Monitoring autocorrelated process: a geometric brownian motion process approach

Abstract

Autocorrelated process control is common in today's modern industrial process control practice. The current practice of autocorrelated process control is to eliminate the autocorrelation by using an appropriate model such as Box-Jenkins models or other models and then to conduct process control operation based on the residuals. In this paper we show that many time series are governed by a geometric Brownian motion (GBM) process. Therefore, in this case, by using the properties of a GBM process, we only need an appropriate transformation and model the transformed data to come up with the condition needs in traditional process control. An industrial example of cocoa powder production process in a Malaysian company will be presented and discussed to illustrate the advantages of the GBM approach.