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On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process

Author

Listed:
  • Saber Ali

    (School of Economics and Statistics, Guangzhou University, Guangzhou 510000, China)

  • Zameer Abbas

    (Department of Statistics, Government Ambala Muslim College Sargodha, Sargodha 40100, Pakistan)

  • Hafiz Zafar Nazir

    (Departemnt of Statistics, University of Sargodha, Sargodha 40100, Pakistan)

  • Muhammad Riaz

    (Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Xingfa Zhang

    (School of Economics and Statistics, Guangzhou University, Guangzhou 510000, China)

  • Yuan Li

    (School of Economics and Statistics, Guangzhou University, Guangzhou 510000, China)

Abstract

Statistical process control (SPC) tools are used for the investigation and identification of unnatural variations in the manufacturing, industrial, and service processes. The control chart, the basic and the most famous tool of SPC, is used for process monitoring. Generally, control charts are constructed under normality assumption of the quality characteristic of interest, but in practice, it is quite hard to hold the normality assumption. In such situations, parametric charts tend to offer more frequent false alarms and invalid out-of-control performance. To rectify these problems, non-parametric control charts are used, as these have the same in-control run length properties for all the continuous distributions and are known as in-control robust. This study intends to develop a new non-parametric exponentially weighted moving average (NPEWMA) chart based on sign statistics under a ranked set sampling scheme that is hereafter named (NPREWMA-SN). The run-length profiles of the NPREWMA-SN chart are computed using the Monte Carlo simulation method. The proposed scheme is compared with NPEWMA-SN and classical EWMA- X ¯ charts, using different run length measures. The comparison reveals the in-control robustness and superiority of the proposed scheme over its competitors in detecting all kinds of shifts in the process location. A practical application related to the substrate manufacturing process is included to show the demonstration of the proposed chart.

Suggested Citation

  • Saber Ali & Zameer Abbas & Hafiz Zafar Nazir & Muhammad Riaz & Xingfa Zhang & Yuan Li, 2020. "On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1497-:d:408709
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    References listed on IDEAS

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    1. Chakraborti, S. & Eryilmaz, S. & Human, S.W., 2009. "A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1054-1065, February.
    2. Graham, M.A. & Chakraborti, S. & Human, S.W., 2011. "A nonparametric exponentially weighted moving average signed-rank chart for monitoring location," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2490-2503, August.
    3. S. Chakraborti & P. van der Laan & M. A. van de Wiel, 2004. "A class of distribution‐free control charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 443-462, August.
    4. Abdul Haq, 2020. "A nonparametric EWMA chart with auxiliary information for process mean," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(5), pages 1232-1247, March.
    Full references (including those not matched with items on IDEAS)

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