IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i18p2211-d632282.html
   My bibliography  Save this article

On the Use of Copula for Quality Control Based on an AR(1) Model

Author

Listed:
  • Timothy M. Young

    (Center for Renewable Carbon, The University of Tennessee, 2506 Jacob Drive, Knoxville, TN 37996-4563, USA)

  • Ampalavanar Nanthakumar

    (Department of Mathematics, State University of New York at Oswego, Oswego, NY 13126, USA)

  • Hari Nanthakumar

    (Department of Economics and mathematics, Columbia University, New York, NY 10027, USA)

Abstract

Manufacturing for a multitude of continuous processing applications in the era of automation and ‘Industry 4.0’ is focused on rapid throughput while producing products of acceptable quality that meet customer specifications. Monitoring the stability or statistical control of key process parameters using data acquired from online sensors is fundamental to successful automation in manufacturing applications. This study addresses the significant problem of positive autocorrelation in data collected from online sensors, which may impair assessment of statistical control. Sensor data collected at short time intervals typically have significant autocorrelation, and traditional statistical process control (SPC) techniques cannot be deployed. There is a plethora of literature on techniques for SPC in the presence of positive autocorrelation. This paper contributes to this area of study by investigating the performance of ‘Copula’ based control charts by assessing the average run length (ARL) when the subsequent observations are correlated and follow the AR(1) model. The conditional distribution of y t given y t − 1 is used in deriving the control chart limits for three different categories of Copulas: Gaussian, Clayton, and Farlie-Gumbel-Morgenstern Copulas. Preliminary results suggest that the overall performance of the Clayton Copula and Farlie-Gumbel-Morgenstern Copula is better compared to other Archimedean Copulas. The Clayton Copula is the more robust with respect to changes in the process standard deviation as the correlation coefficient increases.

Suggested Citation

  • Timothy M. Young & Ampalavanar Nanthakumar & Hari Nanthakumar, 2021. "On the Use of Copula for Quality Control Based on an AR(1) Model," Mathematics, MDPI, vol. 9(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2211-:d:632282
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/18/2211/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/18/2211/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yongxin Liao & Fernando Deschamps & Eduardo de Freitas Rocha Loures & Luiz Felipe Pierin Ramos, 2017. "Past, present and future of Industry 4.0 - a systematic literature review and research agenda proposal," International Journal of Production Research, Taylor & Francis Journals, vol. 55(12), pages 3609-3629, June.
    2. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    3. Everette S. Gardner, Jr. & Ed. Mckenzie, 1985. "Forecasting Trends in Time Series," Management Science, INFORMS, vol. 31(10), pages 1237-1246, October.
    4. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
    5. So, Mike K.P. & Yeung, Cherry Y.T., 2014. "Vine-copula GARCH model with dynamic conditional dependence," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 655-671.
    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. Zhang, Bangzheng & Wei, Yu & Yu, Jiang & Lai, Xiaodong & Peng, Zhenfeng, 2014. "Forecasting VaR and ES of stock index portfolio: A Vine copula method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 112-124.
    2. Quanrui Song & Jianxu Liu & Songsak Sriboonchitta, 2019. "Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    3. BenSaïda, Ahmed, 2018. "The contagion effect in European sovereign debt markets: A regime-switching vine copula approach," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 153-165.
    4. Zhou, Rui & Ji, Min, 2021. "Modelling mortality dependence: An application of dynamic vine copula," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 241-255.
    5. Han, Xuyuan & Liu, Zhenya & Wang, Shixuan, 2022. "An R-vine copula analysis of non-ferrous metal futures with application in Value-at-Risk forecasting," Journal of Commodity Markets, Elsevier, vol. 25(C).
    6. Han, Yingwei & Li, Jie, 2022. "Should investors include green bonds in their portfolios? Evidence for the USA and Europe," International Review of Financial Analysis, Elsevier, vol. 80(C).
    7. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, vol. 4(4), pages 1-15, October.
    8. Chu, Amanda M.Y. & Ip, Chun Yin & Lam, Benson S.Y. & So, Mike K.P., 2022. "Vine copula statistical disclosure control for mixed-type data," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    9. Jianxu Liu & Mengjiao Wang & Songsak Sriboonchitta, 2019. "Examining the Interdependence between the Exchange Rates of China and ASEAN Countries: A Canonical Vine Copula Approach," Sustainability, MDPI, vol. 11(19), pages 1-20, October.
    10. Acar, Elif F. & Czado, Claudia & Lysy, Martin, 2019. "Flexible dynamic vine copula models for multivariate time series data," Econometrics and Statistics, Elsevier, vol. 12(C), pages 181-197.
    11. DAVID E. ALLEN & MICHAEL McALEER & ROBERT J. POWELL & ABHAY K. SINGH, 2018. "Non-Parametric Multiple Change Point Analysis Of The Global Financial Crisis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 1-23, June.
    12. Rand Kwong Yew Low, 2018. "Vine copulas: modelling systemic risk and enhancing higher‐moment portfolio optimisation," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(S1), pages 423-463, November.
    13. Roger M. Cooke & Harry Joe & Bo Chang, 2020. "Vine copula regression for observational studies," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 141-167, June.
    14. Madden, Gary & Tan, Joachim, 2007. "Forecasting telecommunications data with linear models," Telecommunications Policy, Elsevier, vol. 31(1), pages 31-44, February.
    15. Sony, Michael & Naik, Subhash, 2020. "Industry 4.0 integration with socio-technical systems theory: A systematic review and proposed theoretical model," Technology in Society, Elsevier, vol. 61(C).
    16. Sleire, Anders D. & Støve, Bård & Otneim, Håkon & Berentsen, Geir Drage & Tjøstheim, Dag & Haugen, Sverre Hauso, 2022. "Portfolio allocation under asymmetric dependence in asset returns using local Gaussian correlations," Finance Research Letters, Elsevier, vol. 46(PB).
    17. Joanna Wyrwa, 2020. "A review of the European Union financial instruments supporting the innovative activity of enterprises in the context of Industry 4.0 in the years 2021-2027," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 8(1), pages 1146-1161, September.
    18. Armstrong, J. Scott & Green, Kesten C. & Graefe, Andreas, 2015. "Golden rule of forecasting: Be conservative," Journal of Business Research, Elsevier, vol. 68(8), pages 1717-1731.
    19. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    20. Zhang, Dalu, 2014. "Vine copulas and applications to the European Union sovereign debt analysis," International Review of Financial Analysis, Elsevier, vol. 36(C), pages 46-56.

    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:gam:jmathe:v:9:y:2021:i:18:p:2211-:d:632282. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.