IDEAS home Printed from https://ideas.repec.org/a/taf/tprsxx/v54y2016i17p5073-5094.html
   My bibliography  Save this article

Optimal exponentially weighted moving average charts with estimated parameters based on median run length and expected median run length

Author

Listed:
  • H.W. You
  • Michael B.C. Khoo
  • P. Castagliola
  • Liang Qu

Abstract

This paper examines the exponentially weighted moving average (EWMA) chart with estimated process parameters. As the run length distribution is skewed when the process is in-control or slightly out-of-control, the average run length (ARL) provides less meaningful interpretation of a chart’s performance. Therefore, in this paper, the median run length (MRL) and expected MRL (EMRL) are used as alternative performance criteria. Additionally, the methodology for computing the EMRL of the EWMA chart with known process parameters is presented. Since the performance of the EWMA chart is affected by estimation error, a study on the minimum number of Phase-I samples required so that the chart with estimated parameters has a desired performance is conducted. As this study reveals that a large number of Phase-I samples are needed, optimal design procedures for minimising the out-of-control MRL and EMRL of the EWMA chart with estimated process parameters are suggested. By using these proposed procedures, the EWMA chart with estimated parameters will have a closer performance to its known parameters counterpart, even with a reasonable number of Phase-I samples. The construction of the MRL based EWMA chart with estimated parameters is illustrated using real data and compared with the corresponding chart based on ARL.

Suggested Citation

  • H.W. You & Michael B.C. Khoo & P. Castagliola & Liang Qu, 2016. "Optimal exponentially weighted moving average charts with estimated parameters based on median run length and expected median run length," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5073-5094, September.
  • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:17:p:5073-5094
    DOI: 10.1080/00207543.2016.1145820
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207543.2016.1145820
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/00207543.2016.1145820?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Khoo, Michael B.C. & Teoh, W.L. & Castagliola, Philippe & Lee, M.H., 2013. "Optimal designs of the double sampling X¯ chart with estimated parameters," International Journal of Production Economics, Elsevier, vol. 144(1), pages 345-357.
    2. Shichang Du & Xufeng Yao & Delin Huang, 2015. "Engineering model-based Bayesian monitoring of ramp-up phase of multistage manufacturing process," International Journal of Production Research, Taylor & Francis Journals, vol. 53(15), pages 4594-4613, August.
    3. Ying Zhang & Philippe Castagliola & Zhang Wu & Michael Khoo, 2011. "The synthetic [Xbar] chart with estimated parameters," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 676-687.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Moi Hua Tuh & Cynthia Mui Lian Kon & Hong Siang Chua & Man Fai Lau & Yee Hui Robin Chang, 2023. "Evaluating the Performance of Synthetic Double Sampling np Chart Based on Expected Median Run Length," Mathematics, MDPI, vol. 11(3), pages 1-23, January.

    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. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
    2. Axel Gandy & Jan Terje Kvaløy, 2013. "Guaranteed Conditional Performance of Control Charts via Bootstrap Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 647-668, December.
    3. Zhang, Min & Nie, Guohua & He, Zhen, 2014. "Performance of cumulative count of conforming chart of variable sampling intervals with estimated control limits," International Journal of Production Economics, Elsevier, vol. 150(C), pages 114-124.
    4. Jinho Kim & Myong K. Jeong & Elsayed A. Elsayed, 2017. "Monitoring multistage processes with autocorrelated observations," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2385-2396, April.
    5. H. You & Michael Khoo & P. Castagliola & Yanjing Ou, 2015. "Side sensitive group runs $$\bar{{X}}$$ X ¯ chart with estimated process parameters," Computational Statistics, Springer, vol. 30(4), pages 1245-1278, December.
    6. Lei Yong Lee & Michael Boon Chong Khoo & Sin Yin Teh & Ming Ha Lee, 2015. "A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-18, May.
    7. Zhou, Chengyu & Fang, Xiaolei, 2023. "A convex two-dimensional variable selection method for the root-cause diagnostics of product defects," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    8. Chang-Ho Lee & Dong-Hee Lee & Young-Mok Bae & Seung-Hyun Choi & Ki-Hun Kim & Kwang-Jae Kim, 2022. "Approach to derive golden paths based on machine sequence patterns in multistage manufacturing process," Journal of Intelligent Manufacturing, Springer, vol. 33(1), pages 167-183, January.
    9. Sangahn Kim & Mehmet Turkoz, 2022. "Bayesian sequential update for monitoring and control of high-dimensional processes," Annals of Operations Research, Springer, vol. 317(2), pages 693-715, October.

    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:taf:tprsxx:v:54:y:2016:i:17:p:5073-5094. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TPRS20 .

    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.