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Monte Carlo Simulation using @Risk

Monte Carlo Simulation using @Risk. Robert C. Patev North Atlantic Division – Regional Technical Specialist (978) 318-8394. Topics Introduction @Risk Basics Reliability Reporting Guidelines @Risk Demonstration. Monte Carlo Simulation Types of simulation methods

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Monte Carlo Simulation using @Risk

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  1. Monte Carlo Simulationusing @Risk Robert C. Patev North Atlantic Division – Regional Technical Specialist (978) 318-8394

  2. Topics • Introduction • @Risk Basics • Reliability • Reporting Guidelines • @Risk Demonstration

  3. Monte Carlo Simulation • Types of simulation methods • Direct – brute force method • Stratified – effort in regions • Latin Hypercube – form of stratified sampling • Importance – selected shift in distributions • Adaptive – form of importance sampling

  4. Introduction to @Risk • Monte Carlo Simulation (MCS) • Spreadsheet add-in • Excel Macros • User friendly interface • Easy input • Many probability distribution functions • Graphical output

  5. CAVEAT to @Risk • “Let the engineer beware” • Not just a “black box” that gives the correct answer or decision • Tool to assist in making decisions and arriving at a solution • Understand the inputs to your model • Understand limitations in your spreadsheets • Cautiously scrutinize and review output (Does it make sense?)

  6. @Risk Use within the Corps of Engineers • Reliability Analysis • Structural • Geotechnical • Economic Analysis • Major Rehabilitation Projects • System Studies • ORMSS, GLSLS

  7. @Risk Capabilities • Easily adds MCS to existing spreadsheet model • Fast execution time • Save MCS results quickly • User-defined macros • Complete statistical analysis • Input • Output • Sensitivity

  8. @Risk Basics • Iterations vs. simulations • Iteration - an iteration is a single sampling of random variables • Simulation - x number of iterations • Monte Carlo Simulation methods • Direct sampling • Latin hypercube sampling

  9. 1.0 1.0 Cumulative Probability Cumulative Probability 0 0 Direct Sampling Latin Hypercube Monte Carlo Simulationusing @Risk

  10. @Risk Basics • Random number seed generator • -1 to 32767 (default = 0) • Convergence • Input random variables • Selected output cells • User-defined macros

  11. @Risk Basics • Random Variables • Numerous discrete/continuous distributions • Correlation • Positive/negative • Examine outputs • Truncation • Physical limitations to data • Examine results

  12. Negative Random Variable B Random Variable B Random Variable A Random Variable A • @Risk Basics Positive

  13. Truncation 0.4 pdf 0 XL XU • @Risk Basics Area under curve = 1

  14. Reliability Using @Risk • Reliability R = 1 - P(u) where, P(u) = Npu / N Npu = Number of unsatisfactory performances at limit state < 1.0 N = number of iterations

  15. Random Variables • Distributions • Statistical parameters (min/max, mean, std. dev., …) • Distribution types • Questions - Why use, Where come from, How applied in model, What other distributions can be used • Correlation/truncation • Justification • Plots of simulated distributions for random variables and selected “output” cells from simulation

  16. Sensitivity/Convergence • Sensitivity • Identifies the most “critical” variables to the output • Range: +1 to -1 (closest to (+/-)1, model most sensitive) • R-squared method/Rank correlation coefficient • Convergence • Limit state functions • Probability of unsatisfactory performance

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