IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v44y2017i11p2075-2093.html
   My bibliography  Save this article

A distribution-free multivariate CUSUM control chart using dynamic control limits

Author

Listed:
  • Wenjuan Liang
  • Xiaolong Pu
  • Dongdong Xiang

Abstract

In modern quality control, it is becoming common to simultaneously monitor several quality characteristics of a process with rapid evolving data-acquisition technology. When the multivariate process distribution is unknown and only a set of in-control data is available, the bootstrap technique can be used to adjust the constant limit of the multivariate cumulative sum (MCUSUM) control chart. To further improve the performance of the control chart, we extend the constant control limit to a sequence of dynamic control limits which are determined by the conditional distribution of the charting statistics given the sprint length. Simulation results show that the novel control chart with dynamic control limits offers a better ARL performance, compared with the traditional MCUSUM control chart. Despite it, the proposed control chart is considerably computer-intensive. This leads to the development of a more flexible control chart which uses a continuous function of the sprint length as the control limit sequences. More importantly, the control chart is easy to implement and can reduce the computational time significantly. A white wine data illustrates that the novel control chart performs quite well in applications.

Suggested Citation

  • Wenjuan Liang & Xiaolong Pu & Dongdong Xiang, 2017. "A distribution-free multivariate CUSUM control chart using dynamic control limits," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2075-2093, August.
  • Handle: RePEc:taf:japsta:v:44:y:2017:i:11:p:2075-2093
    DOI: 10.1080/02664763.2016.1247784
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2016.1247784
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664763.2016.1247784?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. Han, Dong & Tsung, Fugee, 2006. "A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 368-386, March.
    2. Xiaobei Shen & Changliang Zou & Wei Jiang & Fugee Tsung, 2013. "Monitoring poisson count data with probability control limits when sample sizes are time varying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 625-636, December.
    3. Margavio, Thomas M. & Conerly, Michael D. & Woodall, William H. & Drake, Laurel G., 1995. "Alarm rates for quality control charts," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 219-224, August.
    4. Qin Zhou & Changliang Zou & Zhaojun Wang & Wei Jiang, 2012. "Likelihood-Based EWMA Charts for Monitoring Poisson Count Data With Time-Varying Sample Sizes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1049-1062, September.
    5. Liu, Yafen & He, Zhen & Shu, Lianjie & Wu, Zhang, 2009. "Statistical computation and analyses for attribute events," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3412-3425, July.
    6. Bersimis, Sotiris & Psarakis, Stelios & Panaretos, John, 2006. "Multivariate Statistical Process Control Charts: An Overview," MPRA Paper 6399, University Library of Munich, Germany.
    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. Chi Zhang & Fugee Tsung & Dongdong Xiang, 2016. "Monitoring censored lifetime data with a weighted‐likelihood scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 631-646, December.
    2. Xiaobei Shen & Changliang Zou & Wei Jiang & Fugee Tsung, 2013. "Monitoring poisson count data with probability control limits when sample sizes are time varying," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 625-636, December.
    3. Ali, Sajid & Pievatolo, Antonio, 2018. "Time and magnitude monitoring based on the renewal reward process," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 97-107.
    4. Molly C. Klanderman & Kathryn B. Newhart & Tzahi Y. Cath & Amanda S. Hering, 2020. "Fault isolation for a complex decentralized waste water treatment facility," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 931-951, August.
    5. Zhou, Qin & Luo, Yunzhao & Wang, Zhaojun, 2010. "A control chart based on likelihood ratio test for detecting patterned mean and variance shifts," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1634-1645, June.
    6. Seven Knoth, 2005. "Fast initial response features for EWMA control charts," Statistical Papers, Springer, vol. 46(1), pages 47-64, January.
    7. Linus Schiöler & Marianne Fris�n, 2012. "Multivariate outbreak detection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 223-242, April.
    8. Bersimis, Sotiris & Koutras, Markos V. & Maravelakis, Petros E., 2014. "A compound control chart for monitoring and controlling high quality processes," European Journal of Operational Research, Elsevier, vol. 233(3), pages 595-603.
    9. Guanfu Liu & Xiaolong Pu & Lei Wang & Dongdong Xiang, 2015. "CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1635-1644, August.
    10. Wen-An Yang, 2016. "Simultaneous monitoring of mean vector and covariance matrix shifts in bivariate manufacturing processes using hybrid ensemble learning-based model," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 845-874, August.
    11. Muhammad Ali Raza & Komal Iqbal & Muhammad Aslam & Tahir Nawaz & Sajjad Haider Bhatti & Gideon Mensah Engmann, 2023. "Mixed Exponentially Weighted Moving Average—Moving Average Control Chart with Application to Combined Cycle Power Plant," Sustainability, MDPI, vol. 15(4), pages 1-17, February.
    12. Minya Xu & Ping-Shou Zhong & Wei Wang, 2016. "Detecting Variance Change-Points for Blocked Time Series and Dependent Panel Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 213-226, April.
    13. Rafajlowicz, Ewaryst & Pawlak, Mirosław & Steland, Ansgar, 2004. "Non-parametric vertical box control chart for monitoring the mean," Technical Reports 2004,52, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Nishimura, Kazuya & Matsuura, Shun & Suzuki, Hideo, 2015. "Multivariate EWMA control chart based on a variable selection using AIC for multivariate statistical process monitoring," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 7-13.
    15. Marianne Frisen & Eva Andersson & Linus Schioler, 2010. "Evaluation of multivariate surveillance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 2089-2100.
    16. Frisén, Marianne & Andersson, Eva & Schiöler, Linus, 2009. "Sufficient reduction in multivariate surveillance," Research Reports 2009:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    17. Bei Wang & Xuefeng Yan, 2019. "Real-time monitoring of chemical processes based on variation information of principal component analysis model," Journal of Intelligent Manufacturing, Springer, vol. 30(2), pages 795-808, February.
    18. Sotirios Bersimis & Stavros Degiannakis & Dimitrios Georgakellos, 2017. "Real-time monitoring of carbon monoxide using value-at-risk measure and control charting," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 89-108, January.
    19. Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
    20. Sotiris Bersimis & Kostas Triantafyllopoulos, 2020. "Dynamic Non-parametric Monitoring of Air-Pollution," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1457-1479, December.

    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:japsta:v:44:y:2017:i:11:p:2075-2093. 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/CJAS20 .

    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.