logic can include branching – both probabilistic and conditional
– When resource loaded schedules are used – provides integrated cost and schedule
probabilistic model
Basics of Monte Carlo

21. First let’s be convinced that PERT has
limited usefulness
 The original paper (Malcolm 1959) states
– The method is “the best that could be done in a real
situation within tight time constraints.”
– The time constraint was One Month
 The PERT time made the assumption that the
standard deviation was about 1/6 of the range (b–
a), resulting in the PERT formula.
 It has been shown that the PERT mean and
standard deviation formulas are poor
approximations for most Beta distributions (Keefer
1983 and Keefer 1993).
– Errors up to 40% are possible for the PERT mean
– Errors up to 550% are possible for the PERT standard
deviation
Basics of Monte Carlo

22. Critical Path and Mostly Likelies
 Critical Path’s are Deterministic
– At least one path exists through
the network
– The critical path is identified by
adding the “single point” estimates
– The critical predicts the completion
date only if everything goes
according to plan (we all know this
of course)
 Schedule execution is Probabilistic
– There is a likelihood that some durations will comprise a path that is off the critical
path
– The single number for the estimate – the “single point estimate” is in fact a most
likely estimate
– The completion date is not the most likely date, but is a confidence interval in the
probability distribution function resulting from the convolution of all the distributions
along all the paths to the completion of the project
Basics of Monte Carlo

23. Deterministic PERT Uses Three Point
Estimates In A Static Manner
 Durations are defined as three point estimates
– These estimates are very subjective if captured individually by asking…
– “What is the Minimum, Maximum, and Most Likely”
 Critical path is defined from these
estimates is the algebraic addition of
three point estimates
 Project duration is based on the
algebraic addition of the times along
the critical path
 This approach has some serious
problems from the outset
– Durations must be independent
– Most likely is not the same as the
average
Basics of Monte Carlo

24. Foundation of Monte Carlo Theory
George Louis Leclerc, Comte de Buffon,
asked what was the probability that the needle
would fall across one of the lines, marked in
green.
That outcome occurs only if: A  l sin
Basics of Monte Carlo

25. Mechanics of Risk+ integrated with
Microsoft Project
Any credible schedule is a credible model of its dynamic behavior. This
starts with a Monte Carlo model of the schedule’s network of tasks
Mechanics of Risk+

26. The Simplest Risk+ elements
Task to “watch” Most Likely Distribution
(Number3) (Duration3) (Number1)
Optimistic Pessimistic
(Duration1) (Duration2)
Mechanics of Risk+

27. The output of Risk+
Date: 9/26/2005 2:14:02 PM Completion Std Deviation: 4.83 days
Samples: 500 95% Confidence Interval: 0.42 days
Task to “watch” Unique ID: 10 Each bar represents 2 days
Name: Task 10
0.16 1.0 Completion Probability Table
Cumulative Probability
0.9
0.14 Prob Date Prob Date
0.8
0.12 0.05 2/17/06 0.55 3/1/06
0.7
Frequency
0.10 2/21/06 0.60 3/2/06
0.10 0.6 0.15 2/22/06 0.65 3/3/06
0.08 0.5 0.20 2/22/06 0.70 3/3/06
0.4 0.25 2/23/06 0.75 3/6/06
0.06
0.3 0.30 2/24/06 0.80 3/7/06 80% confidence
0.04 0.35 2/27/06 0.85 3/8/06
0.2
0.40 2/27/06 0.90 3/9/06 that task will
0.02 0.1 0.45 2/28/06 0.95 3/13/06 complete by
2/10/06 3/1/06 3/17/06
0.50 3/1/06 1.00 3/17/06
Completion Date
3/7/06
 The height of each box indicates  The standard deviation of the
how often the project complete in a completion date and the 95%
given interval during the run confidence interval of the expected
 The S–Curve shows the cumulative completion date are in the same
probability of completing on or units as the “most likely remaining
before a given date. duration” field in the schedule
Mechanics of Risk+

