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 journalArticle

    2 Citations (Scopus)

    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)
    JournalCommunications in Statistics: Simulation and Computation
    DOIs
    StateAccepted/In press - Jan 1 2019

    Fingerprint

    Statistical Process Control
    Statistical process control
    Control Charts
    Copula
    Conditional Distribution
    Sun
    Tail Dependence
    Statistics
    Control charts
    Average Run Length
    Conditional Variance
    Regression
    Verify

    Keywords

    • Copula
    • copula Markov SPC
    • directional dependence

    Cite this

    Control charts of mean and variance using copula Markov SPC and conditional distribution by copula. / Kim, Jong-Min; Baik, Jaiwook; Reller, Mitch.

    In: Communications in Statistics: Simulation and Computation, 01.01.2019.

    Research output: Contribution to journalArticle

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