IDEAS home Printed from https://ideas.repec.org/a/taf/tprsxx/v54y2016i11p3294-3310.html
   My bibliography  Save this article

The T -super-2 chart with mixed samples to control bivariate autocorrelated processes

Author

Listed:
  • Roberto Campos Leoni
  • Marcela Aparecida Guerreiro Machado
  • Antonio Fernando Branco Costa

Abstract

In this paper, we propose the use of the T -super-2 chart with the mixed sampling strategy (MS) to monitor the mean vector of bivariate processes with observations that fit to a first-order vector autoregressive model. With the MS, rational subgroups of size n are taken from the process and the selected units are regrouped to form the mixed samples. The units of the mixed samples are units selected from the last two rational subgroups. The aim of the proposed sampling strategy is to reduce the negative effect of the autocorrelation on the performance of the T -super-2 chart. When the two variables are autocorrelated, the MS always enhances the T -super-2 chart performance, however, the mixed samples are not recommended for bivariate processes with only one autocorrelated variable which is rarely affected by the assignable cause.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:11:p:3294-3310
    DOI: 10.1080/00207543.2015.1102983
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207543.2015.1102983
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207543.2015.1102983?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. Wu, Jianmou & Makis, Viliam, 2008. "Economic and economic-statistical design of a chi-square chart for CBM," European Journal of Operational Research, Elsevier, vol. 188(2), pages 516-529, July.
    2. 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.
    3. Xia Pan & Jeffrey Jarrett, 2012. "Why and how to use vector autoregressive models for quality control: the guideline and procedures," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(3), pages 935-948, April.
    4. Franco, Bruno Chaves & Celano, Giovanni & Castagliola, Philippe & Costa, Antonio Fernando Branco, 2014. "Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies," International Journal of Production Economics, Elsevier, vol. 151(C), pages 121-130.
    5. Pan, Xia & Jarrett, Jeffrey, 2007. "Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation," International Journal of Production Economics, Elsevier, vol. 106(1), pages 204-216, March.
    6. Antonio F. B. Costa & Philippe Castagliola, 2011. "Effect of measurement error and autocorrelation on the X¯ chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 661-673, December.
    7. Thuntee Sukchotrat & Seoung Kim & Fugee Tsung, 2010. "One-class classification-based control charts for multivariate process monitoring," IISE Transactions, Taylor & Francis Journals, vol. 42(2), pages 107-120.
    8. Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2011. "Variable parameter and double sampling charts in the presence of correlation: The Markov chain approach," International Journal of Production Economics, Elsevier, vol. 130(2), pages 224-229, April.
    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.
    10. 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.
    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. Yaping Li & Haiyan Li & Zhen Chen & Ying Zhu, 2022. "An Improved Hidden Markov Model for Monitoring the Process with Autocorrelated Observations," Energies, MDPI, vol. 15(5), pages 1-13, February.

    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. 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.
    2. Jeffrey Jarrett, 2014. "The quality movement in hospital care," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3153-3167, November.
    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. A. Snoussi, 2011. "SPC for short-run multivariate autocorrelated processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2303-2312.
    5. Du, Shichang & Lv, Jun, 2013. "Minimal Euclidean distance chart based on support vector regression for monitoring mean shifts of auto-correlated processes," International Journal of Production Economics, Elsevier, vol. 141(1), pages 377-387.
    6. Xiang, Yisha, 2013. "Joint optimization of X¯ control chart and preventive maintenance policies: A discrete-time Markov chain approach," European Journal of Operational Research, Elsevier, vol. 229(2), pages 382-390.
    7. Song, Zhi & Mukherjee, Amitava & Zhang, Jiujun, 2021. "Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment," European Journal of Operational Research, Elsevier, vol. 289(1), pages 177-196.
    8. Franco, Bruno Chaves & Celano, Giovanni & Castagliola, Philippe & Costa, Antonio Fernando Branco, 2014. "Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies," International Journal of Production Economics, Elsevier, vol. 151(C), pages 121-130.
    9. Naderkhani, Farnoosh & Makis, Viliam, 2016. "Economic design of multivariate Bayesian control chart with two sampling intervals," International Journal of Production Economics, Elsevier, vol. 174(C), pages 29-42.
    10. Teoh, W.L. & Khoo, Michael B.C. & Castagliola, Philippe & Yeong, W.C. & Teh, S.Y., 2017. "Run-sum control charts for monitoring the coefficient of variation," European Journal of Operational Research, Elsevier, vol. 257(1), pages 144-158.
    11. Peruchi, Rogério Santana & Balestrassi, Pedro Paulo & de Paiva, Anderson Paulo & Ferreira, João Roberto & de Santana Carmelossi, Michele, 2013. "A new multivariate gage R&R method for correlated characteristics," International Journal of Production Economics, Elsevier, vol. 144(1), pages 301-315.
    12. Panagiotidou, S. & Tagaras, G., 2012. "Optimal integrated process control and maintenance under general deterioration," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 58-70.
    13. Chakraborty Ashit B. & Khurshid Anwer, 2013. "Measurement Error Effect on the Power of Control Chart for the Ratio of Two Poisson Distributions," Stochastics and Quality Control, De Gruyter, vol. 28(1), pages 15-21, October.
    14. 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.
    15. Xiao, Xiao & Jiang, Wei & Luo, Jianwen, 2019. "Combining process and product information for quality improvement," International Journal of Production Economics, Elsevier, vol. 207(C), pages 130-143.
    16. 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.
    17. Tomohiro, Ryosuke & Arizono, Ikuo & Takemoto, Yasuhiko, 2020. "Economic design of double sampling Cpm control chart for monitoring process capability," International Journal of Production Economics, Elsevier, vol. 221(C).
    18. Iziy Azamsadat & Sadeghpour Gildeh Bahram & Monabbati Ehsan, 2017. "Comparison Between the Economic-Statistical Design of Double and Triple Sampling X¯\bar{X} Control Charts," Stochastics and Quality Control, De Gruyter, vol. 32(1), pages 49-61, June.
    19. 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.
    20. Ou, Yanjing & Wu, Zhang & Tsung, Fugee, 2012. "A comparison study of effectiveness and robustness of control charts for monitoring process mean," International Journal of Production Economics, Elsevier, vol. 135(1), pages 479-490.

    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:11:p:3294-3310. 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.