28. A Well Formed Risk+ Schedule
For Risk+ to provide useful information, the underlying schedule must
be well formed on some simple way.
Mechanics of Risk+

29. A Well formed Risk+ Schedule
 A good critical path network
– No constraint dates
– Lowest level tasks have predecessors and
successors
– 80% of relationships are finish to start
 Identify risk tasks
– These are “reporting tasks”
– Identify the preview task to watch during
simulation runs
 Defining the probability distribution profile for each task
– Bulk assignment is an easy way to start
– A – F ranking is another approach
– Individual risk profile assignments is best but tedious
Mechanics of Risk+

30. Analyzing the Risk+ Simulation
 Risk+ generates one or more of
the following outputs:
– Earliest, expected, and latest
completion date for each reporting
task
– Graphical and tabular displays of the
completion date distribution for each
reporting task
– The standard deviation and
confidence interval for the
completion date distribution for each
reporting task
– The criticality index (percentage of
time on the critical path) for each
task
– The duration mean and standard deviation for each task
– Minimum, expected, and maximum cost for the total project
– Graphical and tabular displays of cost distribution for the total project
– The standard deviation and confidence interval for cost at the total project level
Mechanics of Risk+

31. Programmatic Risk Ranking
The variance in task duration must be defined in some systematic way.
Capturing three point values is the least desirable.
Programmatic Risk Ranking

32. Thinking about risk ranking
 These classifications can be used to avoid asking the “3
point” question for each task
 This information will be maintained in the IMS
 When updates are made the percentage change can be
applied across all tasks
Classification Uncertainty Overrun
A Routine, been done before Low 0% to 2%
B Routine, but possible difficulties Medium to Low 2% to 5%
C Development, with little technical difficulty Medium 5% to 10%
D Development, but some technical difficulty Medium High 10% to 15%
E Significant effort, technical challenge High 15% to 25%
F No experience in this area Very High 25% to 50%
Programmatic Risk Ranking

33. Steps in characterizing uncertainty
 Use an “envelope” method to characterize the minimum,
maximum and “most likely”
 Fit this data to a statistical distribution
 Use conservative assumptions
 Apply greater uncertainty to less mature technologies
 Confirm analysis matches intuition
Remember Sir Francis Bacon’s quote
about beginning with uncertainty and
ending with certainty.
If we start with a what we think is a
valid number we will tend to continue
with that valid number.
When in fact we should speak only in
terms of confidence intervals and
probabilities of success.
Programmatic Risk Ranking

34. Sobering observations about 3 point
estimates when asking engineers
 In 1979, Tversky and Kahneman proposed an
alternative to Utility theory. Prospect theory asserts that
people make predictably irrational decisions.
 The way that a choice of decisions is presented can
sway a person to choose the less rational decision from
a set of options.
 Once a problem is clearly and reasonably presented,
rarely does a person think outside the bounds of the
frame.
 Source:
– “The Causes of Risk Taking By Project Managers,”
Proceedings of the Project Management Institute Annual
Seminars & Symposium November 1–10, 2001 •
Nashville, Tennessee
– Tversky, Amos, and Daniel Kahneman. 1981. The Framing
of Decisions and the Psychology of Choice. Science 211
(January 30): 453–458
Programmatic Risk Ranking

35. Building a Credible Schedule
A credible schedule contains a well formed network, explicit risk
mitigations, proper margin for these risks, and a clear and concise
critical path(s). All of this is prologue to analyzing the schedule.
Building a Credible Schedule

36. Good schedules have a contingency plans
 The schedule contingency
needed to make the plan credible
can be derived from the Risk+
analysis
 The schedule contingency is the Is This Our
amount of time added (or Contingency
subtracted) from the baseline Plan ?
schedule necessary to achieve
the desired probability of an under
run or over run.
 The schedule contingency can be determined through
– Monte Carlo simulations (Risk+)
– Best judgment from previous experience
– Percentage factors based on historical experience
– Correlation analysis for dependency impacts
Building a Credible Schedule

