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Comparative Analysis of Spacecraft Schedule by Classical and Quantum Monte Carlo Simulations

EVM/Schedules Track

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A schedule risk management methodology currently accepted at NASA is based on the represen- tation of durations or costs of risky tasks by distribution functions taken from project history or suggested by experts and using Monte Carlo simulation of the project schedule or cost estimate. Though empirical, this “expert opinion” methodology has proven efficient in providing the basic uncertainty of project cost and duration for the current plan without further mitigation. A new method of schedule analysis calculates the correlation function of randomly delayed tasks and exhibits systematic milestone delay with fully symmetric (normal) individual task distributions. To describe random correlations of many tasks the method involves some elements of quantum mechanics and depicts project tasks by “wave functions”.

This paper compares probability calculations performed by this new quantum mechanical me- thod with traditional Monte Carlo simulations results. A 72-task notional spacecraft schedule was analyzed by two methods independently, with risk input through Risk Register supplied by experts. Both approaches predicted ~24 months launch delay at the 70% confidence level with relative discrepancy less than 14%. With two approaches using entirely different algorithms, these results matched each other remarkably well.

The presentation will describe that although the numerical results are relatively close, they were obtained through entirely different algorithms with the classical approach requiring slightly more inputs. In the classical approach, monte carlo calculations are dependent on likelihood and con- sequence risk inputs usually gathered by in-depth interviews of project experts. In this exercise a new approach, the Risk Driver approach, was used in which the probability and impact range was assessed for the risks usually found in the risk register, and the risks were then assigned to activities for simulation. In the quantum approach, monte carlo simulations are calculated with only symmetric distributions for activity duration variation and one cumulative risk parameter to define S-curve position between these limits yet a right-skewed probability density function re- sults due to quantum effects. In addition, a “natural” quantum uncertainty is expressed without any external risk characterization required within the distribution. This presentation will show that complementary evaluation of milestone probability with classical and quantum approaches enhances confidence in the final results and substantially increases the credibility of schedule risk assessment as a technical discipline.


David R. Graham
Before coming back to the Air Force Cost Analysis Agency, David worked at NASA HQ’s in Washington DC from April 2003 – May 2008. Prior to his NASA assignment, he worked at the Aerospace Corporation for two years supporting the Intelligence Community Cost Analysis Improvement Group (IC CAIG). He began at the Space & Missile Systems Center (SMC), Los Angeles AFB, CA in Jan, 1979. He has held a variety of budget, cost performance, cost estimator, cost-risk and program analyst positions up to the present. His career has taken him from Los Angeles to Washington DC and back three times, finally coming back to where he started at SMC and living in the Redondo Beach area. His work includes earned value analysis, cost estimating, cost-risk analysis, cost as an independent variable (CAIV), Activity Based Costing, aircraft modification financial analysis and space launch range pricing. David is a SCEA Certified Cost Estimator, past president of the SoCal SCEA Chapter (1996-1999) and a former SCEA Board Member. David is looking forward to becoming the SoCal SCEA Chapter president again and reinvigorating the membership with a series of luncheon seminars on cost estimating, cost-risk and cost management tools.