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Efficient Design and Sensitivity Analysis of Control Charts Using Monte Carlo Simulation

Author

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  • Michael C. Fu

    (The Robert H. Smith School of Business, Institute for Systems Research, University of Maryland, College Park, Maryland 20742-1815)

  • Jian-Qiang Hu

    (Department of Manufacturing Engineering, Boston University, Boston, Massachusetts 02215)

Abstract

The design of control charts in statistical quality control addresses the optimal selection of the design parameters (such as the sampling frequency and the control limits) and includes sensitivity analysis with respect to system parameters (such as the various process parameters and the economic costs of sampling). The advent of more complicated control chart schemes has necessitated the use of Monte Carlo simulation in the design process, especially in the evaluation of performance measures such as average run length. In this paper, we apply two gradient estimation procedures---perturbation analysis and the likelihood ratio/score function method---to derive estimators that can be used in gradient-based optimization algorithms and in sensitivity analysis when Monte Carlo simulation is employed. We illustrate the techniques on a general control chart that includes the Shewhart chart and the exponentially-weighted moving average chart as special cases. Simulation examples comparing the estimators with each other and with "brute force" finite differences demonstrate the possibility of significant variance reduction in settings of practical interest.

Suggested Citation

  • Michael C. Fu & Jian-Qiang Hu, 1999. "Efficient Design and Sensitivity Analysis of Control Charts Using Monte Carlo Simulation," Management Science, INFORMS, vol. 45(3), pages 395-413, March.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:3:p:395-413
    DOI: 10.1287/mnsc.45.3.395
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    Citations

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    Cited by:

    1. Hachicha, Wafik & Ammeri, Ahmed & Masmoudi, Faouzi & Chachoub, Habib, 2010. "A comprehensive literature classification of simulation optimisation methods," MPRA Paper 27652, University Library of Munich, Germany.
    2. Ozdemir, Deniz & Yucesan, Enver & Herer, Yale T., 2006. "Multi-location transshipment problem with capacitated transportation," European Journal of Operational Research, Elsevier, vol. 175(1), pages 602-621, November.
    3. Lianjie Shu & Wenpo Huang & Wei Jiang, 2014. "A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 223-237, April.
    4. Gong, Y. & Yucesan, E., 2006. "The Multi-Location Transshipment Problem with Positive Replenishment Lead Times," ERIM Report Series Research in Management ERS-2006-048-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. Zhenyu Cui & Michael C. Fu & Jian-Qiang Hu & Yanchu Liu & Yijie Peng & Lingjiong Zhu, 2020. "On the Variance of Single-Run Unbiased Stochastic Derivative Estimators," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 390-407, April.
    6. Özdemir, Deniz & Yücesan, Enver & Herer, Yale T., 2013. "Multi-location transshipment problem with capacitated production," European Journal of Operational Research, Elsevier, vol. 226(3), pages 425-435.
    7. Michael C. Fu, 2008. "What you should know about simulation and derivatives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 723-736, December.

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