1 / 16

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

urania
Download Presentation

Monte Carlo Simulation using @Risk

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related