A note on moving average forecasts of long memory processes with an application to quality control

Abstract

Standard quality control chart interpretation assumes that the observed data are uncorrelated. The presence of autocorrelation in process data has adverse effects on the performance of control charts. The objective of this paper is to assess the behavior of moving average forecast-based control charts on data having correlation that is persistent over very long time horizons, i.e., long-range dependent. We show that charts based on exponentially weighted moving average (EWMA) prediction do not perform well at detecting process shifts in long-range dependent data. We then introduce a new type of control chart, the hyperbolically weighted moving average (HWMA) chart, designed specifically for long-range dependent data. The HWMA charts perform better than the EWMA charts at detecting changes in the level of a long-memory process and also provide competitive performance for process data having only short-range dependence. © 2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.