37. Schedule quality and accuracy
 Accuracy range
– Similar for each estimate class
 Consistent with estimate
– Level of project definition
– Purpose
– Preparation effort
 Monte Carlo simulation
– Analysis of results shows quality attained versus the quality sought
(expected accuracy ranges)
 Achieving specified accuracy requirements
– Select value at end points of confidence interval
– Calculate percentages from base schedule completion date, including
the contingency
Building a Credible Schedule

38. Technical Performance Measures
 Technical Performance Measures are one method of showing risk by
done
– Specific actions taken in the IMS to move the compliance forward toward the
goal
 Activities that
assessing the
increasing compliance
to the technical
performance measure
can be show in the
IMS
– These can be
Accomplishment
Criteria
Building a Credible Schedule

39. The Monte Carlo Process starts with the 3 point
estimates
 Estimates of the task duration are still needed, just
like they are in PERT
These three
point estimates – Three point estimates could be used
are not the PERT – But risk ranking and algorithmic generation of the
ones. “spreads” is a better approach
They are derived
from the ordinal  Duration estimates must be parametric rather than
risk ranking numeric values
process.
This allows them
– A geometric scale of parametric risk is one approach

to be “calibrated” Branching probabilities need to be defined
for the domain,
correlated with – Conditional paths through the schedule can be evaluated
the technical risk using Monte Carlo tools
model.
– This also demonstrate explicit risk mitigation planning to
answer the question “what if this happens?”
Building a Credible Schedule

40. Expert Judgment is required to build a Risk
Management approach
 Expert judgment is typically the basis of cost and schedule
Building the
estimates
variance
– Expert judgment is usually the weakest area of process and
values for the
quantification
ordinal risk
– Translating from English (SOW) to mathematics (probabilistic
rank is a
risk model) is usually inconsistent at best and erroneous at
technical worst
process,
 One approach
requiring
engineering – Plan for the “best case” and preclude a self–fulfilling
prophesy
judgment.
– Budget for the “most likely” and recognize risks and
uncertainties
– Protect for the “worst case” and acknowledge the conceivable
in the risk mitigation plan
 The credibility of the “best case” estimates if crucial to the
success of this approach
Building a Credible Schedule

41. Guiding the Risk Factor Process requires
careful weighting of each level of risk
 For tasks marked “Low” a reasonable
Min Most Max
approach is to score the maximum 10% Likely
greater than the minimum.
Low 1.0 1.04 1.10
 The “Most Likely” is then scored as a
Low+ 1.0 1.06 1.15
geometric progression for the remaining
categories with a common ratio of 1.5 Moderate 1.0 1.09 1.24
 Tasks marked “Very High” are bound at Moderate+ 1.0 1.14 1.36
200% of minimum. High 1.0 1.20 1.55
– No viable project manager would like a task High+ 1.0 1.30 1.85
grow to three times the planned duration
without intervention Very High 1.0 1.46 2.30
 The geometric progress is somewhat Very High+ 1.0 1.68 3.00
arbitrary but it should be used instead of
a linear progression
Building a Credible Schedule

42. Assume now we have a well formed schedule – now
what?
 With all the “bone head” elements
For the role of removed, we can say we have a
PP&C is to
move “reporting well formed schedule
past
performance” to  But the real role of Planning is to
“forecasting
future forecast the future, provide
performance” it
must break the alternative Plan’s for this forecast
mold of using
static models of
and actively engage all the
cost and participants in the projects in the
schedule
Planning Process
Building a Credible Schedule

