Multivariate EWMA control chart with highly asymmetric gamma distributions

Abstract

In this paper, we investigated the performance of the multivariate exponentially weighted moving average (MEWMA) control chart under highly asymmetric gamma distributions. Simulation procedures were used to obtain probabilistic control limits of the chart using a specific underlying distribution with known parameters (Phase II). The performance of the chart was evaluated under three different mean vector shifts, and the best values for the smoothing constant were identified. Results were compared with the existing proposal of using normal limits. Our results suggested that for three or more variables, probabilistic control limits lead to a better performance of the chart. We extended the analysis to the T² chart and compared the efficiency of both strategies. MEWMA chart performance was better than T² chart in all the cases analysed. A real application with Phase I reference data is described. The parameters of the marginal gamma distributions were estimated and a specific algorithm was then employed to determine the appropriate values of the smoothing constant and upper control limit of the MEWMA chart (Phase II). The relevance of this method lies in the fact that it can be adapted to any practical situation in which gamma model is suitable.

Keywords:

• Average run length (ARL)
• multivariate statistical process control (MSPC)
• probabilistic control limits
• T² chart

Acknowledgements

The authors wish to thank the valuable collaboration of Dr. Daniela Dianda who wrote the routines of the algorithm proposed by Bustos et al. in R language, making all the necessary adaptations in the simulations procedures in order to find the upper control limits of the chart. We also thank Msc Nicolás Ballarini, who reviewed the English version of the manuscript. Finally, we thank the editor and two anonymous reviewers for their many helpful comments that have resulted in significant improvement of this article.