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Copyright © 2008, 2009, Lewis & Fowler
Programmatic Risk Management:
A “not so simple” introduction to the complex but critical process of building a “credible” schedule
Workshop, Lewis & Fowler Team, Denver, Colorado
October 6th and October 14th 2008
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Programmatic Risk Management Work (Handbook)
Copyright © 2008, 2009, Lewis & Fowler
Agenda
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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
Copyright © 2008, 2009, Lewis & Fowler
When we say “Risk Management” What do we really mean?
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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 Pieces4/69
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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.
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!
Risk in Five Easy Pieces5/69
Copyright © 2008, 2009, Lewis & Fowler
No Single Point Estimate can be correct without knowing the variance Single Point Estimates use sample data to
calculate a single value (a statistic) that serves as a "best guess" for an unknown (fixed or random) population parameter
Bayesian Inference is a statistical inference where evidence or observations are used to infer the probability that a hypothesis may be true
Identifying underlying statistical behavior of the 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
When estimating cost and duration for planning purposes using Point Estimates results in the least likely result.
A result with a 50/50 chance of being true.
Risk in Five Easy Pieces6/69
Copyright © 2008, 2009, Lewis & Fowler
Without Integrating $, Time, and TPM you’re driving in the rearview mirror
Addressing customer satisfaction means incorporating product requirements and planned quality into the Performance Measurement Baseline to assure the true performance of the project is made visible.
Cost
($)
Schedule (t)
TechnicalPerformance (TPM)
Risk in Five Easy Pieces7/69
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Without a model for risk management, you’re driving in the dark with the headlights turn off
Risk Management means using a proven risk management process, adapting this to the project environment, and using this process for everyday decision making.
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 in Five Easy Pieces8/69
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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 Pieces9/69
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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 Statistics10/69
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Uncertainty and Risk are not the same thing – don’t confuse them Uncertainty stems from
unknown probability distributions– Requirements change impacts– Budget Perturbations– Re–work, and re–test
phenomena– Contractual arrangements
(contract type, prime/sub relationships, etc)
– Potential for disaster (labor troubles, shuttle loss, satellite “falls over”, war, hurricanes, etc.)
– Probability that if a discrete event occurs it will invoke a project delay
Risk stems from known probability distributions– Cost estimating methodology
risk resulting from improper models of cost
– Cost factors such as inflation, labor rates, labor rate burdens, etc
– Configuration risk (variation in the technical inputs)
– Schedule and technical risk coupling
– Correlation between risk distributions
Basic Statistics11/69
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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
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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 Statistics13/69
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Statistics at a Glance
Probability distribution – A function that describes the probabilities of possible outcomes in a "sample space.”
Random variable – variable a function of the result of a statistical experiment in which each outcome has a definite probability of occurrence.
Determinism – a theory that phenomena are causally determined by preceding events or natural laws.
Standard deviation (sigma value) – An index that characterizes the dispersion among the values in a population.
Bias –The expected deviation of the expected value of a statistical estimate from the quantity it estimates.
Correlation – A measure of the joint impact of two variables upon each other that reflects the simultaneous variation of quantities.
Percentile – A value on a scale of 100 indicating the percent of a distribution that is equal to or below it.
Monte Carlo sampling – A modeling technique that employs random sampling to simulate a population being studied.
Basic Statistics14/69
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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 Statistics15/69
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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 Statistics16/69
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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 Statistics17/69
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Statistics of a Triangle Distribution
Triangle distributions are useful when there is limited information about the characteristics of the random variables are all that is available.
This is common in project cost and schedule estimates.
Mode = 2000 hrs
Median = 3415 hrs
Mean = 3879 hrs
Minimum 1000 hrs
Maximum6830 hrs
50% of all possible values are under this area of the curve. This is the definition of the median
Basic Statistics18/69
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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 Carlo19/69
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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 Carlo20/69
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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 Carlo21/69
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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 Carlo22/69
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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 Carlo23/69
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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: sinA l
Basics of Monte Carlo24/69
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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+25/69
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The Simplest Risk+ elements
Task to “watch”(Number3)
Most Likely(Duration3)
Pessimistic(Duration2)
Optimistic(Duration1)
Distribution(Number1)
Mechanics of Risk+26/69
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The output of Risk+
The height of each box indicates how often the project complete in a given interval during the run
The S–Curve shows the cumulative probability of completing on or before a given date.