43. We’re really after the management of schedule
margin as part of planning
 Plan the risk alternatives that  Assign duration and resource
“might” be needed estimates to both branches
– Each mitigation has a Plan B  Turn off for alternative for a
branch “success” path assessment
– Keep alternatives as simple as  Turn off primary for a “failure” path
possible (maybe one task)
assessment
 Assess probability of the alternative
occurring
Plan B
30% Probability
of failure
80% Confidence for completion
with current margin
70% Probability
of success
Plan A Current Margin Future Margin
Duration of Plan B  Plan A + Margin
Building a Credible Schedule

44. Successful margin management requires the
reuse of unused durations
 Programmatic Margin is added between  Margin that is not used in the IMS for risk
Development, Production and Integration mitigation will be moved to the next
& Test phases sequence of risk alternatives
 Risk Margin is added to the IMS where – This enables us to buy back schedule margin
risk alternatives are identified for activities further downstream
– This enables us to control the ripple effect of
schedule shifts on Margin activities
Downstream
Duration of Plan B < Plan A + Margin Activities shifted to
Plan B left 2 days
Plan B
3 Days Margin Used
Plan A
5 Days Margin
First Identified Risk Alternative in IMS Plan A 5 Days Margin
Second Identified Risk 2 days will be added
to this margin task
Alternative in IMS to bring schedule
back on track
Building a Credible Schedule

45. Simulation Considerations
 Schedule logic and constraints
– Simplify logic – model only paths which, by
inspection, may have a significant bearing on the
final result
– Correlate similar activities
– No open ends
– Use only finish–to–start relationships with no
lags
– Model relationships other than finish–to–start as
activities with base durations equal to the lag
value
– Eliminate all date constraints
– Consider using branching for known alternatives
Building a Credible Schedule

46. The contents of the schedule
 Constraints
 Lead/Lag
 Task relationships
 Durations
 Network topology
Building a Credible Schedule

47. Simulation Considerations
 Selection of Probability Distributions
– Develop schedule simulation inputs concurrently
with the cost estimate
• Early in process – use same subject matter experts
• Convert confidence intervals into probability duration
distributions
– Number of distributions vary depending on
software
– Difficult to develop inputs required for
distributions
– Beta and Lognormal better than triangular; avoid
exclusive use of Normal distribution
Building a Credible Schedule

48. Sensitivity Analysis describes which
tasks drive the completion times
 Concentrates on inputs most likely to
improve quality (accuracy)
 Identifies most promising opportunities
where additional work will help to
narrow input ranges
 Methods
– Run multiple simulations
– Use criticality index
– “Tornado” or Pareto graph
Building a Credible Schedule

49. What we get in the end is a Credible
Model of the schedule
All models are wrong. Some
models are useful.
– George Box (1919 – )
Concept generator from Ramon
Lull’s Ars Magna (C. 1300)
Building a Credible Schedule

50. Conclusion
At this point there is too much information. Processing this information
will take time, patience, and most of all practice with the tools and the
results they produce.
Conclusion

51. Conclusions
 Project schedule status must be
assessed in terms of a critical path
through the schedule network
 Because the actual durations of each
task in the network are uncertain (they
are random variables following a
probability distribution function), the
project schedule duration must be
modeled statistically
Conclusion

52. Conclusions
 Quality (accuracy) is measured at the
end points of achieved confidence
interval (suggest 80% level)
 Simulation results depend on:
– Accuracy and care taken with base schedule
logic
– Use of subject matter experts to establish
inputs
– Selection of appropriate distribution types
– Through analysis of multiple critical paths
– Understanding which activities and paths
have the greatest potential impact
Conclusion

53. Conclusions
 Cost and schedule estimates are made up of many
independent elements.
– When each element is planned as best case – e.g. a
probability of achievement of 10%
– The probability of achieving best case for a two–element
estimate is 1%
– For three elements, 0.01%
– For many elements, infinitesimal
– In effect, it is zero.
 In the beginning no attempt should be made to
distinguish between risk and uncertainty
– Risk involves uncertainty but it is indeed more
– For initial purposes it is unimportant
– The effect is combined into one statistical factor called
“risk,” which can be described by a single probability
distribution function
Conclusion

