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Monitoring of Linear Profiles Using Linear Mixed Model in the Presence of Measurement Errors

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  • Wenhui Liu

    (School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin 300071, China)

  • Zhonghua Li

    (School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin 300071, China)

  • Zhaojun Wang

    (School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin 300071, China)

Abstract

In the application of control charts, most of the research in profile monitoring is based on accurate measurements. Measurement errors, however, often exist in many manufacturing and service environments. In this paper, we apply linear mixed models in the presence of measurement errors in fixed effects. We discuss three modified multivariate charts, namely Hotelling’s T 2 , multivariate exponential weighted moving average (MEWMA) control chart, and multivariate cumulative sum (MCUSUM) control chart. Performance comparisons are made in terms of the average run length (ARL) and average extra quadratic loss (AEQL). Finally, a real data example on healthcare expenditures is used to illustrate the implementation of the proposed monitoring schemes.

Suggested Citation

  • Wenhui Liu & Zhonghua Li & Zhaojun Wang, 2022. "Monitoring of Linear Profiles Using Linear Mixed Model in the Presence of Measurement Errors," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4641-:d:996791
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    References listed on IDEAS

    as
    1. Xuemin Zi & Changliang Zou & Fugee Tsung, 2012. "A distribution-free robust method for monitoring linear profiles using rank-based regression," IISE Transactions, Taylor & Francis Journals, vol. 44(11), pages 949-963.
    2. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
    3. Zhang, Jiujun & Li, Zhonghua & Wang, Zhaojun, 2009. "Control chart based on likelihood ratio for monitoring linear profiles," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1440-1448, February.
    4. Paria Soleimani & Ali Narvand & Sadigh Raissi, 2013. "Online monitoring of auto correlated linear profiles via mixed model," International Journal of Manufacturing Technology and Management, Inderscience Enterprises Ltd, vol. 27(4/5/6), pages 238-250.
    5. Petros Maravelakis & John Panaretos & Stelios Psarakis, 2004. "EWMA Chart and Measurement Error," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(4), pages 445-455.
    6. Xu-Ping Zhong & Wing-Kam Fung & Bo-Cheng Wei, 2002. "Estimation in Linear Models with Random Effects and Errors-in-Variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 595-606, September.
    7. Hua Xin & Wan-Ju Hsieh & Yuhlong Lio & Tzong-Ru Tsai, 2020. "Nonlinear Profile Monitoring Using Spline Functions," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    8. Changliang Zou & Xianghui Ning & Fugee Tsung, 2012. "LASSO-based multivariate linear profile monitoring," Annals of Operations Research, Springer, vol. 192(1), pages 3-19, January.
    9. K.P. Tran & P. Castagliola & G. Celano, 2016. "The performance of the Shewhart-RZ control chart in the presence of measurement error," International Journal of Production Research, Taylor & Francis Journals, vol. 54(24), pages 7504-7522, December.
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