Autocorrelated multivariate process control: a geometric brownian motion approach

Abstract

In real life we always come across autocorrelated multivariate process where the present process is related to the previous process. This type of process can be modeled using the traditional multivariate time series models and then the process control can be conducted based on the residual which becomes univariate in nature. However, in this paper, we show that many time series are governed by a geometric Brownian motion (GBM) process. In this case, instead of time series modeling, we only need an appropriate transformation to come up with the condition required in the traditional multivariate process control. Therefore, under GBM process, traditional multivariate process control can be used on the transformed time series data. A real industrial example will be given to illustrate the advantage of the proposed method.