Mathematics and Statistics Vol. 8(5), pp. 520 - 526
DOI: 10.13189/ms.2020.080504
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Construction of Bivariate Copulas on a Multivariate Exponentially Weighted Moving Average Control Chart

Sirasak Sasiwannapong ¹, Saowanit Sukparungsee ¹, Piyapatr Busababodhin ², Yupaporn Areepong ^1,*
1 Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Thailand
² Department of Mathematics, Faculty of Science, Mahasarakham University, Thailand

ABSTRACT

The control chart is an important tool in multivariate statistical process control (MSPC), which for monitoring, control, and improvement of the process control. In this paper, we propose six types of copula combinations for use on a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart. Observations from an exponential distribution with dependence measured with Kendall's tau for moderate and strong positive and negative dependence (where ) among the observations were generated by using Monte Carlo simulations to measure the Average Run Length (ARL) as the performance metric and should be sufficiently large when the process is in-control on a MEWMA control chart. In this study, we develop an approach performance on the MEWMA control chart based on copula combinations by using the Monte Carlo simulations.The results show that the out-of-control (ARL₁) values for were less than for in almost all cases. The performances of the Farlie-Gumbel-Morgenstern×Ali-Mikhail-Haq copula combination was superior to the others for all shifts with strong positive dependence among the observations and . Moreover, when the magnitudes of the shift were very large, the performance metric values for observations with moderate and strong positive and negative dependence followed the same pattern.

KEYWORDS
Marginal, Joint Distribution, Multivariate Control Chart, Monte Carlo Simulation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Sirasak Sasiwannapong , Saowanit Sukparungsee , Piyapatr Busababodhin , Yupaporn Areepong , "Construction of Bivariate Copulas on a Multivariate Exponentially Weighted Moving Average Control Chart," Mathematics and Statistics, Vol. 8, No. 5, pp. 520 - 526, 2020. DOI: 10.13189/ms.2020.080504.

(b). APA Format:
Sirasak Sasiwannapong , Saowanit Sukparungsee , Piyapatr Busababodhin , Yupaporn Areepong (2020). Construction of Bivariate Copulas on a Multivariate Exponentially Weighted Moving Average Control Chart. Mathematics and Statistics, 8(5), 520 - 526. DOI: 10.13189/ms.2020.080504.