The standard deviation of the completion date and the 95% confidence interval of the expected completion date are in the same units as the “most likely remaining duration” field in the schedule
Date: 9/26/2005 2:14:02 PMSamples: 500Unique ID: 10Name: Task 10
Completion Std Deviation: 4.83 days95% Confidence Interval: 0.42 daysEach bar represents 2 days
Completion Date
Fre
qu
en
cy
Cu
mu
lativ
e P
rob
ab
ility
3/1/062/10/06 3/17/06
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16 Completion Probability Table
Prob ProbDate Date0.05 2/17/060.10 2/21/060.15 2/22/060.20 2/22/060.25 2/23/060.30 2/24/060.35 2/27/060.40 2/27/060.45 2/28/060.50 3/1/06
0.55 3/1/060.60 3/2/060.65 3/3/060.70 3/3/060.75 3/6/060.80 3/7/060.85 3/8/060.90 3/9/060.95 3/13/061.00 3/17/06
Task to “watch”
80% confidence that task will complete by 3/7/06
Mechanics of Risk+27/69
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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+28/69
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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+29/69
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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+30/69
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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 Ranking31/69
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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 Ranking32/69
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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 Ranking33/69
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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, Tenn
– Tversky, Amos, and Daniel Kahneman. 1981. The Framing of Decisions and the Psychology of Choice. Science 211 (January 30): 453–458
Programmatic Risk Ranking34/69
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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 Schedule35/69
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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 amount of time added (or subtracted) from the baseline 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
Is This Our ContingencyPlan ?
Building a Credible Schedule36/69
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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 Schedule37/69
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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 Schedule38/69
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The Monte Carlo Process starts with the 3 point estimates
Estimates of the task duration are still needed, just like they are in PERT– Three point estimates could be used– But risk ranking and algorithmic generation of the
“spreads” is a better approach
Duration estimates must be parametric rather than numeric values– A geometric scale of parametric risk is one approach
Branching probabilities need to be defined– Conditional paths through the schedule can be
evaluated using Monte Carlo tools– This also demonstrate explicit risk mitigation
planning to answer the question “what if this happens?”
These three point estimates are not the PERT ones.
They are derived from the ordinal risk ranking process.
This allows them to be “calibrated” for the domain, correlated with the technical risk model.
Building a Credible Schedule39/69
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Expert Judgment is required to build a Risk Management approach Expert judgment is typically the basis of cost and
schedule estimates– Expert judgment is usually the weakest area of process
and quantification– Translating from English (SOW) to mathematics
(probabilistic risk model) is usually inconsistent at best and erroneous at worst
One approach– Plan for the “best case” and preclude a self–fulfilling
prophesy– 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 the variance values for the ordinal risk rank is a technical process, requiring engineering judgment.
Building a Credible Schedule40/69
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Guiding the Risk Factor Process requires careful weighting of each level of risk
For tasks marked “Low” a reasonable approach is to score the maximum 10% greater than the minimum.
The “Most Likely” is then scored as a geometric progression for the remaining categories with a common ratio of 1.5
Tasks marked “Very High” are bound at 200% of minimum.– No viable project manager would like a task
grow to three times the planned duration without intervention
The geometric progress is somewhat arbitrary but it should be used instead of a linear progression
Min Most Likely
Max
Low 1.0 1.04 1.10
Low+ 1.0 1.06 1.15
Moderate 1.0 1.09 1.24
Moderate+ 1.0 1.14 1.36
High 1.0 1.20 1.55
High+ 1.0 1.30 1.85
Very High 1.0 1.46 2.30
Very High+ 1.0 1.68 3.00
Building a Credible Schedule41/69
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Assume now we have a well formed schedule – now what?
