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

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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