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by Alan R. Jones
Risk, Opportunity, Uncertainty and Other Random Models
Cover
Title
Copyright
Dedication
Contents
List of Figures
List of Tables
Foreword
1 Introduction and objectives
1.1 Why write this book? Who might find it useful? Why five volumes?
1.1.1 Why write this series? Who might find it useful?
1.1.2 Why five volumes?
1.2 Features you'll find in this book and others in this series
1.2.1 Chapter context
1.2.2 The lighter side (humour)
1.2.3 Quotations
1.2.4 Definitions
1.2.5 Discussions and explanations with a mathematical slant for Formula-philes
1.2.6 Discussions and explanations without a mathematical slant for Formula-phobes
1.2.7 Caveat augur
1.2.8 Worked examples
1.2.9 Useful Microsoft Excel functions and facilities
1.2.10 References to authoritative sources
1.2.11 Chapter reviews
1.3 Overview of chapters in this volume
1.4 Elsewhere in the ‘Working Guide to Estimating & Forecasting’ series
1.4.1 Volume I: Principles, Process and Practice of Professional Number Juggling
1.4.2 Volume II: Probability, Statistics and Other Frightening Stuff
1.4.3 Volume III: Best Fit Lines and Curves, and Some Mathe-Magical Transformations
1.4.4 Volume IV: Learning, Unlearning and Re-Learning Curves
1.4.5 Volume V: Risk, Opportunity, Uncertainty and Other Random Models
1.5 Final thoughts and musings on this volume and series
References
2 Norden-Rayleigh Curves for solution development
2.1 Norden-Rayleigh Curves: Who, what, where, when and why?
2.1.1 Probability Density Function and Cumulative Distribution Function
2.1.2 Truncation options
2.1.3 How does a Norden-Rayleigh Curve differ from the Rayleigh Distribution?
2.1.4 Some practical limitations of the Norden-Rayleigh Curve
2.2 Breaking the Norden-Rayleigh ‘Rules’
2.2.1 Additional objectives: Phased development (or the ‘camelling’)
2.2.2 Correcting an overly optimistic view of the problem complexity:The Square Rule
2.2.3 Schedule slippage due to resource ramp-up delays: The Pro Rata Product Rule
2.2.4 Schedule slippage due to premature resource reduction
2.3 Beta Distribution: A practical alternative to Norden-Rayleigh
2.3.1 PERT-Beta Distribution: A viable alternative to Norden-Rayleigh?
2.3.2 Resource profiles with Norden-Rayleigh Curves and Beta Distribution PDFs
2.4 Triangular Distribution: Another alternative to Norden-Rayleigh
2.5 Truncated Weibull Distributions and their Beta equivalents
2.5.1 Truncated Weibull Distributions for solution development
2.5.2 General Beta Distributions for solution development
2.6 Estimates to Completion with Norden-Rayleigh Curves
2.6.1 Guess and Iterate Technique
2.6.2 Norden-Rayleigh Curve fitting with Microsoft Excel Solver
2.6.3 Linear transformation and regression
2.6.4 Exploiting Weibull Distribution's double log linearisation constraint
2.6.5 Estimates to Completion – Review and conclusion
2.7 Chapter review
References
3. Monte Carlo Simulation and other random thoughts
3.1 Monte Carlo Simulation:Who, what, why, where, when and how
3.1.1 Origins of Monte Carlo Simulation: Myth and mirth
3.1.2 Relevance to estimators and planners
3.1.3 Key principle: Input variables with an uncertain future
3.1.4 Common pitfalls to avoid
3.1.5 Is our Monte Carlo output normal?
3.1.6 Monte Carlo Simulation: A model of accurate imprecision
3.1.7 What if we don't know what the true Input Distribution Functions are?
3.2 Monte Carlo Simulation and correlation
3.2.1 Independent random uncertain events – How real is that?
3.2.2 Modelling semi-independent uncertain events (bees and hedgehogs)
3.2.3 Chain-Linked Correlation models
3.2.4 Hub-Linked Correlation models
3.2.5 Using a Hub-Linked model to drive a background isometric correlation
3.2.6 Which way should we go?
3.2.7 A word of warning about negative correlation in Monte Carlo Simulation
3.3 Modelling and analysis of Risk, Opportunity and Uncertainty
3.3.1 Sorting the wheat from the chaff
3.3.2 Modelling Risk Opportunity and Uncertainty in a single model
3.3.3 Mitigating Risks, realising Opportunities and contingency planning
3.3.4 Getting our Risks, Opportunities and Uncertainties in a tangle
