IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v61y2014i3p223-237.html
   My bibliography  Save this article

A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts

Author

Listed:
  • Lianjie Shu
  • Wenpo Huang
  • Wei Jiang

Abstract

Conventional control charts are often designed to optimize out‐of‐control average run length (ARL), while constraining in‐control ARL to a desired value. The widely employed grid search approach in statistical process control (SPC) is time‐consuming with unsatisfactory accuracy. Although the simulation‐based ARL gradient estimators proposed by Fu and Hu [Manag Sci 45 (1999), 395–413] can alleviate this issue, it still requires a large number of simulation runs to significantly reduce the variance of gradient estimators. This article proposes a novel ARL gradient estimation approach based on integral equation for efficient analysis and design of control charts. Although this article compares with the results of Fu and Hu [Manag Sci 45 (1999), 395–413] based on the exponentially weighted moving average (EWMA) control chart, the proposed approach has wide applicability as it can generally fit into any control chart with Markovian property under any distributions. It is shown that the proposed method is able to provide a fast, accurate, and easy‐to‐implement algorithm for the design and analysis of EWMA charts, as compared to the simulation‐based gradient estimation method. Moreover, the proposed gradient estimation method facilitates the computation of high‐order derivatives that are valuable in sensitivity analysis. The code is written in Matlab, which is available on request. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 223–237, 2014

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:3:p:223-237
    DOI: 10.1002/nav.21579
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21579
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21579?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Rigdon, Steven E., 1995. "A double-integral equation for the average run length of a multivariate exponentially weighted moving average control chart," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 365-373, September.
    2. Wenpo Huang & Lianjie Shu & Wei Jiang & Kwok-Leung Tsui, 2013. "Evaluation of run-length distribution for CUSUM charts under gamma distributions," IISE Transactions, Taylor & Francis Journals, vol. 45(9), pages 981-994.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Amir Ahmadi-Javid & Mohsen Ebadi, 2017. "Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)," Papers 1708.06160, arXiv.org.
    4. 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.
    5. Amir Ahmadi-Javid & Mohsen Ebadi, 2021. "Economic design of memory-type control charts: The fallacy of the formula proposed by Lorenzen and Vance (1986)," Computational Statistics, Springer, vol. 36(1), pages 661-690, March.
    6. 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.
    7. 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.
    8. Ming Lee & Michael Khoo, 2014. "Design of a multivariate exponentially weighted moving average control chart with variable sampling intervals," Computational Statistics, Springer, vol. 29(1), pages 189-214, February.
    9. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:61:y:2014:i:3:p:223-237. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.