A self-oriented control chart for multivariate process location

Abstract

In this work we present comparative studies as well as new proposals on methods for statistical process control. Specifically, multivariate control charts with emphasis on monitoring the mean vector of Gaussian processes with individual observations. The statistical process control where only one observation is available at each instant of time is a difficult problem to approach, since it is not possible to accurately estimate the current process centre by means of Shewhart-type control charts, in which case it is essential to utilise non-Shewhart control charts, i.e., to consider at the current instant also information from past observations. Regard to this, several experiments were initially carried out in order to verify the robustness of the traditional methods based on the non-centrality parameter. Next, we investigated alternatives to the most common method used in practical applications, the MEWMA scheme, such as sliding window schemes for estimation of the current mean vector of the process. Finally, new control charts have been proposed, also based on the non-centrality parameter, but utilising a different criterion to obtain a linear transformation, more efficient than the known method Principal Component Analysis. It was found through experiments that the proposed statistics fills a gap regarding to the application of automata schemes for monitoring the centre of multivariate processes, being more efficient in terms of speed detection of shifts than the traditional quadratic approaches for a wide range of distances.