1. ©GoldSim Technology Group LLC., 2004 Probabilistic Simulation “Uncertainty is a sign of humility, and humility is just the ability or the willingness to learn.” - Charlie Sheen

2. ©GoldSim Technology Group LLC., 2004 Agenda Definitions Defining stochastic inputs Modeling Risk and Reliability

3. ©GoldSim Technology Group LLC., 2004 Uncertainty Doubt, lack of certainty State of having a limited knowledge Impossible to exactly describe existing state or future outcome

4. ©GoldSim Technology Group LLC., 2004 Error vs. Uncertainty Error: Derived or assumed value  true value Uncertainty represents a range of true possibilities

5. ©GoldSim Technology Group LLC., 2004 Types of Uncertainty Parameter uncertainty –Roughness coefficient, infiltration parameter Uncertainty in future events –Equipment failure –Accident –Population growth Model uncertainty –Simplifications and approximations –Representations of a process –Time dependent

6. ©GoldSim Technology Group LLC., 2004 Memory and Correlation Streamflow Climate uncertainty and environmental response

7. ©GoldSim Technology Group LLC., 2004 Uncertainty in Model Input Identify uncertainty components –Add components to the model? –Simplify? –Physically based vs. Empirical Goal: Quantify combined effect of the components

8. ©GoldSim Technology Group LLC., 2004 Validating Model Uncertainty Best fit parametric distribution –Requires historic dataset (non-biased) –Tools: Excel, MatLab User-defined distribution (non-parametric) Subjective assessments and judgment –Expert elicitation (multi-disciplinary)

9. ©GoldSim Technology Group LLC., 2004 Why Uncertainty Modeling? Quantify risk associated with uncertainty Quantify cost associated with the risk Visualize a range of possibility Correlate uncertain parameters Explore combinations of possibilities Propagation of uncertainty

10. ©GoldSim Technology Group LLC., 2004 Quantifying Uncertainty A probability distribution is a mathematical representation of the relative likelihood of an uncertain variable having certain specific values. Height = probability density (integrate to get probability) PDFs:

11. ©GoldSim Technology Group LLC., 2004 Probability Distribution Views Probability density function (PDF) Cumulative distribution function (CDF) Complimentary cumulative distribution function (CCDF)

12. ©GoldSim Technology Group LLC., 2004 Monte Carlo Simulation Nuclear weapons project Los Alamos NL 1940’s Random inputs from a prob. Distribution Deterministic computation on each input Aggregate results Random InputsComputationsAggregate Results Iterate Computations on Random Inputs

13. ©GoldSim Technology Group LLC., 2004 Risk vs. Reliability Modeling Risk: –Predicting the probability of a (usually bad) outcome Reliability: –Analyzing the ways that systems can fail (and be repaired) in order to increase their design life, and eliminate or reduce the likelihood of failures, downtime and safety risks.

14. ©GoldSim Technology Group LLC., 2004 GoldSim Examples …switch to GoldSim…