Variance Estimation

# Variance Estimation - Output Analysis Variance Estimation...

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Output Analysis: Variance Estimation IE680 Output Analysis : Variance Estimation Output Analysis: Variance Estimation Jong-hyun Ryu 1

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Output Analysis: Variance Estimation IE680 Contents Motivation (Quality Control Chart) Collecting output data Type of simulations Steady-State Simulation Stochastic Stationary Process Variance Estimation Methods Replication Method Batch mean methods Non-overlapping vs. Overlapping Standardized Time Series Additional Methods 2
Output Analysis: Variance Estimation IE680 Motivation Quality Control Chart Simple Control Chart (Shewhart Control Chart) Design of Shewhart Control Chart Control Limits Results from incorrect control limits If overestimated detection delay If underestimated high false alarm rate Estimating process variance (standard deviation) is critical. ˆ 3 ˆ 3 UCL x LCL x σ = + = - 3

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Output Analysis: Variance Estimation IE680 Type of simulations Terminating vs. non-terminating simulations Terminating simulations Runs for some duration of time T E , where E is a specified event that stops the simulation. Starts at time 0 under well-specified initial conditions. Ends at the stopping time T E . Bank example: Opens at 8:30 am (time 0) with no customers present and 8 of the 11 teller working (initial conditions), and closes at 4:30 pm (T e ) The simulation analyst chooses to consider it a terminating system because the object of interest is one day’s operation. 4
Output Analysis: Variance Estimation IE680 Type of simulations Non-terminating simulation Runs continuously, or at least over a very long period of time. Examples: assembly lines that shut down infrequently, telephone systems, hospital emergency rooms. Initial conditions defined by the analyst. Runs for some analyst-specified period of time T E . Study the steady-state (long-run) properties of the system, properties that are not influenced by the initial conditions of the model. Terminating or non-terminating The objectives of the simulation study The nature of the system. 5

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Output Analysis: Variance Estimation IE680 Output Analysis for Steady-State Simulation Consider a single run of a simulation model to estimate a steady-state or long-run characteristics of the system. The single run produces observations Y1, Y2, . .. (generally the samples of an autocorrelated time series). Performance measures: Point estimator and confidence interval Independent of the initial conditions 6
Estimation IE680 Output Analysis for Steady-State Simulation The sample size is a design choice, with several considerations in mind: Any bias in the point estimator that is due to artificial or arbitrary initial conditions (bias can be severe if run length is too short). Desired precision of the point estimator.

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Variance Estimation - Output Analysis Variance Estimation...

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