With all the “bone head” elements removed, we can say we have a well formed schedule
But the real role of Planning is to forecast the future, provide alternative Plan’s for this forecast and actively engage all the participants in the projects in the Planning Process
For the role of PP&C is to move “reporting past performance” to “forecasting future performance” it must break the mold of using static models of cost and schedule
Building a Credible Schedule42/69
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We’re really after the management of schedule margin as part of planning
Plan the risk alternatives that “might” be needed
– Each mitigation has a Plan B branch
– Keep alternatives as simple as possible (maybe one task)
Assess probability of the alternative occurring
Assign duration and resource estimates to both branches
Turn off for alternative for a “success” path assessment
Turn off primary for a “failure” path assessment
30% Probabilityof failure
70% Probabilityof success
Plan B
Plan A Current Margin Future Margin
80% Confidence for completion with current margin
Duration of Plan B Plan A + Margin
Building a Credible Schedule43/69
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Successful margin management requires the reuse of unused durations
Programmatic Margin is added between Development, Production and Integration & Test phases
Risk Margin is added to the IMS where risk alternatives are identified
Margin that is not used in the IMS for risk mitigation will be moved to the next sequence of risk alternatives – This enables us to buy back schedule margin
for activities further downstream – This enables us to control the ripple effect of
schedule shifts on Margin activities
5 Days Margin
5 Days Margin
Plan B
Plan A
Plan B
Plan AFirst Identified Risk Alternative in IMS
Second Identified Risk Alternative in IMS
3 Days Margin Used
Downstream Activities shifted to left 2 days
Duration of Plan B < Plan A + Margin
2 days will be added to this margin task to bring schedule back on track
Building a Credible Schedule44/69
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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
alternativesBuilding a Credible Schedule
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The contents of the schedule
Constraints Lead/Lag Task relationships Durations Network topology
Building a Credible Schedule46/69
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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 Schedule47/69
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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 Schedule48/69
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What we get in the end is a Credible Model of the schedule
Concept generator from Ramon Lull’s Ars Magna (C. 1300)
All models are wrong. Some models are useful.– George Box (1919 – )
Building a Credible Schedule49/69
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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.
Conclusion50/69
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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
Conclusion51/69
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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
Conclusion52/69
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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
Conclusion53/69
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What are we really after in the end?
As the program proceeds so does:– Increasing
accuracy– Reduced
schedule risk– Increasing
visual confirmation that success can be reached
Current Estimate Accuracy
Conclusion54/69
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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
Conclusion55/69
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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
Conclusion56/69
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The End
This is actually the beginning, since building a risk tolerant, credible, robust schedule requires constant “execution” of the plan.
A planning algorithm from Aristotle’s De Motu Animalium c. 400 BC
Conclusion57/69
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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.PDF
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
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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–Posed Inverse problem of PERT Scheduling,” William F. Pickard, Inverse Problems 20, pp. 1565–1581, 2004
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Resources
14. “Schedule Risk Analysis: Why It Is Important and How to Do It, “Stephen A. Book, Proceedings of the Ground Systems Architecture Workshop (GSAW 2002), Aerospace Corporation, March 2002, http://sunset.usc.edu/GSAW/gsaw2002/s11a/book.pdf
