Performance Comparison of the Hotelling’s T2 and DMEWMA Control Charts Using Bivariate Copulas for Small Shifts - Kuvattana, Sasigarn (Thai Journal of Science and Technology, 2021)
Multivariate control charts are an important tool in statistical process control for identifying an out-of-control process. Most multivariate control charts were designed to assume that the observations are an independence and normal distribution, but it is not valid in practice. This paper proposes the copulas modeling for dependence and non-normal multivariate cases and compare bivariate copulas on Hotelling’s T2 and double multivariate exponentially weighted moving average (DMEWMA) control charts. Observations are from an exponential distribution with Monte Carlo simulation when the parameter shifts are 1.02, 1.04, 1.06, 1.08, and 1.1. The level of dependence of observations is measured by Kendall’s tau as 0.8 and -0.8 for normal, Frank and Clayton copulas. The performance of control charts is based on the average run length (ARL) in each copula. The results show that in the case of one and two-parameter shifts, the performance of the Hotelling’s T2 is better than DMEWMA control chart for all modifications.