The generalized likelihood ratio test for statistical process control of autocorrelated processes

This paper presents an on-line Statistical Process Control (SPC) technique, based on a Generalized Likelihood Ratio Test (GLRT), for detecting and estimating mean shifts in autocorrelated processes that follow a normally distributed Autoregressive Integrated Moving Average (ARIMA) model. The GLRT is applied to the uncorrelated residuals of the appropriate time-series model. The performance of the GLRT is compared to two other commonly applied residual-based tests – a Shewhart individuals chart and a CUSUM test. A wide range of ARIMA models are considered, with the conclusion that the best residual-based test to use depends on the particular ARIMA model used to describe the autocorrelation. For many models, the GLRT performance is far superior to either a CUSUM or Shewhart test, while for others the difference is negligible or the CUSUM test performs slightly better. Simple, intuitive guidelines are provided for determining which residual-based test to use. Additional advantages of the GLRT are that it directly provides estimates of the magnitude and time of occurrence of the mean shift, and can be used to distinguish different types of faults, e.g., a sustained mean shift versus a temporary spike.