3.3.5 Dealing with High Probability Risks
3.3.6 Beware of False Prophets: Dealing with Low Probability High Impact Risks
3.3.7 Using Risk or Opportunity to model extreme values of Uncertainty
3.3.8 Modelling Probabilities of Occurrence
3.3.9 Other random techniques for evaluating Risk, Opportunity and Uncertainty
3.4 ROU Analysis: Choosing appropriate values with confidence
3.4.1 Monte Carlo Risk and Opportunity Analysis is fundamentally flawed!
3.5 Chapter review
References
4 Risk, Opportunity and Uncertainty: A holistic perspective
4.1 Top-down Approach to Risk, Opportunity and Uncertainty
4.1.1 Top-down metrics
4.1.2 Marching Army Technique: Cost-schedule related variability
4.1.3 Assumption Uplift Factors: Cost variability independent of schedule variability
4.1.4 Lateral Shift Factors: Schedule variability independent of cost variability
4.1.5 An integrated Top-down Approach
4.2 Bridging into the unknown: Slipping and Sliding Technique
4.3 Using an Estimate Maturity Assessment as a guide to ROU maturity
4.4 Chapter review
References
5 Factored Value Technique for Risks and Opportunities
5.1 The wrong way
5.2 A slightly better way
5.3 The best way
5.4 Chapter review
Reference
6 Introduction to Critical Path and Schedule Risk Analysis
6.1 What is Critical Path Analysis?
6.2 Finding a Critical Path using Binary Activity Paths in Microsoft Excel
6.3 Using Binary Paths to find the latest start and finish times, and float
6.4 Using a Critical Path to Manage Cost and Schedule
6.5 Modelling variable Critical Paths using Monte Carlo Simulation
6.6 Chapter review
References
7 Finally, after a long wait ... Queueing Theory
7.1 Types of queues and service discipline
7.2 Memoryless queues
7.3 Simple single channel queues (M/M/1 and M/G/l)
7.3.1 Example of Queueing Theory in action M/M/1 or M/G/l
7.4 Multiple channel queues (M/M/c)
7.4.1 Example of Queueing Theory in action M/M/c or M/G/c
7.5 How do we spot a Poisson Process?
7.6 When is Weibull viable?
7.7 Can we have a Poisson Process with an increasing/decreasing trend?
7.8 Chapter review
References
Epilogue
Glossary of estimating and forecasting terms
Legend for Microsoft Excel Worked Example Tables in Greyscale
Index
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List of Figures
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Foreword
Tables
2.1 Cumulative Distribution Function of a Standard Rayleigh Probability Distribution
2.2 Norden-Rayleigh Curves are Independent of the Time Scale
2.3 Stretching Time to Model the Optimistic View of Premature Resource Reduction
2.4 Determining the Marching Army Parameters
2.5 Determining the Marching Army Parameters – Alternative Model
2.6 Marching Army Parameters and Penalties
2.7 Marching Army Parameters and Penalties
2.8 Options for Modelling Premature Resource Reduction by Disaggregation (Bactrian Camel)
2.9 Summary of Cost and Schedule Penalties Using Disaggregation Technique
2.10 Calculation of the Modal Re-Positioning Parameters
2.11 Summary of Cost and Schedule Penalties Using the Modal Re-Positioning Technique
2.12 Best Fit Beta Distribution for a Truncated Rayleigh Distribution Using Excel's Solver
2.13 Solver Results for the Best Fit Beta Distribution for a Range of NRC Truncation Ratios
2.14 Triangular Distribution Approximation to a Norden-Rayleigh Curve
2.15 Options for Creating EACs for Norden-Rayleigh Curves
2.16 Solver Model Set-Up for Norden-Rayleigh Curve Forecast
2.17 Solver Model Results for Norden-Rayleigh Curve Forecast
2.18 Solver Model Setup tor Linear Transformation of a Norden-Rayleigh Curve
2.19 Solver Model Results for Linear Transformation of a Norden-Rayleigh Curve (1)
2.20 Solver Model Results for Linear Transformation of a Norden-Rayleigh Curve (2)
2.21 Solver Outturn Creep Follows the Average of the Two Schedule Slippage Cost Rules
2.22 Transformation of a ‘Perfect’ Norden-Rayleigh Curve to a Linear Form
2.23 Solver Setup Exploiting the Linear Transformation Property of a Norden-Rayleigh Curve
2.24 Solver Results Exploiting the Linear Transformation Property of a Norden-Rayleigh Curve (1)
2.25 Solver Results Exploiting the Linear Transformation Property of a Norden-Rayleigh Curve (2)
