Trivariate Copulas on the MEWMA Control Chart

Abstract

Copulas are used to model multivariate distribution with continuous margins and dependence observations. This paper proposes four types of copulas on the multivariate exponentially weighted moving average (MEWMA) control chart for trivariate case. Observations are generated by an exponential distribution based on the Monte Carlo simulation for the Clayton, Frank, Gumbel and normal copulas and the mean shifts are 1.05, 1.25, 1.5, 2, 2.5 and 3. The performance of the control charts describes in terms of the average run length (ARL). Levels of the dependence of random variables are measured by Kendall’s tau as 0.2, 0.5 and 0.8 for small, moderate and large dependencies. The results reveal that the Clayton copula performs the ARL₁ values less than the others for almost mean shifts.