John N. Dyer

A SIMULATION STUDY AND EVALUATION OF MULTIVARIATE FORECAST BASED CONTROL CHARTS APPLIED TO ARMA PROCESSES

Much research had been performed in the area of control charting techniques for monitoring autocorrelated processes, especially regarding forecast based monitoring schemes. Forecast based monitoring schemes involve fitting an appropriate time-series model to the process, generating one step ahead forecast errors, and monitoring the forecast errors with traditional control charts. Another method introduced into the literature involves using multivariate control charts to monitor the ARMA derived one-step-ahead (OSA) and two-step-ahead (TSA) forecast errors. This article provides a broad simulation study and evaluation of the suggested multivariate approaches in regards to various ARMA(1,1) and AR(1) processes, and a comparison to their univariate counterparts.

The reverse moving average control chart for monitoring autocorrelated processes

Forecast-based monitoring schemes have been researched extensively in regards to applying traditional control charts to forecast errors arising from various autocorrelated processes. The dynamic response and behavior of forecast errors after experiencing a shift in the process mean make it difficult to choose a suitable control chart. In this paper we propose the reverse moving average control chart as a new forecast-based monitoring scheme, compare the new control chart to traditional methods applied to various ARMA(1,1), AR(1), and MA(1) processes, and make recommendations concerning the most appropriate control chart to use in a variety of situations when charting autocorrelated processes.