2.26 Solver Outturn Creep Follows a Weighted Average of the Two Schedule Slippage Cost Rules
2.27 Comparison of Outturn Predictions Using Four Techniques
3.1 Sum of the Values of Two Dice Based on 10,800 Random Rolls (Twice)
3.2 Example Monte Carlo Simulation of Ten Independently Distributed Cost Variables
3.3 Comparison of Summary Output Statistics Between Two Corresponding Simulations
3.4 Example Distributions that Might be Substituted by Other Distributions of a Similar Shape
3.5 Beta and Triangular Distributions with Similar Shapes
3.6 Comparison of Two Monte Carlo Simulations with Appropriate Substituted Distributions
3.7 Comparison of Two Monte Carlo Simulations with Inappropriate Substituted Distributions (1)
3.8 Comparison of Two Monte Carlo Simulations with Inappropriate Substituted Distributions (2)
3.9 Making an Appropriate Informed Choice of Distribution for Monte Carlo Simulation
3.10 Choosing Beta Distribution Parameters for Monte Carlo Simulation Based on the Mode
3.11 Comparison of Monte Carlo Simulations with 100% and 0% (Independent) Correlated Events
3.12 Monte Carlo Output Correlation with 50% Chain-Linked Input Correlation
3.13 Output Correlation Matrix where the Chain-Link Sequence has been Reversed
3.14 Monte Carlo Output Correlation with 50% Hub-Linked Input Correlation
3.15 Monte Carlo Output Correlation with 50% Isometric Hub-Linked Input Correlation
3.16 Comparison of Chain-Linked, Hub-Linked and Background Isometric Correlation Models
3.17 Monte Carlo Output Correlation with 50% Negative Chain-Linked Input Correlation
3.18 Monte Carlo Input Data with a Single Risk at 50% Probability of Occurrence
3.19 Monte Carlo Input Data with Four Risks and One Opportunity
3.20 Risk Exposure and Risk and Opportunity Ranking Factor
3.21 Swapping an Uncertainty Range with a Paired Opportunity and Risk Around a Fixed Value
3.22 Residual Risk Exposure
3.23 Example Probabilities Aligned with Qualitative Assessments of Risk/Opportunity Likelihood
3.24 The Known Unknown Matrix
3.25 The Known Unknown Matrix–Monte Carlo View
4.1 Top-Down Approach Using March Army Technique and Uplift Factors
4.2 Slipping and Sliding Technique as an Aid to Budgeting
4.3 Estimate Maturity Assessment for Defined Risks and Opportunities
4.4 Estimate Maturity Assessment as a Guide to Risk, Opportunity & Uncertainty Technique
5.1 Factored Most Likely Value Technique for Baseline and Risk Contingency
5.2 Factored Mean Value Technique for Baseline and Risk Contingency
6.1 Activity Start and End Date Options
6.2 Binary Activity Matrix Representing Each Activity Path Through the Network
6.3 Calculation of Earliest Finish and Start Dates in an Activity Network
6.4 Calculation of Latest Finish and Start Dates in an Activity Network
6.5 Calculation of Activity Float in an Activity Network
6.6 Calculation of Activity Float in an Activity Network
6.7 Uncertainty Ranges Around Activity Durations
6.8 Critical Path Uncertainty
7.1 Kendall's Notation to Characterise Various Queueing Systems
7.2 Example Simple Repair Facility with a Single Service Channel and Unbounded Repair Times
7.3 Example of Simple Repair Facility with a Bounded Repair Time Distribution
7.4 Example of a 3-Channel Repair Facility with an Unbounded Repair Time Distribution
7.5 Example of a 3-Channel Repair Facility with a Bounded Repair Time Distribution
7.6 Comparing the Observed Repair Arisings per Month with a Poisson Distribution
7.7 Calculating the Chi-Squared Test for Goodness of Fit (Long Hand) over a 12 Month Period
7.8 Calculating the Chi-Squared Test for Goodness of Fit (Long Hand) over a 12 Month Period (2)
7.9 Calculating the Chi-Squared Test for Goodness of Fit (Long Hand) over a 12 Month Period (3)
7.10 Calculating the Chi-Squared Test for Goodness of Fit (Long Hand) over a 24 Month Period (1)
7.11 Calculating the Chi-Squared Test for Goodness of Fit (Long Hand) over a 24 Month Period (2)
7.12 Some Potential Techniques for Analysing Arising Rate Trends
7.13 Example of a G/M/1 Queueing Model with an Initially Decreasing Arising Rate
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