IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4641-d996791.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4641/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/24/4641/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. 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.
    5. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
    6. 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.
    7. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mejia, Paula & Meléndez Arjona, Marcela, 2012. "Middle-Class Entrepreneurs and Social Mobility through Entrepreneurship in Colombia," IDB Publications (Working Papers) 4082, Inter-American Development Bank.
    2. Inmaculada Garc�a-Mainar & V�ctor M. Montuenga-G�mez, 2017. "Subjective educational mismatch and signalling in Spain," Documentos de Trabajo dt2017-03, Facultad de Ciencias Económicas y Empresariales, Universidad de Zaragoza.
    3. Xuejun Wang & Aiting Shen & Zhiyong Chen & Shuhe Hu, 2015. "Complete convergence for weighted sums of NSD random variables and its application in the EV regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 166-184, March.
    4. Maïlys Korber, 2019. "Does Vocational Education Give a Labour Market Advantage over the Whole Career? A Comparison of the United Kingdom and Switzerland," Social Inclusion, Cogitatio Press, vol. 7(3), pages 202-223.
    5. Verbeek, M.J.C.M. & Nijman, T.E., 1990. "Can cohort data be treated as genuine panel data?," Other publications TiSEM 17fd5894-9eef-426e-b402-0, Tilburg University, School of Economics and Management.
    6. Andrzej Cieślik & Bartłomiej Rokicki, 2016. "Individual wages and regional market potential," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 24(4), pages 661-682, October.
    7. Tullio Jappelli & Marco Pagano, 1994. "Personal Saving in Italy," NBER Chapters, in: International Comparisons of Household Saving, pages 237-268, National Bureau of Economic Research, Inc.
    8. Borsch-Supan, Axel & Reil-Held, Anette & Rodepeter, Ralf & Schnabel, Reinhold & Winter, Joachim, 2001. "The German Savings Puzzle," Research in Economics, Elsevier, vol. 55(1), pages 15-38, March.
    9. Kasraian, Dena & Maat, Kees & van Wee, Bert, 2018. "Urban developments and daily travel distances: Fixed, random and hybrid effects models using a Dutch pseudo-panel over three decades," Journal of Transport Geography, Elsevier, vol. 72(C), pages 228-236.
    10. Verbeek, Marno & Vella, Francis, 2005. "Estimating dynamic models from repeated cross-sections," Journal of Econometrics, Elsevier, vol. 127(1), pages 83-102, July.
    11. Ozdamar, Oznur & Giovanis, Eleftherios, 2016. "Being Healthy in Turkey: A Pseudo-Panel Data Analysis," MPRA Paper 95838, University Library of Munich, Germany.
    12. Kevin X.D. Huang & Zheng Liu, 2005. "Temptation and Self-Control: Some Evidence from the Consumer Expenditure Survey," 2005 Meeting Papers 770, Society for Economic Dynamics.
    13. Clemens Noelke & Daniel Horn, 2011. "Social Transformation and the Transition from Vocational Education to Work," Budapest Working Papers on the Labour Market 1105, Institute of Economics, Centre for Economic and Regional Studies.
    14. Sule Alan & Orazio Attanasio & Martin Browning, 2009. "Estimating Euler equations with noisy data: two exact GMM estimators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(2), pages 309-324, March.
    15. Hippolyte d’Albis & Ikpidi Badji, 2017. "Intergenerational inequalities in standards of living in France," Economie et Statistique / Economics and Statistics, Institut National de la Statistique et des Etudes Economiques (INSEE), issue 491-492, pages 71-92.
    16. Ching-Hsin Wang & Feng-Chia Li, 2020. "Economic design under gamma shock model of the control chart for sustainable operations," Annals of Operations Research, Springer, vol. 290(1), pages 169-190, July.
    17. Felici, Marco & Kenny, Geoff & Friz, Roberta, 2023. "Consumer savings behaviour at low and negative interest rates," European Economic Review, Elsevier, vol. 157(C).
    18. Diane J. Macunovich, 1999. "The fortunes of one's birth: Relative cohort size and the youth labor market in the United States," Journal of Population Economics, Springer;European Society for Population Economics, vol. 12(2), pages 215-272.
    19. Orazio P. Attanasio & Laura Blow & Robert Hamilton & Andrew Leicester, 2009. "Booms and Busts: Consumption, House Prices and Expectations," Economica, London School of Economics and Political Science, vol. 76(301), pages 20-50, February.
    20. Ilmiawan Auwalin, 2021. "The effect of a credit policy change on microenterprise upward transition and growth: evidence from Indonesia," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 11(4), pages 611-636, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4641-:d:996791. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.