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A side-sensitive synthetic chart for the multivariate coefficient of variation

Author

Listed:
  • Wai Chung Yeong
  • Sok Li Lim
  • Zhi Lin Chong
  • Michael B C Khoo
  • Sajal Saha

Abstract

Control charts for the coefficient of variations (γ) are receiving increasing attention as it is able to monitor the stability in the ratio of the standard deviation (σ) over the mean (μ), unlike conventional charts that monitor the μ and/or σ separately. A side-sensitive synthetic (SS) chart for monitoring γ was recently developed for univariate processes. The chart outperforms the non-side-sensitive synthetic (NSS) γ chart. However, the SS chart monitoring γ for multivariate processes cannot be found. Thus, a SS chart for multivariate processes is proposed in this paper. A SS chart for multivariate processes is important as multiple quality characteristic that are correlated with each other are frequently encountered in practical scenarios. Based on numerical examples, the side-sensitivity feature that is included in the multivariate synthetic γ chart significantly improves the sensitivity of the chart based on the run length performance, particularly in detecting small shifts (τ), and for small sample size (n), as well as a large number of variables (p) and in-control γ (γ0). The multivariate SS chart also significantly outperforms the Shewhart γ chart, and marginally outperforms the Multivariate Exponentially Weighted Moving Average (MEWMA) γ chart when shift sizes are moderate and large. To show its implementation, the proposed multivariate SS chart is adopted to monitor investment risks.

Suggested Citation

  • Wai Chung Yeong & Sok Li Lim & Zhi Lin Chong & Michael B C Khoo & Sajal Saha, 2022. "A side-sensitive synthetic chart for the multivariate coefficient of variation," PLOS ONE, Public Library of Science, vol. 17(7), pages 1-18, July.
    • Handle: RePEc:plo:pone00:0270151
    DOI: 10.1371/journal.pone.0270151
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    References listed on IDEAS

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    1. Waie Chung Yeong & Ping Yin Lee & Sok Li Lim & Peh Sang Ng & Khai Wah Khaw, 2021. "Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length," PLOS ONE, Public Library of Science, vol. 16(7), pages 1-18, July.
    2. XueLong Hu & AnAn Tang & YuLong Qiao & JinSheng Sun & BaoCai Guo, 2020. "On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-20, October.
    3. Nguyen, Quoc-Thông & Giner-Bosch, Vicent & Tran, Kim Duc & Heuchenne, Cédric & , e.a., 2021. "One-sided variable sampling interval EWMA control charts for monitoring the multivariate coefficient of variation in the presence of measurement errors," LIDAM Reprints ISBA 2021037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Ming Ha Lee & Michael B C Khoo & XinYing Chew & Patrick H H Then, 2020. "Economic-statistical design of synthetic np chart with estimated process parameter," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-11, April.
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