Construction of Bivariate Copulas on a Multivariate Exponentially Weighted Moving Average Control Chart

Saowanit Sukparungsee,Piyapatr Busababodhin,Sirasak Sasiwannapong,Yupaporn Areepong

doi:10.13189/ms.2020.080504

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.

Highlights

Multivariate Statistical Process Control (MSPC) is an important method for process monitoring, control and improvement in many areas such as engineering, economics, environmental statistics, finance and etc
We develop an approach performance on the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart based on copula combinations by using the Monte Carlo simulations.The results show that the out-of-control (ARL1)
Many processes are non-normal and correlated, so multivariate control charts need to be able to cope with related joint distributions

Summary

Introduction

Multivariate Statistical Process Control (MSPC) is an important method for process monitoring, control and improvement in many areas such as engineering, economics, environmental statistics, finance and etc. A control chart is a common tool for MSPC for detecting changes in the vector means of the process. Hotelling’s T2 was the first multivariate control chart [2], followed by the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart as a better alternative for detecting small shifts in the process vector mean [3,4]. Most multivariate detection procedures are based on the assumption that the observations are independent and identically distributed (i.i.d.) and follow a multivariate normal distribution. Many processes are non-normal and correlated, so multivariate control charts need to be able to cope with related joint distributions.

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