Control charts of mean and variance using copula Markov SPC and conditional distribution by copula

Jong-Min Kim, Jaiwook Baik, Mitch Reller

    Research output: Contribution to journalArticlepeer-review

    4 Scopus citations

    Abstract

    We propose control charts of mean and variance by using the Emura, Long, and Sun (2017) copula Markov statistical process control (SPC) and conditional distribution with diverse copula functions. To verify our new method, we generate bivariate simulated data by an asymmetric copula function and then make the conditional uniform transformed data by employing diverse copula distributions. We apply the conditional uniform transformed data to the Emura, Long, and Sun (2017) copula Markov SPC chart to investigate how copula directional dependence and copula tail dependence can affect the control charts of the mean and variance. For an illustrated example, we use Major League Baseball (MLB) batting average (BA) and earned run average (ERA) data from 1998 to 2016 seasons to detect a large abnormal variation of MLB statistics by using the proposed method. We show that the average run lengths (ARLs) of the control charts of conditional variance are affected by directional dependence by using the Gaussian copula beta regression (Kim and Hwang, 2017) and copula tail dependence.

    Original languageEnglish (US)
    Pages (from-to)85-102
    Number of pages18
    JournalCommunications in Statistics: Simulation and Computation
    Volume50
    Issue number1
    DOIs
    StatePublished - 2021

    Bibliographical note

    Funding Information:
    The authors would like to thank the Editor, the Associate Editor, and the anonymous learned referee whose helpful suggestions and insightful comments greatly improved the quality of this article.

    Publisher Copyright:
    © 2019 Taylor & Francis Group, LLC.

    Copyright:
    Copyright 2020 Elsevier B.V., All rights reserved.

    Keywords

    • Copula
    • copula Markov SPC
    • directional dependence

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