Proposal of multivariate control chart using exponentially log-likelihood for detection of change in mean and variability

Yuma Ueno, Yasushi Nagata

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    This study aims to detect various small changes in multivariate control charts. In previous studies, the MEWMA control chart was proposed as a detection of mean vector change, the MEWMC control chart was proposed as a detection of variance covariance matrix change, and the ELR control chart was proposed as a detection of the change of the mean vector and the variance covariance matrix. This study proposes two method using log-likelihood. The first method (MEWML control chart) uses the statistic obtained by directly weighting the log-likelihood. The second method (MEWMML control chart) uses obtained maximum likelihood estimate from log-likelihood using the maximum likelihood method. As a result of Monte Carlo simulations using the ARL evaluation index, the study shows that the MEWML control chart is useful for variance covariance matrix change, and the MEWMML control chart is the most useful for various patterns.

    Original languageEnglish
    Title of host publicationMathematical Methods and Computational Techniques in Science and Engineering II
    PublisherAmerican Institute of Physics Inc.
    Volume1982
    ISBN (Electronic)9780735416987
    DOIs
    Publication statusPublished - 2018 Jul 27
    Event2nd International Conference on Mathematical Methods and Computational Techniques in Science and Engineering - Cambridge, United Kingdom
    Duration: 2018 Feb 162018 Feb 18

    Other

    Other2nd International Conference on Mathematical Methods and Computational Techniques in Science and Engineering
    CountryUnited Kingdom
    CityCambridge
    Period18/2/1618/2/18

    Fingerprint

    charts
    proposals
    maximum likelihood estimates
    statistics
    evaluation

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Ueno, Y., & Nagata, Y. (2018). Proposal of multivariate control chart using exponentially log-likelihood for detection of change in mean and variability. In Mathematical Methods and Computational Techniques in Science and Engineering II (Vol. 1982). [020016] American Institute of Physics Inc.. https://doi.org/10.1063/1.5045422

    Proposal of multivariate control chart using exponentially log-likelihood for detection of change in mean and variability. / Ueno, Yuma; Nagata, Yasushi.

    Mathematical Methods and Computational Techniques in Science and Engineering II. Vol. 1982 American Institute of Physics Inc., 2018. 020016.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Ueno, Y & Nagata, Y 2018, Proposal of multivariate control chart using exponentially log-likelihood for detection of change in mean and variability. in Mathematical Methods and Computational Techniques in Science and Engineering II. vol. 1982, 020016, American Institute of Physics Inc., 2nd International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, Cambridge, United Kingdom, 18/2/16. https://doi.org/10.1063/1.5045422
    Ueno Y, Nagata Y. Proposal of multivariate control chart using exponentially log-likelihood for detection of change in mean and variability. In Mathematical Methods and Computational Techniques in Science and Engineering II. Vol. 1982. American Institute of Physics Inc. 2018. 020016 https://doi.org/10.1063/1.5045422
    Ueno, Yuma ; Nagata, Yasushi. / Proposal of multivariate control chart using exponentially log-likelihood for detection of change in mean and variability. Mathematical Methods and Computational Techniques in Science and Engineering II. Vol. 1982 American Institute of Physics Inc., 2018.
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