Autocorrelated process monitoring using triggered cuscore charts

Some of the most widely-investigated control charting techniques for autocorrelated data are based on time series residuals. If the mean shift in the autocorrelated process is a sudden step shift, the resulting mean shift in the residuals is time varying and has been referred to as the fault signature. Traditional residual based charts, such as a Shewhart, CUSUM, or EWMA on the residuals, do not make use of the information contained in the dynamics of the fault signature. In contrast, methods such as the Cuscore chart or Generalized Likelihood Ratio Test (GLRT) do incorporate this information. In order for the Cuscore chart to fully benefit from this, its detector coefficients should coincide with the fault signature. This is impossible to ensure, however, since the exact form of the fault signature depends on the time of occurrence of the mean shift, which is generally not known a priori. Any mismatch between the detector and the fault signature will adversely affect the Cuscore performance. This paper proposes a CUSUM-triggered Cuscore chart to reduce the mismatch between the detector and fault signature. A variation to the CUSUM-triggered Cuscore chart that uses a GLRT to estimate the mean shift time of occurrence is also discussed. It is shown that the triggered Cuscore chart performs better than the standard Cuscore chart and the residual-based CUSUM chart. Examples are provided to illustrate its use.