15. “Evaluation of the Risk Analysis and Cost Management (RACM) Model,” Matthew S. Goldberg, Institute for Defense Analysis, 1998. http://www.thedacs.com/topics/earnedvalue/racm.pdf
16. “PERT Completion Times Revisited,” Fred E. Williams, School of Management, University of Michigan–Flint, July 2005, http://som.umflint.edu/yener/PERT%20Completion%20Revisited.htm
17. “Overcoming Project Risk: Lessons from the PERIL Database,” Tom Hendrick , Program Manager, Hewlett Packard, 2003, http://www.failureproofprojects.com/Risky.pdf
18. “The Heart of Risk Management: Teaching Project Teams to Combat Risk,” Bruce Chadbourne, 30th Annual Project Management Institute 1999 Seminara and Symposium, October 1999, http://www.risksig.com/Articles/pmi1999/rkalt01.pdf
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Resources
20. Project Risk Management Resource List, NASA Headquarters Library, http://www.hq.nasa.gov/office/hqlibrary/ppm/ppm22.htm#art
21. “Quantify Risk to Manage Cost and Schedule,” Fred Raymond, Acquisition Quarterly, Spring 1999, http://www.dau.mil/pubs/arq/99arq/raymond.pdf
22. “Continuous Risk Management,” Cost Analysis Symposium, April 2005, http://www1.jsc.nasa.gov/bu2/conferences/NCAS2005/papers/5C_–_Cockrell_CRM_v1_0.ppt
23. “A Novel Extension of the Triangular Distribution and its Parameter Estimation,” J. Rene van Dorp and Samuel Kotz, The Statistician 51(1), pp. 63 – 79, 2002. http://www.seas.gwu.edu/~dorpjr/Publications/JournalPapers/TheStatistician2002.pdf
24. “Distribution of Modeling Dependence Cause by Common Risk Factors,” J. Rene van Dorp, European Safety and Reliability 2003 Conference Proceedings, March 2003, http://www.seas.gwu.edu/~dorpjr/Publications/ConferenceProceedings/Esrel2003.pdf
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25. “Improved Three Point Approximation To Distribution Functions For Application In Financial Decision Analysis,” Michele E. Pfund, Jennifer E. McNeill, John W. Fowler and Gerald T. Mackulak, Department of Industrial Engineering, Arizona State University, Tempe, Arizona, http://www.eas.asu.edu/ie/workingpaper/pdf/cdf_estimation_submission.pdf
26. “Analysis Of Resource–constrained Stochastic Project Networks Using Discrete–event Simulation,” Sucharith Vanguri, Masters Thesis, Mississippi State University, May 2005, http://sun.library.msstate.edu/ETD–db/theses/available/etd–04072005–123743/restricted/SucharithVanguriThesis.pdf
27. “Integrated Cost / Schedule Risk Analysis,” David T. Hulett and Bill Campbell, Fifth European Project Management Conference, June 2002.
28. “Risk Interrelation Management – Controlling the Snowball Effect,” Olli Kuismanen, Tuomo Saari and Jussi Vähäkylä, Fifth European Project Management Conference, June 2002.
29. The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, David Salsburg, W. H. Freeman, 2001
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30. “Triangular Approximations for Continuous Random Variables in Risk Analysis,” David G. Johnson, The Business School, Loughborough University, Liecestershire.
31. “Statistical Dependence through Common Risk Factors: With Applications in Uncertainty Analysis,” J. Rene van Dorp, European Journal of Operations Research, Volume 161(1), pp. 240–255.
32. “Statistical Dependence in the risk analysis for Project Networks Using Monte Carlo Methods,” J. Rene van Dorp and M. R. Dufy, International Journal of Production Economics, 58, pp. 17–29, 1999. http://www.seas.gwu.edu/~dorpjr/Publications/JournalPapers/Prodecon1999.pdf
33. “Risk Analysis for Large Engineering Projects: Modeling Cost Uncertainty for Ship Production Activities,” M. R. Dufy and J. Rene van Dorp, Journal of Engineering Valuation and Cost Analysis, Volume 2. pp. 285–301, http://www.seas.gwu.edu/~dorpjr/Publications/JournalPapers/EVCA1999.pdf
34. “Risk Based Decision Support techniques for Programs and Projects,” Barney Roberts and David Frost, Futron Risk Management Center of Excellence, http://www.futron.com/pdf/RBDSsupporttech.pdf
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35. Probabilistic Risk Assessment Procedures Guide for NASA Managers and Practitioners, Office of Safety and Mission Assurance, April 2002. http://www.hq.nasa.gov/office/codeq/doctree/praguide.pdf
36. “Project Planning: Improved Approach Incorporating Uncertainty,” Vahid Khodakarami, Norman Fenton, and Martin Neil, Track 15 EURAM2005: “Reconciling Uncertainty and Responsibility” European Academy of Management. http://www.dcs.qmw.ac.uk/~norman/papers/project_planning_khodakerami.pdf
37. “A Distribution for Modeling Dependence Caused by Common Risk Factors,” J. Rene van Dorp, European Safety and Reliability 2003 Conference Proceedings, March 2003.
