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Unformatted text preview: 1 IE 372 Simulation  Handout 7 SIMULATION OUTPUT ANALYSIS (Law & Kelton) When some simulation input parameters are random variables, simulation outputs are also random variables. Therefore, we need to statistically analyze the simulation results. It is not sufficient to come up with a point estimate, but there is a need, for example, to construct a confidence interval (CI) for the random variable of interest. From the perspective of output analysis, we can classify simulations under two categories. 1. Terminating simulation: We are interested in performance of a system that starts with some specific conditions and terminates upon occurrence of a specific event. For example, Most service systems start the day empty and idle, continue accepting customers until a specific time, and are closed after completing service of these customers. (An exception is hospital emergency rooms.) Combat starts with a certain weapon and ammunition availability, and ends when attrition goals are satisfied or ammunition are consumed. 2. Steadystate simulation: We are interested in performance of a system as time approaches infinity. For example, although they shot down at the end of the day, many manufacturing systems can be assumed to operate continuously because their operation starts in the morning from where it was left the previous evening. Analysis of steadystate simulations is much more difficult. 2 Review: Assumptions of Estimation Normality Assumption Given a population with unknown mean μ and known variance 2 σ , we can construct a CI for the mean as 1 / 2 X z n α σ ± where X is the average of a random (iid) sample of size n . If population is nonnormal, CI is not accurate with small n (say 30 n < ). If population is nonnormal but n is sufficiently large (say 30 n ≥ ), CI is still good by Central Limit Theorem (CLT). If population variance 2 σ is unknown, we can construct a CI for the mean as 1, 1 / 2 n s X t n α ± where X and 2 s are the average and variance of a random sample of size n . We can use the student t distribution if population is normal. If population is nonnormal but n is sufficiently large (say 30 n ≥ ), we can approximate the CI as 1 / 2 s X z n α ± , again by exploiting the CLT. Independence Assumption If the sample used in calculating X and 2 s is iid then ( ) E X μ = and 2 2 ( ) E s σ = , i.e. X and 2 s are unbiased estimators of μ and 2 σ . If the sample is correlated X is still an unbiased estimator of μ . If individual observations in the sample are positively correlated then 2 2 ( ) E s σ < , i.e. 2 s underestimates 2 σ and CI becomes narrower then it should be....
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This note was uploaded on 05/23/2010 for the course IE 372 taught by Professor T during the Spring '10 term at Middle East Technical University.
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