54. What are we really after in the end?
 As the program
proceeds so
does:
– Increasing
accuracy
– Reduced
schedule risk
– Increasing
visual
confirmation Current Estimate Accuracy
that success
can be reached
Conclusion

55. Points to remember
 Good project management is good risk
management
 Risk management is how adults manage projects
 The only thing we manage is project risk
 Risks impact objectives
 Risks come from the decisions we make while
trying to achieve the objectives
 Risks require a factual condition and have potential
negative consequences that must be mitigated in
the schedule
Conclusion

56. Usage is needed before understanding is
acquired
Here and elsewhere, we shall not
obtain the best insights into things
until we actually see them growing
from the beginning.
— Aristotle
Conclusion

57. The End
A planning algorithm from
Aristotle’s De Motu Animalium
c. 400 BC
This is actually the beginning, since building a risk tolerant, credible,
robust schedule requires constant “execution” of the plan.
Conclusion

58. Resources
1. “The Parameters of the Classical PERT: An Assessment of its Success,”
Rafael Herrerias Pleguezuelo,
http://www.cyta.com.ar/biblioteca/bddoc/bdlibros/pert_van/PARAMETROS.PD
F
2. “Advanced Quantitative Schedule Risk Analysis,” David T. Hulett, Hulett &
Associates, http://www.projectrisk.com/index.html
3. “Schedule Risk Analysis Simplified,” David T. Hulett, Hulett & Associates,
http://www.projectrisk.com/index.html
4. “Project Risk Management: A Combined Analytical Hierarchy Process and
Decision Tree Approach,” Prasanta Kumar Dey, Cost Engineering, Vol. 44,
No. 3, March 2002.
5. “Adding Probability to Your ‘Swiss Army Knife’,” John C. Goodpasture,
Proceedings of the 30th Annual Project Management Institute 1999 Seminars
and Symposium, October, 1999.
6. “Modeling Uncertainty in Project Scheduling,” Patrick Leach, Proceedings of
the 2005 Crystal Ball User Conference
7. “Near Critical Paths Create Violations in the PERT Assumptions of Normality,”
Frank Pokladnik and Robert Hill, University of Houston, Clear Lake,
http://www.sbaer.uca.edu/research/dsi/2003/procs/237–4203.pdf
Resources

59. Resources
8. “Teaching SuPERT,” Kenneth R. MacLeod and Paul F. Petersen,
Proceedings of the Decision Sciences 2003 Annual Meeting, Washington DC,
http://www.sbaer.uca.edu/research/dsi/2003/by_track_paper.html
9. “The Beginning of the Monte Carlo Method,” N. Metropolis, Los Alamos
Science, Special Issue, 1987.
http://www.fas.org/sgp/othergov/doe/lanl/pubs/00326866.pdf
10. “Defining a Beta Distribution Function for Construction Simulation,” Javier
Fente, Kraig Knutson, Cliff Schexnayder, Proceedings of the 1999 Winter
Simulation Conference.
11. “The Basics of Monte Carlo Simulation: A Tutorial,” S. Kandaswamy,
Proceedings of the Project Management Institute Annual Seminars &
Symposium, November, 2001.
12. “The Mother of All Guesses: A User Friendly Guide to Statistical Estimation,”
Francois Melese and David Rose, Armed Forces Comptroller, 1998,
http://www.nps.navy.mil/drmi/graphics/StatGuide–web.pdf
13. “Inverse Statistical Estimation via Order Statistics: A Resolution of the Ill–
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38. “Probabilistic PERT,” Arthur Nadas, IBM Journal of Research and
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39. “Ranked Nodes: A Simple and effective way to model qualitative in large–
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41. “The Causes of Risk Taking by Project Managers,” Michael Wakshull,
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69. Niwot Ridge LLC
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