Construction of Bivariate Copulas on the Hotelling’s T2 Control Chart
Keywords:Marginal distribution, joint distribution, multivariate control chart, Monte Carlo simulation
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 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.