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An Improved Batch Means Procedure for Simulation Output Analysis

Author

Listed:
  • Natalie M. Steiger

    (Maine Business School, University of Maine, Orono, Maine 04469)

  • James R. Wilson

    (Department of Industrial Engineering, North Carolina State University, Raleigh, North Carolina 27695)

Abstract

We formulate and evaluate the Automated Simulation Analysis Procedure (ASAP), an algorithm for steady-state simulation output analysis based on the method of nonover-lapping batch means (NOBM). ASAP delivers a confidence interval for an expected response that is centered on the sample mean of a portion of a simulation-generated time series and satisfies a user-specified absolute or relative precision requirement. ASAP operates as follows: The batch size is progressively increased until either (a) the batch means pass the von Neumann test for independence, and then ASAP delivers a classical NOBM confidence interval; or (b) the batch means pass the Shapiro-Wilk test for multivariate normality, and then ASAP delivers a correlation-adjusted confidence interval. The latter adjustment is based on an inverted Cornish-Fisher expansion for the classical NOBM t-ratio, where the terms of the expansion are estimated via an autoregressive-moving average time series model of the batch means. After determining the batch size and confidence-interval type, ASAP sequentially increases the number of batches until the precision requirement is satisfied. An extensive experimental study demonstrates the performance improvements achieved by ASAP versus well-known batch means procedures, especially in confidence-interval coverage probability.

Suggested Citation

  • Natalie M. Steiger & James R. Wilson, 2002. "An Improved Batch Means Procedure for Simulation Output Analysis," Management Science, INFORMS, vol. 48(12), pages 1569-1586, December.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:12:p:1569-1586
    DOI: 10.1287/mnsc.48.12.1569.438
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    References listed on IDEAS

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    1. Natalie M. Steiger & James R. Wilson, 2001. "Convergence Properties of the Batch Means Method for Simulation Output Analysis," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 277-293, November.
    2. R. W. Conway, 1963. "Some Tactical Problems in Digital Simulation," Management Science, INFORMS, vol. 10(1), pages 47-61, October.
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    6. George S. Fishman & L. Stephen Yarberry, 1997. "An Implementation of the Batch Means Method," INFORMS Journal on Computing, INFORMS, vol. 9(3), pages 296-310, August.
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    Cited by:

    1. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    2. Ali Tafazzoli & James R. Wilson & Emily K. Lada & Natalie M. Steiger, 2011. "Performance of Skart: A Skewness- and Autoregression-Adjusted Batch Means Procedure for Simulation Analysis," INFORMS Journal on Computing, INFORMS, vol. 23(2), pages 297-314, May.
    3. Yuanhui Zhang & Haipeng Wu & Brian T. Denton & James R. Wilson & Jennifer M. Lobo, 2019. "Probabilistic sensitivity analysis on Markov models with uncertain transition probabilities: an application in evaluating treatment decisions for type 2 diabetes," Health Care Management Science, Springer, vol. 22(1), pages 34-52, March.
    4. Barry L. Nelson, 2004. "50th Anniversary Article: Stochastic Simulation Research in Management Science," Management Science, INFORMS, vol. 50(7), pages 855-868, July.
    5. Dashi I. Singham & Lee W. Schruben, 2012. "Finite-Sample Performance of Absolute Precision Stopping Rules," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 624-635, November.
    6. Emily K. Lada & James R. Wilson & Natalie M. Steiger & Jeffrey A. Joines, 2007. "Performance of a Wavelet-Based Spectral Procedure for Steady-State Simulation Analysis," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 150-160, May.

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