IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v42y2015i8p1635-1644.html
   My bibliography  Save this article

CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid

Author

Listed:
  • Guanfu Liu
  • Xiaolong Pu
  • Lei Wang
  • Dongdong Xiang

Abstract

It is often encountered in the literature that the log-likelihood ratios (LLR) of some distributions (e.g. the student t distribution) are not monotonic. Existing charts for monitoring such processes may suffer from the fact that the average run length (ARL) curve is a discontinuous function of control limit. It implies that some pre-specified in-control (IC) ARLs of these charts may not be reached. To guarantee the false alarm rate of a control chart lower than the nominal level, a larger IC ARL is usually suggested in the literature. However, the large IC ARL may weaken the performance of a control chart when the process is out-of-control (OC), compared with a just right IC ARL. To overcome it, we adjust the LLR to be a monotonic one in this paper. Based on it, a multiple CUSUM chart is developed to detect range shifts in IC distribution. Theoretical result in this paper ensures the continuity of its ARL curve. Numerical results show our proposed chart performs well under the range shifts, especially under the large shifts. In the end, a real data example is utilized to illustrate our proposed chart.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:8:p:1635-1644
    DOI: 10.1080/02664763.2015.1004625
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2015.1004625
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2015.1004625?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. Jian Li & Fugee Tsung & Changliang Zou, 2013. "Directional change‐point detection for process control with multivariate categorical data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(2), pages 160-173, March.
    3. Luo, Yunzhao & Li, Zhonghua & Wang, Zhaojun, 2009. "Adaptive CUSUM control chart with variable sampling intervals," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2693-2701, May.
    4. MacEachern, Steven N. & Rao, Youlan & Wu, Chunjie, 2007. "A Robust-Likelihood Cumulative Sum Chart," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1440-1447, December.
    5. P. J. Harrison, 1999. "Statistical process control and model monitoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(2), pages 273-292.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Trevor Harris & Bo Li & J. Derek Tucker, 2022. "Scalable multiple changepoint detection for functional data sequences," Environmetrics, John Wiley & Sons, Ltd., vol. 33(2), March.
    7. 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.
    8. Zhonghua Li & Peihua Qiu & Snigdhansu Chatterjee & Zhaojun Wang, 2013. "Using p values to design statistical process control charts," Statistical Papers, Springer, vol. 54(2), pages 523-539, May.
    9. Salvador, Manuel & Gargallo, Pilar, 2004. "Automatic monitoring and intervention in multivariate dynamic linear models," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 401-431, October.
    10. 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.
    11. Unarine Netshiozwi & Ali Yeganeh & Sandile Charles Shongwe & Ahmad Hakimi, 2023. "Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme," Mathematics, MDPI, vol. 11(17), pages 1-23, August.
    12. Douglas M. Hawkins & F. Lombard, 2017. "Cusum control for data following the von Mises distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1319-1332, June.
    13. Lee, Pei-Hsi, 2011. "Adaptive R charts with variable parameters," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 2003-2010, May.
    14. Muhammad Riaz & Babar Zaman & Ishaq Adeyanju Raji & M. Hafidz Omar & Rashid Mehmood & Nasir Abbas, 2022. "An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector," Mathematics, MDPI, vol. 10(12), pages 1-27, June.
    15. Manuel Salvador & Pilar Gargallo, 2003. "Automatic selective intervention in dynamic linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1161-1184.
    16. Pei-Hsi Lee & Yi-Hsien Huang & Tsen-I Kuo & Ching-Cheng Wang, 2013. "The effect of the individual chart with variable control limits on the river pollution monitoring," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(4), pages 1803-1812, June.
    17. Mengchen Wang & Trevor Harris & Bo Li, 2023. "Asynchronous Changepoint Estimation for Spatially Correlated Functional Time Series," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 157-176, March.

    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:42:y:2015:i:8:p:1635-1644. 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.