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LASSO-based multivariate linear profile monitoring

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  • Changliang Zou
  • Xianghui Ning
  • Fugee Tsung

Abstract

In many applications of manufacturing and service industries, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. Profile monitoring is for checking the stability of this relationship over time. In some situations, multiple profiles are required in order to model the quality of a product or process effectively. General multivariate linear profile monitoring is particularly useful in practice due to its simplicity and flexibility. However, in such situations, the existing parametric profile monitoring methods suffer from a drawback in that when the profile parameter dimensionality is large, the detection ability of the procedures commonly used T 2 -type charting statistics is likely to decline substantially. Moreover, it is also challenging to isolate the type of profile parameter change in such high-dimensional circumstances. These issues actually inherit from those of the conventional multivariate control charts. To resolve these issues, this paper develops a new methodology for monitoring general multivariate linear profiles, including the regression coefficients and profile variation. After examining the connection between the parametric profile monitoring and multivariate statistical process control, we propose to apply a variable-selection-based multivariate control scheme to the transformations of estimated profile parameters. Our proposed control chart is capable of determining the shift direction automatically based on observed profile data. Thus, it offers a balanced protection against various profile shifts. Moreover, the proposed control chart provides an easy but quite effective diagnostic aid. A real-data example from the logistics service shows that it performs quite well in the application. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:192:y:2012:i:1:p:3-19:10.1007/s10479-010-0797-8
    DOI: 10.1007/s10479-010-0797-8
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Zou, Changliang & Qiu, Peihua, 2009. "Multivariate Statistical Process Control Using LASSO," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1586-1596.
    3. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
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    Cited by:

    1. 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.
    2. Shuguang He & Wei Jiang & Houtao Deng, 2018. "A distance-based control chart for monitoring multivariate processes using support vector machines," Annals of Operations Research, Springer, vol. 263(1), pages 191-207, April.
    3. George Chalamandaris & Nikos E. Vlachogiannakis, 2018. "Are financial ratios relevant for trading credit risk? Evidence from the CDS market," Annals of Operations Research, Springer, vol. 266(1), pages 395-440, July.
    4. 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.
    5. Yu-min Liu & Li Xue, 2015. "The optimization design of EWMA charts for monitoring environmental performance," Annals of Operations Research, Springer, vol. 228(1), pages 113-124, May.

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