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Confidence Intervals for Steady-State Simulations: I. A Survey of Fixed Sample Size Procedures

Author

Listed:
  • Averill M. Law

    (University of Arizona, Tucson, Arizona)

  • W. David Kelton

    (The University of Michigan, Ann Arbor, Michigan)

Abstract

We consider the problem of constructing a confidence interval for the steady-state mean of a stochastic process by means of simulation, and study the five main methods which have been proposed (replication, batch means, autoregressive representation, spectrum analysis, and regeneration cycles) for the case when the length of the simulation is fixed in advance. Comparing the performances of these methods on stochastic models with known steady-state means, we find that the simulator should exercise caution in interpreting the results from a simulation of fixed length, and that the length of a simulation adequate for acceptable performance is highly model-dependent. We also investigate possible sources of error for the methods, and conclude that variance estimator bias is more important than point estimator bias in confidence interval coverage degradation.

Suggested Citation

  • Averill M. Law & W. David Kelton, 1984. "Confidence Intervals for Steady-State Simulations: I. A Survey of Fixed Sample Size Procedures," Operations Research, INFORMS, vol. 32(6), pages 1221-1239, December.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:6:p:1221-1239
    DOI: 10.1287/opre.32.6.1221
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    Cited by:

    1. T. S. Raghu & P. K. Sen & H. R. Rao, 2003. "Relative Performance of Incentive Mechanisms: Computational Modeling and Simulation of Delegated Investment Decisions," Management Science, INFORMS, vol. 49(2), pages 160-178, February.
    2. El-Bouri, Ahmed & Balakrishnan, Subramaniam & Popplewell, Neil, 2008. "Cooperative dispatching for minimizing mean flowtime in a dynamic flowshop," International Journal of Production Economics, Elsevier, vol. 113(2), pages 819-833, June.
    3. K Hoad & S Robinson & R Davies, 2010. "Automated selection of the number of replications for a discrete-event simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1632-1644, November.
    4. George, Halkos & Ilias, Kevork, 2004. "H Ασυμπτωτική Διακύμανση Στην Εκτίμηση Του Στάσιμου Μέσου Υπό Συνθήκες Αυτοσυσχέτισης [Using the asymptotic variance to estimate the stationary mean under autocorrelation]," MPRA Paper 33324, University Library of Munich, Germany.
    5. Halkos, George & Kevork, Ilias, 2002. "Confidence intervals in stationary autocorrelated time series," MPRA Paper 31840, University Library of Munich, Germany.
    6. Halkos, George & Kevork, Ilias, 2006. "Estimating population means in covariance stationary process," MPRA Paper 31843, University Library of Munich, Germany.
    7. Holthaus, Oliver & Rajendran, Chandrasekharan, 1997. "Efficient dispatching rules for scheduling in a job shop," International Journal of Production Economics, Elsevier, vol. 48(1), pages 87-105, January.
    8. Yu Hang Jiang & Tong Liu & Zhiya Lou & Jeffrey S. Rosenthal & Shanshan Shangguan & Fei Wang & Zixuan Wu, 2022. "Markov Chain Confidence Intervals and Biases," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(1), pages 1-29, March.
    9. L. Lambertini & R. Orsini, 1998. "Monopoly, Quality, and Network Externalities," Working Papers 334, Dipartimento Scienze Economiche, Universita' di Bologna.
    10. Rajendran, Chandrasekharan & Holthaus, Oliver, 1999. "A comparative study of dispatching rules in dynamic flowshops and jobshops," European Journal of Operational Research, Elsevier, vol. 116(1), pages 156-170, July.

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