Copula-based multivariate EWMA control charts for monitoring the mean vector of bivariate processes using a mixture model

Abstract

Control charts are the main tools in the statistical process monitoring area to investigate how the quality of production remains stable or changes over the time. This article develops Hotelling’s T² and multivariate exponentially weighted moving average (MEWMA) control charts for monitoring the mean vector of processes when observations come from a mixture copula model including, Gumbel, Clayton, and Frank copulas. The proposed mixture model enables the quality inspectors to cover several dependence levels of observations, from weak and moderate to strong in positive values by Kendall’s tau. To assess the performance of the proposed charts, extensive Monte-Carlo simulations were conducted based on the average run length (ARL) metric for both in-control and out-of-control states by considering a bivariate process with normal marginals. For more illustration, the step-by-step procedure of the proposed monitoring technique implementation has been investigated in a computer manufacturing process with both Phases I and II analysis.

Keywords:

• Copula function
• Hotelling’s T² control chart chart
• MEWMA control chart
• Monte Carlo method
• short run production