Monitoring autocorrelated processes with an exponentially weighted moving average forecast

Abstract

Traditional control charts such as the Shewhart chart, cumulative sum (CUSUM) chart and exponentially weighted moving average (EWMA) chart have been shown to be adversely affected by the presence of autocorrelation in data. Monitoring schemes which use these traditional control charts in conjunction with time series based forecasts have been proposed and shown to have properties superior to schemes based on traditional charts alone. The performance of the Shewhart, EWMA, and CUSUM charts on EWMA forecast errors is investigated. It is shown that the EWMA forecast does not adequately account for autocorrelation for processes following an AR(1) model. As a result, the standard control charts on forecast errors display unexpected statistical properties.