Monte Carlo Simulations

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Monte Carlo Simulations

  1. 1. <ul><li>Monte Carlo Simulations </li></ul><ul><li>Gary Breaux – Sr. Program manager </li></ul><ul><li>Oshkosh Defense </li></ul><ul><li>Nov. 2011 </li></ul>
  2. 2. <ul><li>In a Monte Carlo simulation, </li></ul><ul><li>A random value is selected for each of the tasks based on the range of estimates. </li></ul><ul><li>The model is calculated based on this random value. </li></ul><ul><li>The result of the model is recorded and the process is repeated. </li></ul>
  3. 3. <ul><li>A typical Monte Carlo simulation calculates the model hundreds or thousands of times, each time using different randomly-selected values. </li></ul><ul><li>The completed simulation yields a large results pool with each result based on random input values. </li></ul><ul><li>These results are used to describe the likelihood, or probability, of reaching various results in the model. </li></ul>
  4. 4. Basic Definition <ul><li>A Monte Carlo Simulation (MCS) yields risk analysis by generating models of possible results through substituting a range of values (a probability distribution)… </li></ul><ul><ul><li>for any factor that has inherent uncertainty… </li></ul></ul><ul><ul><li>then running (calculation) cycles… </li></ul></ul><ul><ul><li>using different sets of random values … </li></ul></ul><ul><ul><li>from the probability functions… </li></ul></ul><ul><ul><li>on each cycle. </li></ul></ul>
  5. 5. <ul><li>The Monte Carlo method is based on the generation of multiple trials to determine the expected value of a random variable. </li></ul><ul><li>Vital to the execution is the (mathematical) assumption that each (project) variable/activity being simulated is NOT influenced by other variables (tasks). </li></ul>
  6. 6. Schema of the Monte Carlo Method; <ul><li>Generate random values (formulas) for each of the activities (cost/time). </li></ul><ul><ul><li>=RAND()*(20,000-10,000)+10,000 </li></ul></ul><ul><ul><ul><li>(generates a random value between 10,000 and 20,000) </li></ul></ul></ul><ul><li>Sum each series of random values to arrive at the total project (cost/time). </li></ul>
  7. 7. Three Point Estimates <ul><li>Three point estimates are the weighted average of three estimates for a particular task based on predictive distribution of possible outcomes against a set of choices as; </li></ul><ul><ul><li>B est-Case ( conservative ) </li></ul></ul><ul><ul><li>M ost-Likely ( expected ) </li></ul></ul><ul><ul><li>W orst-Case ( extreme ) </li></ul></ul>
  8. 8. Three Point Estimates cont. <ul><li>The formula is expressed as (E=Estimate): </li></ul><ul><li>E = (B + 4 M + W)/6 </li></ul><ul><ul><ul><li>B = Best-Case (x1) </li></ul></ul></ul><ul><ul><ul><li>M = Most-Likely (x4) </li></ul></ul></ul><ul><ul><ul><li>W = Worst-Case (x1) </li></ul></ul></ul>Best-Case estimate + 4X the Most Likely estimate + the Worst Case estimate / 6 = Estimate (E).
  9. 9. Caveats <ul><li>Depending on; </li></ul><ul><li>the number of uncertainties </li></ul><ul><ul><li>and </li></ul></ul><ul><li>the ranges specified for them </li></ul><ul><li>A MCS could calculate 1k/10k cycles to complete (“skewness”). </li></ul><ul><li>The technique works particularly well when; </li></ul><ul><li>the underlying probabilities are known </li></ul><ul><li>but the results are difficult to determine. </li></ul>
  10. 10. Essential Construct a.k.a. the “ Three Point Estimate ” (“ TIME ” on EACH project task/activity ) <ul><ul><li>Best-Case (Min.) </li></ul></ul><ul><ul><li>Most-Likely (Mean) </li></ul></ul><ul><ul><li>Worst-Case (Max.) </li></ul></ul><ul><ul><li>The 3-point estimate approach does not mathematically consider Complexity. </li></ul></ul>
  11. 11. Execute the Monte Carlo Method (Time) <ul><li>Generate/utilize random (time) values for each activity (RAND function) from relevant sets of data i.e. specific project time elements. </li></ul><ul><li>Determine the number of iterations to run the simulation. </li></ul><ul><li>Apply the values. </li></ul><ul><li>Run the MCS. </li></ul><ul><li>Apply (graphically) the distribution/analysis. </li></ul>
  12. 12. Overlay Plot of MCS http://www.isixsigma.com/index.php?option=com_k2&view=item&id=925:using-monte-carlo-simulation-as-process-control-aid&Itemid=218
  13. 13. MCS (a MATLAB plot)
  14. 14. Tools/Reference <ul><li>Primavera Risk Analysis (Risk Analysis - Primavera). </li></ul><ul><li>@RISK (Risk Analysis and M.C.S. - Palisade). </li></ul><ul><li>ARM (Active Risk Manager – Deltek). </li></ul><ul><li>Crystal Ball (Predictive Modeling - Oracle). </li></ul><ul><li>MATLAB (Mathworks - computational analysis - data interpolation/presentation). </li></ul>http://physics.gac.edu/~huber/envision/instruct/montecar.htm

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