Construction of Bivariate Copulas on the Hotelling’s T2 Control Chart

  • Sanpet Tiengket Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
  • Saowanit Sukparungsee Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
  • Piyapatr Busababodhin Department of Mathematics, Faculty of Science, Mahasarakham University, Kantarawichai, Mahasarakham, Thailand
  • Yupaporn Areepong Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
Keywords: Marginal distribution, joint distribution, multivariate control chart, Monte Carlo simulation

Abstract

In this paper, five types of copulas, which are Gumbel, Clayton, Farlie-Gumbel-Morgenstern (FGM), Frank and Ali-Mikail-Haq (AMH) copulas are presented via construction of bivariate copulas on the Hotelling’s  control chart. The observations are generated from the exponential distribution and the dependent observations are measured by Kendall’s tau  values as weak, moderate and strongly positive dependences where gif.latex?\tau are 0.1, 0.2, 0.5, 0.6, 0.8 and 0.9, respectively. Monte Carlo simulation was used to compare the performance of the control chart with the Average Run Length (ARL) as performance metric. The results indicate that the bivariate copulas approach can be fitted to the Hotelling’s  T2  control chart.

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Published
2019-12-12
Section
Articles