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Nonlinear Profile Monitoring Using Spline Functions

Author

Listed:
  • Hua Xin

    (School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China)

  • Wan-Ju Hsieh

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan)

Abstract

In this study, two new integrated control charts, named T 2 -MAE chart and MS-MAE chart, are introduced for monitoring the quality of a process when the mathematical form of nonlinear profile model for quality measure is complicated and unable to be specified. The T 2 -MAE chart is composed of two memoryless-type control charts and the MS-MAE chart is composed of one memory-type and one memoryless-type control charts. The normality assumption of error terms in the nonlinear profile model for both proposed control charts are extended to a generalized model. An intensive simulation study is conducted to evaluate the performance of the T 2 -MAE and MS-MAE charts. Simulation results show that the MS-MAE chart outperforms the T 2 -MAE chart with less false alarms during the Phase I monitoring. Moreover, the MS-MAE chart is sensitive to different shifts on the model parameters and profile shape during the Phase II monitoring. An example about the vertical density profile is used for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1588-:d:413755
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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. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    3. Zahra Hadidoust & Yaser Samimi & Hamid Shahriari, 2015. "Monitoring and change-point estimation for spline-modeled non-linear profiles in phase II," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2520-2530, December.
    4. Chung-I Li & Nan-Cheng Su & Pei-Fang Su & Yu Shyr, 2014. "The Design of and R Control Charts for Skew Normal Distributed Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(23), pages 4908-4924, December.
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    Cited by:

    1. 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.

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