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The Trinomial ATTRIVAR control chart

Author

Listed:
  • Simões, Felipe Domingues
  • Costa, Antonio Fernando Branco
  • Machado, Marcela Aparecida Guerreiro

Abstract

In this article, we propose the Trinomial - ATTRIVAR (T-ATTRIVAR) control chart where attribute and variable sample data are used to control the process mean. Firstly, two discriminating limits sort the sample items into three excluding categories; that is, items in categories A, B, or AB, are, respectively, items with X dimensions smaller than the lower discriminating limit, larger than the upper discriminating limit, or neither smaller than the lower discriminating limit nor larger than the upper discriminating limit. Depending on the number of sample items in each category, one of three decisions is made: the process is declared in-control, the process is declared out-of-control, or all sample items are also measured. In this last case, the sample mean of X is used to decide the state of the process. Aslam et al. (2015) worked with the particular case where the sample items are classified as defective (items in category - A plus items in category - B) or not-defective (items in category - AB). The strategy of splitting defectives into two excluding categories (A and B) enhances the performance of the ATTRIVAR chart. It is worth to emphasize that the previous attribute classification truncates the X distribution. Consequently, the mathematical development to obtain the ARLs is complex – the Average Run length (ARL) is the average number of samples the control chart requires to signal. With the density function of the sum of truncated X distributions, we obtained the exact ARLs. The exact minimum ARLs are lower than the minimum ARLs Ho and Aparisi (2016) obtained with the Genetic Algorithm.

Suggested Citation

  • Simões, Felipe Domingues & Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2020. "The Trinomial ATTRIVAR control chart," International Journal of Production Economics, Elsevier, vol. 224(C).
    • Handle: RePEc:eee:proeco:v:224:y:2020:i:c:s0925527319303937
    DOI: 10.1016/j.ijpe.2019.107559
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    References listed on IDEAS

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    1. Roberto da Costa Quinino & Linda Lee Ho & Anderson Laécio Galindo Trindade, 2015. "Monitoring the process mean based on attribute inspection when a small sample is available," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1860-1867, November.
    2. Muhammad Aslam & Muhammad Azam & Nasrullah Khan & Chi-Hyuck Jun, 2015. "A mixed control chart to monitor the process," International Journal of Production Research, Taylor & Francis Journals, vol. 53(15), pages 4684-4693, August.
    3. Bezerra, Erica Leandro & Ho, Linda Lee & da Costa Quinino, Roberto, 2018. "GS2: An optimized attribute control chart to monitor process variability," International Journal of Production Economics, Elsevier, vol. 195(C), pages 287-295.
    4. Wu, Zhang & Khoo, Michael B.C. & Shu, Lianjie & Jiang, Wei, 2009. "An np control chart for monitoring the mean of a variable based on an attribute inspection," International Journal of Production Economics, Elsevier, vol. 121(1), pages 141-147, September.
    5. Ho, Linda Lee & Aparisi, Francisco, 2016. "ATTRIVAR: Optimized control charts to monitor process mean with lower operational cost," International Journal of Production Economics, Elsevier, vol. 182(C), pages 472-483.
    6. Lee Ho, Linda & Quinino, Roberto Costa, 2013. "An attribute control chart for monitoring the variability of a process," International Journal of Production Economics, Elsevier, vol. 145(1), pages 263-267.
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