IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v31y2004i3p317-327.html
   My bibliography  Save this article

Multivariate Quality Control Chart for Autocorrelated Processes

Author

Listed:
  • A. A. Kalgonda
  • S. R. Kulkarni

Abstract

Traditional multivariate statistical process control (SPC) techniques are based on the assumption that the successive observation vectors are independent. In recent years, due to automation of measurement and data collection systems, a process can be sampled at higher rates, which ultimately leads to autocorrelation. Consequently, when the autocorrelation is present in the data, it can have a serious impact on the performance of classical control charts. This paper considers the problem of monitoring the mean vector of a process in which observations can be modelled as a first-order vector autoregressive VAR (1) process. We propose a control chart called Z-chart which is based on the single step finite intersection test (Timm, 1996). An important feature of the proposed method is that it not only detects an out of control status but also helps in identifying variable(s) responsible for the out of control situation. The proposed method is illustrated with the help of suitable illustrations.

Suggested Citation

  • A. A. Kalgonda & S. R. Kulkarni, 2004. "Multivariate Quality Control Chart for Autocorrelated Processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(3), pages 317-327.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:3:p:317-327
    DOI: 10.1080/0266476042000184000
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/0266476042000184000
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/0266476042000184000?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. 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.
    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. Jeffrey E. Jarrett & Xia Pan, 2007. "Monitoring Variability and Analyzing Multivariate Autocorrelated Processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(4), pages 459-469.
    2. 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.
    3. Bock, David, 2007. "Consequences of using the probability of a false alarm as the false alarm measure," Research Reports 2007:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    4. Jeffrey Jarrett, 2014. "The quality movement in hospital care," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3153-3167, November.
    5. Roberto Campos Leoni & Marcela Aparecida Guerreiro Machado & Antonio Fernando Branco Costa, 2016. "The T -super-2 chart with mixed samples to control bivariate autocorrelated processes," International Journal of Production Research, Taylor & Francis Journals, vol. 54(11), pages 3294-3310, June.
    6. David Bock, 2008. "Aspects on the control of false alarms in statistical surveillance and the impact on the return of financial decision systems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 213-227.
    7. E. Andersson & D. Bock & M. Frisen, 2006. "Some statistical aspects of methods for detection of turning points in business cycles," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 257-278.
    8. Leoni, Roberto Campos & Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2015. "The effect of the autocorrelation on the performance of the T2 chart," European Journal of Operational Research, Elsevier, vol. 247(1), pages 155-165.
    9. Jarrett, Jeffrey E. & Pan, Xia, 2007. "The quality control chart for monitoring multivariate autocorrelated processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3862-3870, May.

    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. Samari, Goleen & Catalano, Ralph & Alcalá, Héctor E. & Gemmill, Alison, 2020. "The Muslim Ban and preterm birth: Analysis of U.S. vital statistics data from 2009 to 2018," Social Science & Medicine, Elsevier, vol. 265(C).
    2. Amira Dridi & Mohamed El Ghourabi & Mohamed Limam, 2012. "On monitoring financial stress index with extreme value theory," Quantitative Finance, Taylor & Francis Journals, vol. 12(3), pages 329-339, March.
    3. Weihs, Claus & Theis, Winfried & Messaoud, Amor & Hering, Franz, 2004. "Monitoring of the BTA Deep Hole Drilling Process Using Residual Control Charts," Technical Reports 2004,60, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Marta Benková & Dagmar Bednárová & Gabriela Bogdanovská & Marcela Pavlíčková, 2023. "Use of Statistical Process Control for Coking Time Monitoring," Mathematics, MDPI, vol. 11(16), pages 1-30, August.
    5. Johannes Freiesleben & Nicolas Gu'erin, 2015. "Homogenization and Clustering as a Non-Statistical Methodology to Assess Multi-Parametrical Chain Problems," Papers 1505.03874, arXiv.org, revised Dec 2017.
    6. Miguel Flores & Salvador Naya & Rubén Fernández-Casal & Sonia Zaragoza & Paula Raña & Javier Tarrío-Saavedra, 2020. "Constructing a Control Chart Using Functional Data," Mathematics, MDPI, vol. 8(1), pages 1-26, January.
    7. 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.
    8. Thaga K. & Kgosi P. M. & Gabaitiri L., 2007. "Max-Chart for Autocorrelated Processes," Stochastics and Quality Control, De Gruyter, vol. 22(1), pages 87-105, January.
    9. P. Vellaisamy & S. Sankar & M. Taniguchi, 2003. "Estimation and Design of Sampling Plans for Monitoring Dependent Production Processes," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 85-108, March.
    10. A. Snoussi, 2011. "SPC for short-run multivariate autocorrelated processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2303-2312.
    11. Ord, J. Keith & Koehler, Anne B. & Snyder, Ralph D. & Hyndman, Rob J., 2009. "Monitoring processes with changing variances," International Journal of Forecasting, Elsevier, vol. 25(3), pages 518-525, July.
    12. Messaoud, Amor & Weihs, Claus & Hering, Franz, 2008. "Detection of chatter vibration in a drilling process using multivariate control charts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3208-3219, February.
    13. Žmuk Berislav, 2016. "Capabilities of Statistical Residual-Based Control Charts in Short- and Long-Term Stock Trading," Naše gospodarstvo/Our economy, Sciendo, vol. 62(1), pages 12-26, March.
    14. Mohamed El Ghourabi & Amira Dridi & Mohamed Limam, 2015. "A new financial stress index model based on support vector regression and control chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(4), pages 775-788, April.
    15. Ridley, D. & Duke, D., 2007. "Moving -window spectral model based statistical process control," International Journal of Production Economics, Elsevier, vol. 105(2), pages 492-509, February.
    16. Gulser Koksal & Burcu Kantar & Taylan Ali Ula & Murat Caner Testik, 2008. "The effect of Phase I sample size on the run length performance of control charts for autocorrelated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(1), pages 67-87.
    17. Hwarng, H. Brian, 2001. "Insights into neural-network forecasting of time series corresponding to ARMA(p,q) structures," Omega, Elsevier, vol. 29(3), pages 273-289, June.
    18. Croux, C. & Gelper, S. & Mahieu, K., 2010. "Robust Control Charts for Time Series Data," Other publications TiSEM 229a21da-3d8a-4764-9d78-5, Tilburg University, School of Economics and Management.
    19. West, David A. & Mangiameli, Paul M. & Chen, Shaw K., 1999. "Control of complex manufacturing processes: a comparison of SPC methods with a radial basis function neural network," Omega, Elsevier, vol. 27(3), pages 349-362, June.
    20. Siu-Tong Au & Rong Duan & Siamak Hesar & Wei Jiang, 2010. "A framework of irregularity enlightenment for data pre-processing in data mining," Annals of Operations Research, Springer, vol. 174(1), pages 47-66, February.

    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:31:y:2004:i:3:p:317-327. 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.