The impact of a random vector with variables from normal and non‐normal distributions on multivariate control charts

Abstract

AbstractMultivariate control charts are widely used to simultaneously monitor several quality characteristics for detecting the mean changes in manufacturing industry processes. A multivariate Shewhart, multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) are types of multivariate control charts which have been discussed extensively. For those control charts, a multivariate normal distribution is an important assumption that is used to describe a behavior of a set of quality characteristics. However, sometimes the normal assumption is violated. This research explores the sensitivity of an average run length (ARL), the standard deviation of run length (SDRL) and the shape of distribution of run length for multivariate Shewhart, MEWMA, and MCUSUM control charts when the distribution of some quality characteristics (or variables) in a random vector are not normal. The results show how robust or sensitive multivariate control charts are to violations of the multivariate normal assumption.