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JCL in a Nutshell: Exploring the Math of Joint Cost & Schedule Risk Analysis Through Illustrative Examples

Risk Track

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With agencies such as NASA now requiring joint cost and schedule risk analysis, it is important to take time out to understand the mathematics underlying both and how it relates to their integration. Rather than focusing on difficult-to-penetrate equations, this presentation will examine the math behind Joint Cost & Schedule (JCL) risk analysis using illustrative examples. These examples will demonstrate that the combination of cost & schedule risk analysis can lead to counterintuitive results.
Following these demonstrations, several recommendations will be made to the community to encourage discussion and feedback regarding this emergent methodology
The presentation will begin by defining joint cost & schedule risk analysis and listing several methodologies for integrating the two activities. Focusing on the Build Up method utilizing a project’s Integrated-Master Schedule; it will then lay the groundwork for the remainder of the presentation with toy problems examining how traditional cost risk analysis and schedule risk analysis (using only serial tasks) are mathematically analogous. Both the risk-adjusted cost estimate and risk-adjusted finish date represent sums of random variables and thus fall victim to the “Square Root of N Effect” where, without the injection of correlation, the Coefficient of Variation (CV) of the sum is decreased.
Unfortunately, the addition of parallel paths into the schedule dramatically complicates the analysis. No longer represented by the sum of serial tasks, the finish date is now represented by the maximum of the random variables representing the tasks in the schedule. A direct consequence of this is the fact, demonstrated previously by other papers, that increasing the symmetric uncertainty of underlying parallel tasks leads to an increase in the mean finish date. Additionally, parallel tasks fall prey to their own version of the “Square Root of N Effect.” In schedule, ignoring correlation between schedule tasks leads to an overstatement of schedule risk (increases the most likely finish date) and an understatement of the schedule CV (decreases the CV of the project’s duration). Thus, unlike in cost risk analysis where correlation only impacts the spread around the most likely cost, correlation in schedule risk analysis has a direct effect on the most likely finish date itself. Depending on how resources or costs are loaded into the schedule, this contrast between how correlation affects cost and schedule leads to the need to find a “Goldilocks” zone for correlation where it is large enough to prevent the compression of CV for cost, but not so large that it provides a false sense of security by artificially reducing the risk-adjusted finish date. The paper will conclude with recommendations for the correlation to use in JCL risk analysis.


Eric Druker
Booz Allen Hamilton
Eric R. Druker CCEA graduated from the College of William and Mary with a B.S. in Applied Mathematics in 2005 concentrating in both Operations Research and Probability & Statistics with a minor in Economics. He is employed by Booz Allen Hamilton as an Associate and currently serves as President of the St. Louis Society of Cost Estimating & Analysis (SCEA) Chapter. In 2009, he was named SCEA’s National Estimator/Analyst of the Year for Technical Achievement. Mr Druker currently supports NASA’s Cost Analysis Division, performing joint cost & schedule risk analysis across a variety of projects. In his previous position as a Technical/Research Lead at Northrop Grumman, Mr. Druker developed the risk analysis process/methodology used to assess financial risk to the company during Independent Cost Evaluations (ICEs). As a part of this, he participated in or lead over 30 ICEs on Northrop Grumman proposals; briefing results to executive management including the President and CEO of Northrop Grumman. In addition to multiple SCEA conferences, Eric has been an invited presenter at The Naval Postgraduate School’s Acquisition Research Symposium, DoDCAS and NASA’s Project Management Challenge. Prior to coming to Booz Allen, he helped to develop Northrop Grumman’s Independent Cost Evaluation (ICE) risk analysis practices and served as lead author of the Regression and Cost/Schedule Risk modules for the 2008 Cost Estimating Body of Knowledge (CEBoK) update.