38. “Probabilistic PERT,” Arthur Nadas, IBM Journal of Research and Development, 23(3), May 1979, pp. 339–347.
39. “Ranked Nodes: A Simple and effective way to model qualitative in large–scale Bayesian Networks,” Norman Fenton and Martin Neil, Risk Assessment and Decision Analysis Research Group, Department of Computer Science, Queen Mary, University of London, February 21, 2005.
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40. “Quantify Risk to Manage Cost and Schedule,” Fred Raymond, Acquisition Review Quarterly, Spring 1999, pp. 147–154
41. “The Causes of Risk Taking by Project Managers,” Michael Wakshull, Proceedings of the Project Management Institute Annual Seminars & Symposium, November 2001.
42. “Stochastic Project Duration Analysis Using PERT–Beta Distributions,” Ron Davis.
43. “Triangular Approximation for Continuous Random Variables in Risk Analysis,” David G. Johnson, Decision Sciences Institute Proceedings 1998. http://www.sbaer.uca.edu/research/dsi/1998/Pdffiles/Papers/1114.pdf
44. “The Cause of Risk Taking by Managers,” Michael N.Wakshull, Proceedings of the Project Management Institute Annual Seminars & Symposium November 1–10, 2001, Nashville Tennessee , http://www.risksig.com/Articles/pmi2001/21261.pdf
45. “The Framing of Decisions and the Psychology of Choice,” Tversky, Amos, and Daniel Kahneman. 1981, Science 211 (January 30): 453–458, http://www.cs.umu.se/kurser/TDBC12/HT99/Tversky.html
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46. “Three Point Approximations for Continuous Random Variables,” Donald Keefer and Samuel Bodily, Management Science, 29(5), pp. 595 – 609.
47. “Better Estimation of PERT Activity Time Parameters,” Donald Keefer and William Verdini, Management Science, 39(9), pp. 1086 – 1091.
48. “The Benefits of Integrated, Quantitative Risk Management,” Barney B. Roberts, Futron Corporation, 12th Annual International Symposium of the International Council on Systems Engineering, July 1–5, 2001, http://www.futron.com/pdf/benefits_QuantIRM.pdf
49. “Sources of Schedule Risk in Complex Systems Development,” Tyson R. Browning, INCOSE Systems Engineering Journal, Volume 2, Issue 3, pp. 129 – 142, 14 September 1999, http://sbufaculty.tcu.edu/tbrowning/Publications/Browning%20(1999)––SE%20Sch%20Risk%20Drivers.pdf
50. “Sources of Performance Risk in Complex System Development,” Tyson R. Browning, 9th Annual International Symposium of INCOSE, June 1999, http://sbufaculty.tcu.edu/tbrowning/Publications/Browning%20(1999)––INCOSE%20Perf%20Risk%20Drivers.pdf
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51. “Experiences in Improving Risk Management Processes Using the Concepts of the Riskit Method,” Jyrki Konito, Gerhard Getto, and Dieter Landes, ACM SIGSOFT Software Engineering Notes , Proceedings of the 6th ACM SIGSOFT international symposium on Foundations of software engineering SIGSOFT '98/FSE-6, Volume 23 Issue 6, November 1998.
52. “Anchoring and Adjustment in Software Estimation,” Jorge Aranda and Steve Easterbrook, Proceedings of the 10th European software engineering conference held jointly with 13th ACM SIGSOFT international symposium on Foundations of software engineering ESEC/FSE-13
53. “The Monte Carlo Method,” W. F. Bauer, Journal of the Society of Industrial Mathematics, Volume 6, Number 4, December 1958, http://www.cs.fsu.edu/~mascagni/Bauer_1959_Journal_SIAM.pdf.
54. “A Retrospective and Prospective Survey of the Monte Carlo Method,” John H. Molton, SIAM Journal, Volume 12, Number 1, January 1970, http://www.cs.fsu.edu/~mascagni/Halton_SIAM_Review_1970.pdf.
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