Monitoring of serially correlated processes using residual control charts

Control charts act as the most important tool for monitoring of process parameters. The assumption of independence that underpins the implementation of the charts is violated when process observations are correlated. The effect of this issue can lead to the malfunctioning of the usual control charts by causing a large number of false alarms or slowing the detection ability of the chart in unstable situations. In this paper, we investigated the performance of the Mixed EWMA-CUSUM and Mixed CUSUM-EWMA charts for the efficient monitoring of autocorrelated data. The charts are applied to the residuals obtained from fitting an autoregressive (AR) model to the autocorrelated observations. The performance of these charts is compared with the performances of the residual Shewhart, EWMA, CUSUM, combined Shewhart-CUSUM, and combined Shewhart-EWMA charts. Performance criteria such as Average Run Length (ARL) and Extra Quadratic Loss (EQL) are used for the evaluation and comparison of the charts. Illustrative examples are presented to demonstrate the application of the charts to serially correlated observations.