EWMA Charts for Multivariate Output: Some Stochastic Ordering Results

Abstract

We investigate the impact of sustained shifts in the covariance matrix on the run length (RL) of EWMA charts for detecting shifts in the process mean vector of multivariate normal i.i.d. output. We prove that some changes in the covariance matrix can cause an undesirable stochastic decrease in the detection speed of specific shifts in the process mean vector, and this should not be tolerated by practitioners. The illustration of this and other RL-related stochastic ordering results is based on extensive Monte Carlo simulations. This article can be thought as a multivariate extension of the results of Morais and Pacheco (2001) concerning the stochastic behavior of the RL of upper one-sided EWMA schemes for the process mean of i.i.d. output.

Keywords:

• Control schemes
• Run length
• Statistical process control
• Stochastic ordering

Mathematics Subject Classification:

• Primary 62N10, 60E15
• Secondary 62P30

Acknowledgments

This research was partially supported by: Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI) of the Fundação para a Ciência e a Tecnologia (FCT); and the project POSC/EIA/60061/2004.

The first author was partially supported by CEMAT (IST–TU Lisbon) during the preparation of the final draft of this article, while visiting the Department of Statistics of the European University Viadrina (Frankfurt–Oder).